Why is Mach 0.3 the threshold separating compressible and incompressible flow?

I've read that Mach 0.3 is pretty much the upper limit for treating air as an incompressible fluid. The sources I've read seem to treat this as a given, without proof or justification. Why is this the limit? Is there a mathematical justification for this? Also, does this limit only apply to air? If not, then what does the limit depend on?

Water meets the low compressibility requirement, but there are many other considerations in the design of a hydraulic system: Boiling point/vapor pressure: If the system warms up during operation, the fluid may boil, which results in high compressibility and thus decreased effectiveness of the hydraulic system. Hydraulic fluid has a higher boiling point than water to help combat this. Related to this is the concept of vapor pressure. Hydraulic systems often involve small orifices, which can cause cavitation (localized boiling). This cavitation has the same effects as boiling and can cause pitting damage to the components near the cavitated region....

The problem is that the formula $P=I\ V$ is correct when dealing with DC circuits or with AC circuits where there is no lag between the current and the voltage. When dealing with realistic AC circuits, the power is given by $$ P=I\ V\ \cos(\phi), $$ where $\phi$ is the phase difference between the current and the voltage. The unit kVA is a unit of what is called 'apparent power' whereas W is a unit of 'real power'. Apparent power is the maximum possible power attainable when the current and voltage are in phase and real power is the actual...

Wikipedia gives the reason for Mach 0.3 as due to the fact that this achieves ~5% change in density. I found a NASA page that describes (analytically!) the relationship. I cited the source, but I'll reproduce the work here for posterity, in the event their links change. Start with conservation of momentum: $$ (\rho V) dV = -dp \\ $$ where $\rho$ is the fluid density, $V$ is the velocity, and $p$ is the pressure. for isentropic flow: $$ \frac{dp}{p} = \gamma \frac{d\rho}{\rho} \\ dp = \left( \frac{\gamma p}{\rho} \right) d\rho \\ $$ where $\gamma$ is the specific heat ratio....

In the video you've linked to, the spheres are seen on both the leading and trailing edges of the propeller: I expect they are intentional - there are a number of ways to attach a propeller without having to disturb that surface, or using flush caps. Cavitation is caused by a drop in pressure. This would be seen on the trailing edges of the propeller, and is worse on the outer edge of the propeller which is moving faster through water than the inner area. I doubt these spheres have any effect on cavitation at all. It is either a...


Why does column buckling occur when the load is parallel to the column?

I'm studying Euler's work on structural engineering from a book out of curiosity and it is mentioned that he developed a mathematical theory describing the buckling of columns under a parallel load (the weight-force of the load is directed down along the column). The theory is covered quickly without much motivation. But this got me thinking; why does a column "buckle" in the first place? If the load presses the column down, why does the column even start deflecting sideways? I know this happens in real life since this fact is easily confirmeable with household objects, but theoretically, why do objects start deflecting sideways instead of just compressing under loads? This might be something obvious and maybe I'm just overthinking but I find this curious nonetheless.

If the receiver does not detect the sub-carrier for the "colour burst" signal which is transmitted during the horizontal blanking period the receiver switches on the "colour-killer" circuit so the set reverts to black and white mode. The colour-burst signal - 8 to 10 cycles of 3.85 MHz - is unlikely to be generated by random noise. Figure 1. The colorburst signal is transmitted on the "back porch" between the horizontal blanking pulse and the start of that line's luminance signal. The colorburst signal is used to synchronise the QAM (quadrature amplitude modulation) oscillator which can hold its frequency accurately...

Nothing is rigid, the raceways and the ball in a ball-bearing are no exception. The contact area deflects and accommodates the ball in a small contact surface, not a point. Also, the balls take the load in groups. The digrams are from SKF ball-bearings. '

A yahkchal is an example of a type of passively cooled building in Iran They utilise a combination of passive evaporative cooling and thick thermally insulating walls in order to keep the interior temperatures low enough. First, wind is directed into underground aquifers known as qanat . They are then cooled due to the low humidity desert air causing water to evaporate. The cooled air then flows through the interior of the yakhchal, cooling the interior. The thick insulating walls (filled with earth and various insulating materials such as straw and feathers) help to insulate the cool interior from the...

Euler buckling occurs because the world isn't perfect. So that theory assumes that there is an initial infinitesimal deviation along the column (assuming the column is in fact not perfectly vertical*). This deviation causes a bending moment along the beam, which increases the deviation, which increases the bending moment, which increases the deviation... For loads lower than the Euler load, this vicious cycle eventually stabilizes and the beam doesn't buckle. For the Euler load and above, the cycle never stabilizes and the deflection goes to infinity. Obviously the real world has initial deviations and other problems which are much higher...


Why are multiple locomotives attached only to the front for larger trains?

For long freight trains and those that will be climbing to stations at higher altitudes, an extra or two locomotives are attached to the front. I've always wondered why. For argument's sake, if there are 30 bogeys each weighing 10 tons, the three engines are pulling a combined 300 tons. Each must be applying the exact same pull else if one is pulling harder than it is effectively taking on all the work with the other two idling. Plus, the load on the first coupling is 300 tons, on the second 290, and so on. On the other hand, if locomotives are placed after every 10 bogeys, then each is pulling 100 tons only.

For long freight trains and those that will be climbing to stations at higher altitudes, an extra or two locomotives are attached to the front. I've always wondered why. As usual there are multiple issues. Most important is landscape. If more power than a single locomotive can provide is not needed for the whole trip, but only a short stretch, like climbing or crossing a mountain range, then it would be a huge waste of resources to attach them the whole trip. For example, take a 10 hour trip time, where all, except for a 1 hour stretch, can be...

There are a few simple reasons why the speed of a vehicle (road conditions notwithstanding) may be limited: Gearing -- Production vehicles with conventional transmissions have a limited number of gears. For most modern cars, this is usually 5 or 6, whereas older vehicles may have as few as 2 or 3. If the gear ratio of the highest gear is too low ("lower" gears are expressed as larger numerical ratios), it's entirely possible that the engine will redline before air resistance becomes a factor at all. This ties into your first point about the red zone on the tachometer....

As other have pointed out, the main utility is to allow easier cleaning of the tank cars from sediment (solid precipitates). Usually, there is a drain in the lowest point. The reason that it is in the middle is that in this way, you can allow double the incline compared to if you had the drain at one of the ends for the same height. For example, if the allowed height difference is about 15 cm, and about 15 m length, then if you had the drain in: the edge, the angle would be $\arctan\left(\frac{0.15}{15}\right)=0.57^\circ$ or 1%. the middle ,...

If I model this as a simply supported beam having load at mid span [...] I suspect that this is where your analysis went awry. First off, you should always model bridges with distributed loads, not a single concentrated load at midspan. The most significant load on a bridge will almost always be its own self-weight; load-trains are heavy but, well, so are bridges. Secondly, I assume you're thinking of the bridge like this: Indeed, we can see here that the bending moment is greater at midspan. However, that's not the bridge we're looking at, it's missing the cantilevers! So...


Do I need to worry about galvanic corrosion when inserting a steel bar through aluminium?

My design uses a round steel bar inserted through a hole in an aluminium component with a tight fit (no movement). The operating environment is dry, 20-40°C. Do I need to worry about galvanic corrosion, and if so how long will this last before starting to corrode? Also, what storage conditions should I avoid that would accelerate the corrosion?

Short answer : make it thicker. Long answer : The moment of inertia affects the beam's ability to resist flexing. Use one of the many, free, online moment of inertia calculators (like this one ) to see how increasing the height of the beam will have an exponential effect on increasing the stiffness of the beam. And this site helps provide a pictorial view of the load(s) upon a beam depending upon differing configurations, such as where the supports are and where the load is applied. It also provides a calculator to determine the forces involved. Wikipedia has a decent...

BS5950-1:2000 Clause 1.3.23 defines an H-section as having " an overall depth not greater than 1.2 times its overall width ", and Clause 1.3.25 defines an I section as having " an overall depth greater than 1.2 times its overall width ". Note that at exactly a ratio of 1.2, it would be an H section not an I section.

Very probably, no. Galvanic corrosion required the existence of a reactive and conductive medium, which you don't have. If there is some (for example, at least moist air, or similar) best you can do to paint both of the metals, if you can. Generally, if none of the materials would corrode in an environment, galvanic corrosion is a non-issue (in that environment).

We use engineering strain even though it is not the "correct" value because in most cases, specifically in the elastic regime, engineering strain differs negligibly from true strain. For linear elastic, Hookean materials, it is generally the case strain at the elastic limit is very small. Even the strongest steels, for example, have an upper limit when cold worked of about $\sigma_{\textrm{el}}=1\times 10^{9}\ \textrm{Pa}$. The modulus of steel is approximately $E=200\times 10^{9}\ \textrm{Pa}$. Thus $\varepsilon_{\textrm{el}}=0.005=0.5\%$ for the strongest steels. So at the onset of plastic deformation, engineering strain is $0.5\%$. Many useful elastic materials have much lower engineering strain at...


Additional jacking force to overcome stiction/dry friction

It is common to lift bridges to replace bearings, etc. In an ideal world the lifting capacity required of the jacks would be the self-weight of the bridge divided by the number of jacks (+ allowances for wind/snow, etc.). From my (limited) experience, however, bridges begin to 'stick' to their bearings, and an additional allowance for over-coming this has to be provided. Does anyone have any guidance about how to determine this figure?

civil-engineering structures bridges maintenance friction

So there's an incorrect assumption underlying your question. In an ideal world the lifting capacity required of the jacks would be the self-weight of the bridge divided by the number of jacks (+ allowances for wind/snow, etc.). And the assumption there is that the lifting capacity is equivalent only to the weight of the bridge. The problem is that if anything goes wrong, you're likely to see a catastrophic failure of some sort which could lead to irreparable damage. Real world lifts don't operate in that "ideal" manner, and instead rely upon a safety factor in order to make sure...

That looks like a Pratt truss . These trusses have diagonals which go from the outer-top nodes to the inner-bottom nodes (i.e. they connect to the top chord on the node furthest from the center of the span, and to the bottom chord on the node closest to the center). This design means that the diagonals are under tension and the verticals are under compression. Another famous design is the Allan truss , which is the exact opposite: the diagonals go from the inner-top nodes to the outer-bottom nodes, which means that the diagonals are under compression and the verticals...

The loops are known as expansion loops. They need to be placed in pipelines to enable the pipelines to contend with thermal expansion and contraction and other forces that can affect the pipeline. They are typically placed in gas pipelines, irrespective of when the gas is hot or cold - natural gas or steam. The following quote is from Pipeline Design . It's near the end of the page under Pipe Expansion and Supports Steel piping systems are subject to movement because of thermal expansion/contraction and mechanical forces. Piping systems subjected to temperature changes greater than 50°F or temperature changes...

The picture, below, of the exaggerated long section of the Channel Tunnel was taken from Wikipedia . Full-sized image here . Some of the limiting factors for the Channel Tunnel are: Railways don't like steep gradients The tunnels comprising the Channel Tunnel were excavated using tunnel boring machines (TBMs). Like railways, they cannot tolerate steep gradients. The tunnel was excavated in chalk marl (green coloured material in the picture). This was due to its depth (not being too shallow and not being too deep) and its ability to be easily dug but also it would cause major support issues for...


How to correctly size the blades for a small educational wind turbine?

I want to design a small wind turbine that can be easily carried out of the classroom into the sports field in relatively low-wind conditions (5-15km/h) that can power a small ultra-bright 5V LED - just enough to show that it works. How do I calculate the power I can get from different blade diameters in these wind conditions, and the power needed to drive a small DC motor/generator enough to light the LED?

electrical-engineering renewable-energy power-engineering wind-power

As it happens, I just recently went through that calculation myself for a different site. Given the following facts from a quick web search, it isn't difficult to work out the numbers. The maximum efficiency of a (large) windmill is about 40%. The density of air is 1.225 kg/m 3 You need about 50 mW (10 mA at 5V) to light up an LED First, we'll need about 50 mW / 0.40 = 125 mW of air power flowing through the windmill to create the electricity we need (ignoring other factors such as the actual efficiency of a small windmill...

Cross-interference between aircraft is a high unlikely event because all commercial aircraft designs have to pass DO-160 environmental testing requirements. Among the DO-160 testing specification is EMI/EMC Testing. These tests include Radiated Emission, Interference and Immunity Testing. Part of these tests are to answer " Two aircraft are very close together " and " The other aircraft accidentally receives the signal because it is so close. " Below is a picture of an anechoic chamber used to test aircraft. Fly-by-wire allows the aircraft control system to access and command monitoring and control systems. The monitoring and control systems have a...

Some ideas: Wheel Load Distribution : The load is greater on the rear wheels providing the power; more force on the front ones bring no benefit and would provide less traction. Better manoeuvrability from having a shorter wheelbase. Better Ground Clearance in some conditions, especially for bumps and or up a increasing slope for instance. Better Driving : The front wheels now turn around a point closer to the C.G. than with the rear wheels. Not good with vehicle dynamics but this appears better than the rear end 'trailing' behind. Structural : As some people have pointed out, it's better...

At the beginning of my career (1979) as a design engineer at HP, the mechanical engineer created the part design and then rendered it in pencil on paper, and then transferred it onto sheets of vellum paper held onto a huge flat tilting table called a drafting board which had a precision sliding arm on it with which parallel and right angle lines could be drawn anywhere on the sheet. Clever graphical rules were applied to the resulting drawings which permitted auxiliary views of the part to be generated so it could be viewed from any desired angle, as an...


Derivation for bridge natural frequency estimate in Eurocodes

The Eurocodes gives the following equation for estimating a "simply supported bridge subject to bending only"*: $$n_0 = \frac{17.75}{\sqrt{\delta_0}}$$ Where $n_0$ is the natural frequency in hertz $\delta_0$ is the deflection at mid-span under permanent actions in mm The equation is seemly plucked from thin air, and there is no explanation as to where the constant 17.75 comes from. As an engineer I'm loath to use a formula I don't understand, but more than that it would be helpful to learn the fundamentals behind it so that I can see if it can be altered to work with other support conditions. Can anyone provide a derivation / fundamental origin to this relationship? *Full reference is: EN 1991-2:2003 6.4.4 [Note 8] (Equation 6.3), if that helps.

The picture, below, of the exaggerated long section of the Channel Tunnel was taken from Wikipedia . Full-sized image here . Some of the limiting factors for the Channel Tunnel are: Railways don't like steep gradients The tunnels comprising the Channel Tunnel were excavated using tunnel boring machines (TBMs). Like railways, they cannot tolerate steep gradients. The tunnel was excavated in chalk marl (green coloured material in the picture). This was due to its depth (not being too shallow and not being too deep) and its ability to be easily dug but also it would cause major support issues for...

When a reactor is shut down the core produces much less heat, but they do still produce heat through a mechanism known as decay heat . The fact that the core is producing less heat means that the coolant temperature is going to drop, but how far that temperature drops depends on the decay heat generation rate. This in turn is based on operating history, or the power at which the plant was operating before shutdown. This can be large for commercial plants, because they typically operate at or very near capacity and the power companies bring coal or natural...

If we simplify the whole bridge into 2D thin beam with a constant section size, no internal damping and subject only to small vertical deflections, then the natural frequency is determined by simple harmonic motion: $$ n_0 = \frac{1}{2 \pi} \sqrt{ \frac{ k } { m } } $$ Where $ n_0 $ is the natural frequency, $ k $ is the ratio between restorative force and deflection (the equivalent 'spring stiffness') and $m$ is the mass per unit length of the beam. In a beam the restorative force is the internal shear caused by the deflected shape. As the...


How different are dc motor designs from dc generator designs?

Some dc motors can be used as generators as well by applying mechanical torque to the output shaft to induce a current. However, even if a dc motor can do this, I imagine they were not designed for this purpose and thus perform less efficiently when used as a generator rather than as a motor. In my admittedly naive understanding, dc generators and dc motors are essentially the same machinery, but with inputs and outputs reversed. This leads me to believe that some other design considerations are used to make one direction more efficient than the other. How differently are dc generators and dc motors designed to make one direction of input/output more efficient than the other? What can one do electrically or mechanically to improve the efficiency in either direction? In particular, I'm interested in converting a dc motor into a generator and want to know how I can improve its efficiency in converting mechanical energy into electrical energy.

The current limit specification for a wire is limited by the heat that current will produce, and how much heat the wire can dissipate before getting too hot. "Too hot" depends on the circumstances. You will see higher current ratings for the same type of wire in chassis wiring applications than the electrical code allows for home installations, for example. This is mostly due to how hot too hot is. The ultimate limit for extreme applications is that the conductor not melt. Temperatures anywhere near that would be unsafe running along wooden supports inside a wall in a house. As...

From the point of view of the driver of a car, impacting another car is about as bad as crashing against an ideal wall (a wall with zero deformation whatsoever). If there were a plane reflection between the two cars, then vs. Car would be exactly equal to vs. Wall (the contact points between both cars would all be on the same plane, due to reflection, so each car could be considered a wall for the other). But this plane reflection does not exist: What we have instead is a 2-fold rotational reflection . Let's say the left part of...

You want to let air into the pipe when you switch the pump off, without letting water out. Here's a few ways to do this. Make a pinhole in the highest point of the pipe. You will lose a bit of water this way, but if it is above the tank, the water will drip back in (provided it doesn't spray too far.) You could even put it just under the tank lid. Install a tee and riser at the highest point of the pipe. this will need to be high enough to avoid the pump pressure pumping water out...

In Ye olden days DC generators were brushed commutated devices. They had a one or more stator windings and an armature winding. Field wound DC generators as well as motors were commonly connected in one of three methods: Series, Shunt and Compound. Without getting into details, each had its own set of strengths and weaknesses. But you only have to remember these two things: the voltage of a DC motor is dependent on its input shaft speed. Current is a function of torque. More voltage means more RPM's and more amps means more newton-meters (or foot-pounds). So with all that,...


Which turbulence models are suitable for CFD analysis on a streamlined vehicle body?

Many commercial and open-source CFD codes implement several closure methods for the non-linear convective acceleration term of the Reynolds-averaged Navier-Stokes (RANS) equations. Common methods (also known as turbulence models ) include Spalart–Allmaras (S–A) k–ε (k–epsilon) k–ω (k–omega) SST (Menter’s Shear Stress Transport) Reynolds stress equation model Which of these are suitable for CFD simulation of a streamlined vehicle body? The purpose of the simulations is to guide the refinement of the body shape to minimize aerodynamic drag forces. An exemplary answer would briefly outline the advantages and disadvantages of each method for this simulation application. Potentially useful details: The vehicle is a small one-person vehicle with approximate dimensions L = 2.5 m, W = 0.7 m, and H = 0.5 m. It will be travelling at speeds ranging from 0 m/s to approximately 12 m/s. All three wheels are enclosed by the body envelope, and the vehicle has an approximate ground clearance of 15 cm except near the wheels, where the body shell extends down to within 1 cm of the road surface. Normally aerodynamic forces at these speeds are very nearly negligible, but assume that this vehicle is being designed to compete in a "Super Mileage" competition on a smooth track, is very light-weight, and uses low friction drivetrain components throughout, so the aerodynamic forces have a significant effect on the achievable fuel consumption.

mechanical-engineering fluid-mechanics fluid-dynamics simulation modeling

The turbulence model can make a big difference in your simulation . There are many turbulence models around. It becomes a tough job to select one out of them. There is no perfect turbulence model. It all depends on several parameters like Reynold's number, whether the flow is separated, pressure gradients, boundary layer thikness and so on. In this answer, brief information about a few popular models is given along with pros and cons and potential applications. However, interested users can see this excellent NASA website and references therein to know more about turbulence modeling. A) ONE EQUATION MODEL: 1....

In the video you've linked to, the spheres are seen on both the leading and trailing edges of the propeller: I expect they are intentional - there are a number of ways to attach a propeller without having to disturb that surface, or using flush caps. Cavitation is caused by a drop in pressure. This would be seen on the trailing edges of the propeller, and is worse on the outer edge of the propeller which is moving faster through water than the inner area. I doubt these spheres have any effect on cavitation at all. It is either a...

I have written mostly about CFD in this answer, however same points should also work for FEA or other simulation techniques. CFD is mostly used for design optimization and parametric study of the design. Following are a few examples showing how engineers use simulations Selection of a design : Read: A conceptual study of airfoil performance enhancement using CFD. This thesis shows use of CFD for selecting the best design out of a number of candidate designs. Engineers often go for simulations to select 'the one' out of many . Shape optimization using CFD : This paper gives an example...

The current limit specification for a wire is limited by the heat that current will produce, and how much heat the wire can dissipate before getting too hot. "Too hot" depends on the circumstances. You will see higher current ratings for the same type of wire in chassis wiring applications than the electrical code allows for home installations, for example. This is mostly due to how hot too hot is. The ultimate limit for extreme applications is that the conductor not melt. Temperatures anywhere near that would be unsafe running along wooden supports inside a wall in a house. As...


Measuring longer distances with high accuracy

I am involved right now in the fabrication of steel structures on the order of 5-50 feet long. Presently, we measure these structures with garden variety commercial tape measures. Most of the time, we work to a tolerance of about +/-1/16" and don't have any problems. Recently, we're trying to make some items to a very high tolerance (at least +/- 1/32", approaching 1/64" or .016") This tolerance is due to visual not mechanical criteria, but it is still very important to our management. My question is, how can we reliably measure these sorts of distances with that level of precision? I'm prepared to order some NIST traceable tape measures, but it's not clear to me if they'll really improve the situation. Are there other technologies or techniques that could practically be applied in a fabrication setting? Are any surveying tools accurate enough to solve the problem? Cost is obviously a factor, but we're more concerned with repeatability and robustness than price. I realize this tolerance will sound ridiculous to most, but I imagine that some other industries may have to perform similarly, perhaps large engines for ships or power plant components?

measurements tolerance manufacturing-engineering surveying

Answering the question: What are possible types of low cost sensors I can use? There are several types of sensors that can provide millimeter level accuracy. "Low cost" is a very relative term, so you'll need to do some shopping around based on your specific budget. Optical sensors- Included here are those of the type you listed, though it's a very cheap sensor meant more to provide a "yeah something is in front of me, about yay-far-away". There are also laser sensor systems which can provide millimeter level accuracy. Ultrasonic Sensors- Most ultrasonic sensors have relatively low accuracy; in the...

It is more efficient to transmit DC using about the same infrastructure. This is because of several effects: Skin effect experienced with AC. There is no skin effect with DC. Higher voltage allowed with DC for the same transmission lines. The lines have to withstand the peak voltage. With AC, that is 1.4 times higher than the RMS. With DC, the RMS and peak voltages are the same. However, the power transmitted is the current times the RMS, not peak, voltage. No radiation loss with DC. Long transmission lines act as antennas and do radiate some power. That can only...

To get that sort of accuracy over that scale is not trivial and probably won't be cheap. For smaller size up to a few meters a portable CMM would be an option ( here's an example ). These have accuracy on the order of 10 $\mu$m and are used for things like high end/F1 car manufacture. However, CMM type instruments wouldn't be useful for anything larger than a few meters as it is limited by the arm length and must be fixed in place when measuring to get a sensible result. For larger pieces the best performing option would be...


How does a multimeter protect itself from high voltages?

I have used a cheap multimeter to measure voltages in simple DC circuits, but I have seen pictures of them plugged straight into the mains and used to measure various home-built generators. Why doesn't the higher voltage fry the multimeter, and also in theory could a small cheapo multimeter be safely used to measure very high voltages? If you get the setting wrong on the dial, does this matter? I'm not planning to plug one in, nor would I recommend anyone who doesn't know what they're doing to do this either, I'm just wondering how it works.

WARNING : Note that some cheap meters are not suitable for use with 230 VAC AC mains. Some meters may have AC voltage ranges able to conceptually measure to well above AC mains voltage BUT have internal componentry not certified, suitable or safe at eg 230 VAC. Use of such meters to measure such voltages is akin to a safer than usual game of "Russian Roulette" which still may end in death. _________________ Failures may occur to power dissipation in components or to voltage breakdown even when power dissipation is within bounds. Voltage ranges are usually less stressed than most...

Your equation is partly correct. You've calculated the energy per photon ($\hbar \nu$), but you've neglected the number of photons. That's why the units don't match (power is energy per unit time, while you've only got energy for each photon). The ideal power (energy per unit time) depends on the area of the solar panel, $A_p$, the number of photons striking it per unit time ($\Phi$) and the energy of each photon, $E$, such that $W_{Ideal} =A_p \cdot \Phi \cdot E$. A lens or mirror can focus light (a flux of photons) onto a small area. Under really ideal conditions,...

After the 2014 ICCT report revealed that these light-duty passenger diesel vehicles were emitting too much NOx and US regulators confronted VW about the results, VW did some testing and proposed a voluntary software recall to recalibrate the various emissions control devices on the affected vehicles. From the California Air Resources Board's (CARB's) in-use compliance letter to Volkwagen AG, 2015-09-18 , following that recall: To have a more controlled evaluation of the high NOx observed over the road, CARB developed a special dynamometer cycle which consisted of driving the Phase 2 portion of the FTP repeatedly. This special cycle revealed...

From the point of view of the driver of a car, impacting another car is about as bad as crashing against an ideal wall (a wall with zero deformation whatsoever). If there were a plane reflection between the two cars, then vs. Car would be exactly equal to vs. Wall (the contact points between both cars would all be on the same plane, due to reflection, so each car could be considered a wall for the other). But this plane reflection does not exist: What we have instead is a 2-fold rotational reflection . Let's say the left part of...


Estimating whether the flow through a valve or nozzle cavitates

My understanding is that cavitation occurs in the flow of a liquid when the static pressure drops below the vapor pressure, even intermittently. So even if the time-averaged static pressure (what you might measure) is above the vapor pressure, the pressure fluctuations from turbulence or other unsteadiness could be large enough to cause cavitation locally. So comparing the time-averaged static pressure against the vapor pressure isn't enough; you need to add some extra cushion to account for the pressure fluctuations. (This is my interpretation, not having read too deeply into this.) So, in various books, websites, and journal articles I have seen two different types of dimensionless numbers for estimating whether the flow through a valve or nozzle cavitates. They are generally called the cavitation index or cavitation number. They take one of two forms: $$\sigma = \frac{p_\text{in} - p_\text{vapor}}{p_\text{in} - p_\text{out}}$$ or $$\sigma = \frac{p_\text{in} - p_\text{vapor}}{\tfrac{1}{2} \rho V^2}$$ where $p_\text{in}$ is the inlet pressure, $p_\text{out}$ is the outlet pressure, $p_\text{vapor}$ is the vapor pressure, $\rho$ is the liquid density, and $V$ is some characteristic velocity of the flow (say, in the nozzle case, the velocity at the outlet). Some forms of this number are inversions of the numbers above, but these aren't that different. What is the difference between these parameters? Based on energy conservation you can relate the pressure drop to the flow rate, but typically there is an empirical coefficient added in to account for non-idealities. Is there something else I am missing? Is one form preferred over the other? Best I can tell whether to use one or the other depends on what sort of data you have (so, for flow over a turbine blade, the velocity form is preferred), but I've seen both even for nozzles. Where can I get accurate data to predict cavitation based on these numbers? I've tried using some data on atomizer nozzles from various journal articles but generally they use different forms of the cavitation number. Some of the data suggests the flow through the nozzle will cavitate at the pressures I want, but other data for similar nozzles suggests it won't. I'm not sure what the source of the inconsistency is. My understanding could be faulty, the cavitation number model could be too simplistic, the data could be inaccurate, etc.

If you consider only the static forces then indeed the thickness might seem over-engineered. However, engine blocks are not statically loaded. They operate in the range of a few hundred to a few thousand rpm (Revolution Per Minute), so there are dynamic considerations here. Fatigue When materials are subjected to cyclic loading they exhibit a reduction in the allowable stresses. See below for an example: In general, BCC (body-centered cubic) materials (like steel) show a marked drop in strength (close to 50% or more depending on the steel). For these material there is stress (called the endurance limit), for which...

In the video you've linked to, the spheres are seen on both the leading and trailing edges of the propeller: I expect they are intentional - there are a number of ways to attach a propeller without having to disturb that surface, or using flush caps. Cavitation is caused by a drop in pressure. This would be seen on the trailing edges of the propeller, and is worse on the outer edge of the propeller which is moving faster through water than the inner area. I doubt these spheres have any effect on cavitation at all. It is either a...

The difference between the two equations The cavitation number is the ratio of the static pressure difference to the dynamic pressure difference. So, if you want to use the first equation, you would need to take the pressure using a Pitot tube to measure the total pressure, whereas if you want to use the second equation you will need to measure the freestream velocity, but I would recommend measuring it upstream rather than downstream because of possible effects of acceleration and boundary layer growth. Also, your $V$ should be $V_{in}$ such that it corresponds to the same location where $p_{in}$...


I have inherited a product with inconsistent designs sharing the same part number. What do I do?

I am now in charge of a product line my company has been shipping for a decade. One of the previous product engineers was... shall we say, less than conscientious about sustainability and proper documentation. We have shipped hundreds of units, of multiple design variants, under the exact same part number . The manual presently reflects only one variant, meaning many users can't use it. And we've had multiple instances where a user has tried to reorder a unit by part number, only to find that what we ship them does not match what they already had. Obviously, this is terrible. One does not change the specs or user interface of a product without also changing the part number. We will avoid such things in the future. But my question is about the past. We have, on paper, documentation indicating what design variant each serial number corresponds to. My thinking is to create a spreadsheet, and name each variant retroactively, so we can at least support users that call in or place reorders. We would then create proper manual(s) so that the user can, based on their serial number, understand the operation of the units they have. But I'm just making up that solution. It occurs to me that there may be formal, industry-standard methods of dealing with such things. Is there a procedurally-correct way to handle my existing install base?

I don't think there is any formal standard way out of this mess. The good news is that at least tracked the changes by serial number. Inventing different models after fact seems pointless because the customers won't know what models they have. From the customer view, these are all one model but vary by serial number. Document it that way. You could create a different manual for different serial number ranges if the changes are large, or have occasional sections in the manual that only apply to particular serial number ranges. Make sure that the customer can easily find the...

As other have pointed out, the main utility is to allow easier cleaning of the tank cars from sediment (solid precipitates). Usually, there is a drain in the lowest point. The reason that it is in the middle is that in this way, you can allow double the incline compared to if you had the drain at one of the ends for the same height. For example, if the allowed height difference is about 15 cm, and about 15 m length, then if you had the drain in: the edge, the angle would be $\arctan\left(\frac{0.15}{15}\right)=0.57^\circ$ or 1%. the middle ,...

At the beginning of my career (1979) as a design engineer at HP, the mechanical engineer created the part design and then rendered it in pencil on paper, and then transferred it onto sheets of vellum paper held onto a huge flat tilting table called a drafting board which had a precision sliding arm on it with which parallel and right angle lines could be drawn anywhere on the sheet. Clever graphical rules were applied to the resulting drawings which permitted auxiliary views of the part to be generated so it could be viewed from any desired angle, as an...

It is more efficient to transmit DC using about the same infrastructure. This is because of several effects: Skin effect experienced with AC. There is no skin effect with DC. Higher voltage allowed with DC for the same transmission lines. The lines have to withstand the peak voltage. With AC, that is 1.4 times higher than the RMS. With DC, the RMS and peak voltages are the same. However, the power transmitted is the current times the RMS, not peak, voltage. No radiation loss with DC. Long transmission lines act as antennas and do radiate some power. That can only...


What makes the material travel through Archimedes' Screw?

...or in other words, why doesn't the material just stick to the screw, rotating in place, without progressing along its length? In the simplest case, the answer is obvious: gravity. If it's a granular or liquid material and the screw is tilted to a side, it will just roll/slide/flow along the blade, to remain on the bottom side of the tube. But then, Wikipedia says: A variant of the Archimedes' screw can also be found in some injection molding machines, die casting machines and extrusion of plastics, which employ a screw of decreasing pitch to compress and melt the material. Finally, it is also used in a specific type of positive displacement air compressor: the rotary-screw air compressor. On a much larger scale, Archimedes' screws of decreasing pitch are used for the compaction of waste material. In such case the forces - pressure, shearing, viscosity, adhesion, all would outweigh gravity, and probably in some cases friction against the tube walls. For example, in injection molding, what is there to keep the half-molten plastic from forming a clumping mass, sticking to the screw and keeping rotating in place without any progress? When the pressure increases, which force prevents the material from backing up into area of lower pressure?

Trees increase the turbulence of the air that reaches the turbines. That creates all sorts of uneven, rapidly-shifting loads on the blades and structure. That increases the maintenance costs, decreases availability, decreases the capacity factor, and decreases the life expectancy of the turbine. So, higher costs, lower revenue. One of the ways we measure the impact is the surface roughness coefficient $z_0$. Here are the figures from the book " Wind Energy - The Facts ". As you can see, forest and woodland has a much higher $z_0$ than open farmland - and that means higher turbulence. Open land also...

There's actually two kinds of screw conveying: Water lifting with screws happens just as in your gif, in the lower part of an inclined pipe we have water and the screw pushes 'packets' of water upwards. The water can't flow back because there's no path, the blades are not fully submerged. This mode is in principle also possible with solids. source: Wasser Wissen Now, screw conveyors for solids or the screws in extruders and meat grinders or certain dewatering presses work differently: Here it is the friction between the medium and the walls that prevents the material from corotating with...


How does pressure treatment affect the mechanical properties of lumber?

Pressure treated lumber is specified for many exterior applications because of its resistance to insect damage and fungal rot. But how does it compare to untreated wood, mechanically? For example, consider a rim joist supporting the ground floor of a residential structure with a pier and post foundation. If the joist has been damaged by rot in a location that is impractical to fully protect from exposure, I might be tempted to replace the joist with a pressure treated member of the same nominal dimension (in addition to proper flashing) for added protection in that location. Since this is an existing structure, by far the easiest approach is to use a member with the same dimension to replace the rotted joist. However, this relies on the new member meeting the same load-bearing requirements as the old member. Building codes should provide enough wiggle room that in this particular example, there's not much of a safety concern for the homeowner. After all, the rotted joist had not failed, and it would definitely have less strength than the member was originally rated for. In practice, treated and untreated members may be manufactured from different wood species with different mechanical properties to begin with; for the purposes of this question, assume the species is constant. Does pressure treatment result in a member with more or less strength in tension, compression or torsion? Does it affect the durability of the wood* in ways not related to rot or insect damage? * Not the fasteners; that's a different issue that's pretty well-covered online. See this page from Simpson , for example.

After the 2014 ICCT report revealed that these light-duty passenger diesel vehicles were emitting too much NOx and US regulators confronted VW about the results, VW did some testing and proposed a voluntary software recall to recalibrate the various emissions control devices on the affected vehicles. From the California Air Resources Board's (CARB's) in-use compliance letter to Volkwagen AG, 2015-09-18 , following that recall: To have a more controlled evaluation of the high NOx observed over the road, CARB developed a special dynamometer cycle which consisted of driving the Phase 2 portion of the FTP repeatedly. This special cycle revealed...

Pressure treatment does have a small, but documented effect on the strength of the member, particularly if it is 'incised' (has slots or holes cut into it as part of the pressure treating process.) If you're working to American codes, according to the American Wood Council , pressure treated wood is limited to a maximum duration factor of 1.6. This wouldn't matter for your example of fixing a house, because the duration factor would already be much smaller. Effectively, this just restricts the use of pressure treated lumber for resisting impact loads. More importantly, if it is incised which is...


What is a Spiral Curve, and How is it Different from a Normal Curve?

I've heard the term spiral curve used to describe a section of highway that is more aesthetically pleasing to the driver's eye. However, I believe I've driven on enough road to say that I can't definitively tell the difference between any given curve other than how "sharp" it is. Could anyone explain how one can determine if a section of curve on a highway is classified as a "spiral" curve, and are there other advantages besides "making it look good"?

civil-engineering highway-engineering surveying rail

The problem is that the formula $P=I\ V$ is correct when dealing with DC circuits or with AC circuits where there is no lag between the current and the voltage. When dealing with realistic AC circuits, the power is given by $$ P=I\ V\ \cos(\phi), $$ where $\phi$ is the phase difference between the current and the voltage. The unit kVA is a unit of what is called 'apparent power' whereas W is a unit of 'real power'. Apparent power is the maximum possible power attainable when the current and voltage are in phase and real power is the actual...

Spiral A spiral curve is a geometric feature that can be added on to a regular circular curve. The spiral provides a gradual transition from moving in a straight line to moving in a curve around a point (or vise-verse). The use of a spiral is about making the road or track follow the same form that the vehicle naturally takes. In a car, you don't go directly from going straight to fully turning. There is a transition area where you slowly turn the steering wheel. Lateral acceleration is slowly increased as the spiral is entered, or it is slowly...


How is a mechanical system designed and tested without building a physical model?

I am new to mechanical engineering, although I have a scientific background (postgrad in Mathematics), and I (mostly) code for a living. I have an idea about creating a mechanical device; I envisage it will entail gears, linkages and actuators. I have a rough idea where things will fit but I would like to be able to test and tweak the design in software before building the actual device. As a point of clarification, when I say "test," I mean view via animation, for example, whether two items will collide when in motion, or if there is sufficient leeway between them as they move past each other. This allows me to do the design and simulation testing of the parts, before finalising the design and then building the physical system from the design. The stages are: Build the 3D design in software Run simulation to see if it "works," if not fix design and iterate Build physical system from design that "works" I have figured out that the system consists of three subsystems working together. So, I would like to design and test each sub-component before integrating them into the complete system. My question then is this: Is this how design is done in the real world? What are the pros and cons of the scheme I have planned? I am intending to use FreeCAD to do the design and testing.

In the video you've linked to, the spheres are seen on both the leading and trailing edges of the propeller: I expect they are intentional - there are a number of ways to attach a propeller without having to disturb that surface, or using flush caps. Cavitation is caused by a drop in pressure. This would be seen on the trailing edges of the propeller, and is worse on the outer edge of the propeller which is moving faster through water than the inner area. I doubt these spheres have any effect on cavitation at all. It is either a...

Answer: Yes , this is exactly how it is done in the real world. What you have described is what I do in my job to check systems in CAD. Since you indicated you would like me to step through my design process, I have detailed it below. Note that most of this does not involve CAD. CAD is invaluable, but only if you are prepared to get out the pencil and paper first. Also note that this is just my design process, it is by no means the only way to go about things. Preparation When I begin any...

Nothing is rigid, the raceways and the ball in a ball-bearing are no exception. The contact area deflects and accommodates the ball in a small contact surface, not a point. Also, the balls take the load in groups. The digrams are from SKF ball-bearings. '

As others stated before, induction loops are the primary - most reliable method: the coils (usually just several loops of wire) embedded in the road; fed given frequency from a generator, in presence of metal the frequency of the LC circuit changes and the sensor circuitry detects the change of frequency, producing a presence signal. In some cases these may fail to detect bicycles, but they are by far most common as they aren't affected by weather (or more precisely, the detection circuit tunes in to slow changes of frequency caused by weather) and are immune to accidental false positives....


I am making a device for measurements. I would like to measure the distance within accuracy of 1 mm. Range could be 2 cm to 15 cm . I looked at Proximity Sensors but the readings displayed by these sensors are not steady. I wish to measure the thickness of the plate (carbon steel). The two sensors will be mounted on a structure. The sensors will give me the distance of the surface from the sensor. Then I will calculate the thickness of the plate. What are possible types of low cost sensors I can use?

mechanical-engineering measurements sensors tolerance

My first thought is that it might be intended to be a wing nut driver of some sort, but those are usually hollow cylinders with slots for the wings. Ah ... sure enough, it's described as such in this Ebay ad :

Water meets the low compressibility requirement, but there are many other considerations in the design of a hydraulic system: Boiling point/vapor pressure: If the system warms up during operation, the fluid may boil, which results in high compressibility and thus decreased effectiveness of the hydraulic system. Hydraulic fluid has a higher boiling point than water to help combat this. Related to this is the concept of vapor pressure. Hydraulic systems often involve small orifices, which can cause cavitation (localized boiling). This cavitation has the same effects as boiling and can cause pitting damage to the components near the cavitated region....


How much clearance does a car need when turning a corner?

I am contemplating buying a new car. However, the approach to the underground garage in my apartment has a 90 degree frustrating turn. Given the dimensions of the approach and car, what is the max turn circle for the car to fit the garage and turn? given Ackerman steering and the overhanging front part of the car I believe you can use Pythagoreas' theorem to get R min and R max. delta R should be less than the shortest path in the pathway, ie 2.5m. unfortunately the result does not seem plausible. feedback would be greatly appreciated.

Please note : I'm not a building designer by trade, but I have had to investigate related questions for other reasons. I'll let you in on a dirty secret about sanitation lines within buildings - The biggest concern is not about how fast things are flying, it's about maintaining air pressure and providing adequate ventilation. This guide presents a bit of a historical background to tall building design with respect to sanitation system design. This presentation provides some more recent perspective and goes into some of the research that is refining current building standards. The traditional viewpoint is that waste...

Those are counterweights . They work exactly the same as those lead counterbalance weights on the wheels of your automobile. If they left those out, then those connecting rods and bearings would create an out-of-balance condition, and the wheels would vibrate at higher speeds. That could very well damage the wheels. But as a couple of others have nicely pointed out, the violent shaking could derail the train .

It depends on how steep the hill is. On a slight hill, the energy added by gravity is still not enough to overcome rolling friction and air resistance, so the car still needs power to maintain speed. On a steeper hill, the two may balance out, so no power is used, and no power is generated. On a hill that's steep enough to require braking to control the speed, the car recovers energy. It's called regenerative braking. If the car is going too fast, applying the brakes turns the motor into a generator and charges the battery.

To slightly generalize I'll reform the question slightly. A ridged 2-D body (car) has a line $l$ that moves with it. The car can be linearly transformed as long as the instantaneous center of rotation lies along $l$ at least distance $R$ away from a point $c$ that also moves with the car. In this case point $c$ lies in the center of the rear axle and $l$ lies on the rear axle. Now imagine the car's domain is limited to a quarter plane with edges $A$ and $B$. It initially is placed against $A$, far from $B$ with $l$...


How do you ensure physical network interfaces always get the same interface name across reboots on an embedded Linux system?

For an embedded Linux system, if I have two or more network interfaces, how do I ensure that they always get the same interface names every boot In other words, I want, for example, eth0 to always map to one physical Ethernet port, eth1 to the next, etc. My Linux "distribution" is home-grown, and I use devtmpfs for populating /dev. I use busybox for init (and most everything else), along with custom init scripts for system startup and shutdown. I do not need hotplug facilities of mdev or udev -- I'm referring to "fixed" Ethernet ports.

It is more efficient to transmit DC using about the same infrastructure. This is because of several effects: Skin effect experienced with AC. There is no skin effect with DC. Higher voltage allowed with DC for the same transmission lines. The lines have to withstand the peak voltage. With AC, that is 1.4 times higher than the RMS. With DC, the RMS and peak voltages are the same. However, the power transmitted is the current times the RMS, not peak, voltage. No radiation loss with DC. Long transmission lines act as antennas and do radiate some power. That can only...

This works for me with Linux 3.9.0 on an x86_64 architecture. #!/bin/sh # This assumes the interfaces come up with default names of eth*. # The interface names may not be correct at this point, however. # This is just a way to get the PCI addresses of all the active # interfaces. PCIADDRLIST= for dir in /sys/class/net/eth* ; do [ -e $dir/device ] && { PCIADDRLIST="`readlink -f $dir/device` ${PCIADDRLIST}" } done # Now assign the interface names from an ordered list that maps # to the PCI addresses of each interface. # IFNAMES could come from some config file....

When a reactor is shut down the core produces much less heat, but they do still produce heat through a mechanism known as decay heat . The fact that the core is producing less heat means that the coolant temperature is going to drop, but how far that temperature drops depends on the decay heat generation rate. This in turn is based on operating history, or the power at which the plant was operating before shutdown. This can be large for commercial plants, because they typically operate at or very near capacity and the power companies bring coal or natural...

I will expand on DKNguyen answer, because to my knowledge also the two reasons are: reduce contact/bearing stresses (having a significant effect on thin finishes live galvanisation) change the joint tightening characteristics (see joint diagram). reduce contact stresses on surfaces. The basic idea is that since contact stress is defined as: $$\sigma = \frac{F}{A}$$ Obviously the larger the area the less the stress. Also, like Nuclear Hoagie pointed out the area changes with a square law of the diameter. UPDATE 2 - Calculation for M6 bolt (thanks to BenC) *The question gathered enough interest for me to carry out a...


What are left justified and right justified ADC results?

The TI MSP430F20XX series has a 12-bit internal ADC output, which is right-justified. What is the difference between a left-justified output and a right-justified output? What are their pros and cons?

On this processor, the register that holds the conversion result is 16 bits wide. A right-justified result means that bits [( N -1):0] (where N is the number of bits of precision) of the register contain the ADC value and the most-significant bits of the register are set to zero. A left-justified result means that bits [15:(16- N )] of the register hold the result, and bits [(15- N ):0] are set to zero. For example, if your actual conversion result is 0x123, it would be read as 0x0123 if the register was right-justified, and as 0x1230 if it was...

The loops are known as expansion loops. They need to be placed in pipelines to enable the pipelines to contend with thermal expansion and contraction and other forces that can affect the pipeline. They are typically placed in gas pipelines, irrespective of when the gas is hot or cold - natural gas or steam. The following quote is from Pipeline Design . It's near the end of the page under Pipe Expansion and Supports Steel piping systems are subject to movement because of thermal expansion/contraction and mechanical forces. Piping systems subjected to temperature changes greater than 50°F or temperature changes...


From an engineering standpoint, what is the purpose of the indent in a coffee lid?

I've see the same lids every day but I never really thought about their construction. There is an indent in a "Solo Travel Lid" for coffee cups that is just above the hole that you drink the coffee from. You can see the crescent shaped indent in the image. What is it for? Does it somehow increase fluid flow? Is it just a good spot for your upper lip? If so, why is there not a matching one for the nose? I tried googling this but I got no answer.

The current limit specification for a wire is limited by the heat that current will produce, and how much heat the wire can dissipate before getting too hot. "Too hot" depends on the circumstances. You will see higher current ratings for the same type of wire in chassis wiring applications than the electrical code allows for home installations, for example. This is mostly due to how hot too hot is. The ultimate limit for extreme applications is that the conductor not melt. Temperatures anywhere near that would be unsafe running along wooden supports inside a wall in a house. As...

I'm going to set aside the potential legal liability aspects of your question. In part because you didn't ask about them, but also because liability will vary based upon jurisdiction. Obviously, consult an attorney familiar with the relevant law. Ethically, I think you've done everything that you're obligated to do. You have contacted the customer and notified them of an unsafe situation or configuration of the product. And you have (strongly) advised them that they need to discontinue using the older product in the unsafe configuration. If the customer remains insistent about using the product in an unsafe manner, you...

From the "Solo Traveler" patent : A more specific object of the present invention is to provide a lid having an opening formed therethrough to enable drinking, and having a recess formed in the lid adjacent the opening to accommodate the upper lip of one drinking from the cup This is also illustrated in the patent diagrams. I came across this interesting article on the history, use, design, and styles of disposable lids. The Solo Traveler is prominently featured for its excellent aesthetics and design . The article reiterates that: the Solo Traveler lid was designed to accommodate the nose...


What is this Y-shaped screwdriver bit, and what is its purpose?

I found this strange looking bit in a bit set of uncommon bits, including Security Torx, hexalobular, tri-wing, spanner head, 12-point flange, Torq-set and others. It's the only one that I could not identify, what is it for?

This is to make sure they know what the foundation is made of. For all they knew there may have been an old tunnel underneath that would have collapsed when the new building is put on top. London is built on top of an old marsh, this type of soil is very prone to sinking and uneven settling, digging down and reinforcing the foundation alleviates that. It also ensures the foundation is uniform under the building to avoid a new tower of Pisa. Given the age of the city it may have been to scour the land for potential archaeological...

The turbulence model can make a big difference in your simulation . There are many turbulence models around. It becomes a tough job to select one out of them. There is no perfect turbulence model. It all depends on several parameters like Reynold's number, whether the flow is separated, pressure gradients, boundary layer thikness and so on. In this answer, brief information about a few popular models is given along with pros and cons and potential applications. However, interested users can see this excellent NASA website and references therein to know more about turbulence modeling. A) ONE EQUATION MODEL: 1....

My first thought is that it might be intended to be a wing nut driver of some sort, but those are usually hollow cylinders with slots for the wings. Ah ... sure enough, it's described as such in this Ebay ad :

OP injection molding tag is correct. OBall uses injection molding and plastic welding. The OBall is the invention of David E. Silverglate. Toy Ball Apparatus with Reduced Part Count Reduced image from Kids II . It consists of four identical, flat, injection molded, pentagon and hexagon shapes with circular (or elipitical) holes, which are shaped and plastically welded into spheres. Pentagon and hexagon edges are the same size and individual connected circles are only connected along one edge. The four shapes are clearly shown in colors above and from the patent. Solid lines on each part are hard connections, while...


What is the difference between the Polar Moment of Inertia, $ I_P $ and the torsional constant, $ J_T $ of a cross section?

This question is so fundamentally basic that I am almost embarrassed to ask but it came up at work the other day and and nearly no one in the office could give me a good answer. I was calculating the shear stress in a member using the equation, $\frac{Tr}{J_T}$ and noticed, that for a shaft with a circular cross section, $J_T = I_P$. Both $I_P$ and $J_T$ are used to describe an object's ability to resist torsion. $I_P$ is defined as, $ \int_{A} \rho^2 dA $ where $\rho$ = the radial distance to the axis about which $I_P$ is being calculated. But $J_T$ has no exact analytical equations and is calculated largely with approximate equations that no reference I looked at really elaborated on. So my question is, what is the difference between the Polar Moment of Inertia, $ I_P $, and the torsional constant, $ J_T $? Not only mathematically, but practically. What physical or geometric property is each a representation of? Why is $J_T$ so hard to calculate?

mechanical-engineering structural-engineering applied-mechanics stresses

The torsion constant $J_T$ relates the angle of twist to applied torque via the equation: $$ \phi = \frac{TL}{J_T G} $$ where $T$ is the applied torque, $L$ is the length of the member, $G$ is modulus of elasticity in shear, and $J_T$ is the torsional constant. The polar moment of inertia on the other hand, is a measure of the resistance of a cross section to torsion with invariant cross section and no significant warping . The case of a circular rod under torsion is special because of circular symmetry, which means that it does not warp and it's...

As with all good things, it depends. If you can assume that your supports are totally stiff and that the loading on the shelf will be approximately uniform, then you basically have the following structure: A rectangular cross-section (such as a plank) will behave equally under positive or negative bending moment, so your objective should be to balance both. To do so, you want your main span to be $2\sqrt2 \approx 2.83$ times the cantilevers. This is found by calculating the cantilever required to offset half of the bending moment due to a uniform load along a simply supported beam:...

Some ideas: Wheel Load Distribution : The load is greater on the rear wheels providing the power; more force on the front ones bring no benefit and would provide less traction. Better manoeuvrability from having a shorter wheelbase. Better Ground Clearance in some conditions, especially for bumps and or up a increasing slope for instance. Better Driving : The front wheels now turn around a point closer to the C.G. than with the rear wheels. Not good with vehicle dynamics but this appears better than the rear end 'trailing' behind. Structural : As some people have pointed out, it's better...


This is a toy for infants. My son was playing with it, and I started wondering how you could manufacture this. I can't think of any reasonably cheap way it could be done. I believe it's made of plastic and not silicone. It's flexible, but not elastic. My first thought would be injection molding, but I can't see any way to get parts of the mold in and out of the sphere. My wife suggested that perhaps the mold had no interior surface and was rotated like they do with chocolate, but I don't think that's the case, because if you look carefully you'll see that the inside surface is rounded and not flat. Anyway I'm stumped. How do you think they did it?

OP injection molding tag is correct. OBall uses injection molding and plastic welding. The OBall is the invention of David E. Silverglate. Toy Ball Apparatus with Reduced Part Count Reduced image from Kids II . It consists of four identical, flat, injection molded, pentagon and hexagon shapes with circular (or elipitical) holes, which are shaped and plastically welded into spheres. Pentagon and hexagon edges are the same size and individual connected circles are only connected along one edge. The four shapes are clearly shown in colors above and from the patent. Solid lines on each part are hard connections, while...

After the 2014 ICCT report revealed that these light-duty passenger diesel vehicles were emitting too much NOx and US regulators confronted VW about the results, VW did some testing and proposed a voluntary software recall to recalibrate the various emissions control devices on the affected vehicles. From the California Air Resources Board's (CARB's) in-use compliance letter to Volkwagen AG, 2015-09-18 , following that recall: To have a more controlled evaluation of the high NOx observed over the road, CARB developed a special dynamometer cycle which consisted of driving the Phase 2 portion of the FTP repeatedly. This special cycle revealed...

I'm going to set aside the potential legal liability aspects of your question. In part because you didn't ask about them, but also because liability will vary based upon jurisdiction. Obviously, consult an attorney familiar with the relevant law. Ethically, I think you've done everything that you're obligated to do. You have contacted the customer and notified them of an unsafe situation or configuration of the product. And you have (strongly) advised them that they need to discontinue using the older product in the unsafe configuration. If the customer remains insistent about using the product in an unsafe manner, you...


How can I tell if I got counterfeit aluminum?

I recently received an order of extruded aluminum strip 3/32" thick that supposed to be 6061 hardened to specification ASTM B221. However, when we tried to bend it, it broke and the interior looked like cast zinc coated with aluminum. Is 6061 supposed to look that way and be unable to bend 90-degrees? How can I verify that I have solid aluminum and not some fake alloy with zinc in it?

I figured out a simple test. Since the density of 6061 is 2.5 g/cm3 and the density of zinc is over 7 g/cm3, all I had to do was measure the density of the material. This showed that indeed it was aluminum. So, its brittleness is probably just because it was hardened.

The picture, below, of the exaggerated long section of the Channel Tunnel was taken from Wikipedia . Full-sized image here . Some of the limiting factors for the Channel Tunnel are: Railways don't like steep gradients The tunnels comprising the Channel Tunnel were excavated using tunnel boring machines (TBMs). Like railways, they cannot tolerate steep gradients. The tunnel was excavated in chalk marl (green coloured material in the picture). This was due to its depth (not being too shallow and not being too deep) and its ability to be easily dug but also it would cause major support issues for...

Please note : I'm not a building designer by trade, but I have had to investigate related questions for other reasons. I'll let you in on a dirty secret about sanitation lines within buildings - The biggest concern is not about how fast things are flying, it's about maintaining air pressure and providing adequate ventilation. This guide presents a bit of a historical background to tall building design with respect to sanitation system design. This presentation provides some more recent perspective and goes into some of the research that is refining current building standards. The traditional viewpoint is that waste...


What is the process of transferring an engineering license from the United States to Germany?

The United States have different rules about exactly how one obtains an engineering license, but the general process is the FE exam, a few years of work, and the PE exam. Suppose one then wishes to practice engineering in Germany. What are the legal requirements for doing so?

Unlike within the United States and the PE license , it doesn't appear that it's possible to receive an EUR ING license by direct comity . EU Engineering licensing is handled by FEANI , and on their EUR ING page they state: Application is open only to individuals if they are members of an engineering association represented in FEANI through a National Member But it may be possible to join one of the German FEANI members and see if they can support a reciprocity or comity process. 1 1 There are other member organization in other countries, but your question...

Electricity production optimization is a very complex subject. It is also affected by many parameters , which I will try to outline below. TL;DR: Demand is constantly monitored and supply is constantly adjusted TL;DR 2: Lshaver's excellent post is a suggested reading after reading this, because it expands and explains what happens at timescales ranging from the micro-second to minutes timescales. Changes in energy demand during the day First of all, the energy demand during the day, week, month of year can change quite a lot. Below is a typical day in New England. Fluctuation in power energy consumption a...

As other have pointed out, the main utility is to allow easier cleaning of the tank cars from sediment (solid precipitates). Usually, there is a drain in the lowest point. The reason that it is in the middle is that in this way, you can allow double the incline compared to if you had the drain at one of the ends for the same height. For example, if the allowed height difference is about 15 cm, and about 15 m length, then if you had the drain in: the edge, the angle would be $\arctan\left(\frac{0.15}{15}\right)=0.57^\circ$ or 1%. the middle ,...

After the 2014 ICCT report revealed that these light-duty passenger diesel vehicles were emitting too much NOx and US regulators confronted VW about the results, VW did some testing and proposed a voluntary software recall to recalibrate the various emissions control devices on the affected vehicles. From the California Air Resources Board's (CARB's) in-use compliance letter to Volkwagen AG, 2015-09-18 , following that recall: To have a more controlled evaluation of the high NOx observed over the road, CARB developed a special dynamometer cycle which consisted of driving the Phase 2 portion of the FTP repeatedly. This special cycle revealed...


How are spindle speeds calculated for a drill bit? I've seen dozens of charts that highlight the rpm that should be used for specific drill bit types, bit diameter, and material. However, what if my chart doesn't have the particular type of material or bit that I am using? I'd also like to have some intuition to know if the chart looks right or wrong. Upon some quick research, it appears that the "cutting speed" is what is ultimately needed for a particular material. I assume the cutting speed for each material must be looked up? Is there a standard or "go-to" place to find these? Then, information about the drill bit can be used to determine spindle speed. Again, what if I'm using a big hole saw or circle cutter, and it's not listed? How do I model the bit to use the cutting speed to determine rpm (for a given material of course)? I'd also like to know to calculate feed speeds for a drill or mill, but there are presumably more variables. It is probably better answered in another question.

For long freight trains and those that will be climbing to stations at higher altitudes, an extra or two locomotives are attached to the front. I've always wondered why. As usual there are multiple issues. Most important is landscape. If more power than a single locomotive can provide is not needed for the whole trip, but only a short stretch, like climbing or crossing a mountain range, then it would be a huge waste of resources to attach them the whole trip. For example, take a 10 hour trip time, where all, except for a 1 hour stretch, can be...

You are correct that the cutting speed of the material is what determines the rpm for your drill-bit. This actually makes the calculation very simple. $$ \text{Spindle speed (RPM)} = \frac{\text{Cutting speed}}{\text{Circumference}} = \frac{\text{Cutting speed}}{π \cdot \text{Diameter}} $$ The thing you need to be careful of is the units of cutting speed and diameter. For example: Metric: If your cutting speed is in $m/min$ and your diameter is in $mm$ then you need to multiply your cutting speed by 1000 so that it is in $mm/min$ Imperial: If your cutting speed is in $ft/min$ and your diameter is in $inches$...

Biggest advantage is that when connecting to trailers, there are no bleeding issues. Imagine having to connect hydraulic pipes and remove the air bubbles... As for the amount of air - the compressor and receiving tanks are designed for normal use. However if you wish to accompany AC/DC with the air brakes you will run out. Disc brakes already exist in an airbrake version for trucks - came out over 10 years ago IIRC. But one big difference is that if you lose hydraulics on a car braking system then you lose stopping power (except for handbrake etc) but with...

When a reactor is shut down the core produces much less heat, but they do still produce heat through a mechanism known as decay heat . The fact that the core is producing less heat means that the coolant temperature is going to drop, but how far that temperature drops depends on the decay heat generation rate. This in turn is based on operating history, or the power at which the plant was operating before shutdown. This can be large for commercial plants, because they typically operate at or very near capacity and the power companies bring coal or natural...


What causes rechargeable batteries to age? What can be done to extend life of these batteries?

These days most of modern electronics use rechargeable batteries as a power source. Also, these days most modern rechargeable batteries are Lithium Ion or Lithium Polymer based. Like any other devices, over time these rechargeable batteries lose the ability to recharge, retain and discharge energy thus users have to replace the devices or rechargeable batteries. It is my understanding that the rise in battery internal resistance is the primary cause the rechargeable battery aging. Is this accurate? If so what can be done to lower or eliminate the internal resistance in rechargeable batteries. If my understanding is inaccurate what is the cause for rechargeable battery aging? If the causes for battery aging are understood, how can electronic engineers design charging and discharging circuits to extend the rechargeable battery life? References: Battery University All About Batteries, Part 1: Introduction All About Batteries, Part 2: Specifications & Terminology All About Batteries, Part 7: Lithium Thionyl Chloride

energy electrical-engineering energy-storage chemical-engineering battery

It is more efficient to transmit DC using about the same infrastructure. This is because of several effects: Skin effect experienced with AC. There is no skin effect with DC. Higher voltage allowed with DC for the same transmission lines. The lines have to withstand the peak voltage. With AC, that is 1.4 times higher than the RMS. With DC, the RMS and peak voltages are the same. However, the power transmitted is the current times the RMS, not peak, voltage. No radiation loss with DC. Long transmission lines act as antennas and do radiate some power. That can only...

I will expand on DKNguyen answer, because to my knowledge also the two reasons are: reduce contact/bearing stresses (having a significant effect on thin finishes live galvanisation) change the joint tightening characteristics (see joint diagram). reduce contact stresses on surfaces. The basic idea is that since contact stress is defined as: $$\sigma = \frac{F}{A}$$ Obviously the larger the area the less the stress. Also, like Nuclear Hoagie pointed out the area changes with a square law of the diameter. UPDATE 2 - Calculation for M6 bolt (thanks to BenC) *The question gathered enough interest for me to carry out a...

One of the problems that plagued older rechargeable batteries (e.g. Nickel Cadmium ($\text{NiCad}$) and Nickel Metal Hydride ($\text{NiMH}$)) was the memory effect . The memory effect occurs when a rechargeable battery is not fully discharged. It then "forgets" that it has a greater capacity than it thinks it has, and so in the future it discharges less. A good example is a water bottle. Initially, water bottles have a certain capacity for water. Let's say that I drink most of the water in a water bottle during one usage. If the memory effect affected water bottles, I would not be...


Thermoelectric Technology to Harvest Energy from Internal Combustions Engines

Background: In an automobile, only 1 / 3 of the potential energy in the fuel is converted into mechanical energy and significant portion of the energy is lost as heat. There have been previous attempts to recuperate this lost energy. In the early 1990's, Porsche developed automotive thermoelectric generators (ATEG) which didn't go past prototyping stage. Currently, Porsche Motorsports is testing a thermal energy harvesting system in their LeMans series Race car. In addition to Porsche's research, GM is in collaboration with Future Tech, LLC. to explore the idea of using themoelectric technology to harvest energy from internal combustion engines. Other automotive manufactures, such as BMW, are also exploring this technology. Currently the power usage in a Small car is approximately 150 W Full size truck is approximately 500 W If this technology can successfully be implemented, then components such as the radiator, water pump, and alternator could effectively have reduced workload or removed from the system, thus reducing the load to the internal combustion engine. Question: With the growing interest in green technology, are there technology barriers beside efficiency that are preventing the implementation of energy harvesting from internal combustion engines using thermoelectric technology? References: Which one must be used matched output voltage or open circuit voltage? Benefits of Thermoelectric Technology for the Automobile The Promise and Problems of Thermoelectric Generators Modeling of an Automotive ThermoElectricGenerator (ATEG) Thermoelectrics to replace car alternators and improve MPG Thermo-Electric Generator in Turbocharged Diesel Engine Kettering University researchers are working with General Dynamics to convert the unused heat energy of their propulsion systems to useful and clean energy Porsche 919 Hybrid LeMans Racer Goes After The Two Thirds of Gasoline’s Energy That’s Wasted As Heat Germans trying to replace Alternator with Thermoelectric Generators or TEGs Porsche 919 Hybrid LMP1 Le Mans prototype... Footnote The suggested duplicate is related, but still distinctly different. The order of magnitude of energy available to recover from an internal combustion engine is significantly greater than within the GPU of a video card. As such, the economies of scale are different and different solutions are therefore possible.

As with all good things, it depends. If you can assume that your supports are totally stiff and that the loading on the shelf will be approximately uniform, then you basically have the following structure: A rectangular cross-section (such as a plank) will behave equally under positive or negative bending moment, so your objective should be to balance both. To do so, you want your main span to be $2\sqrt2 \approx 2.83$ times the cantilevers. This is found by calculating the cantilever required to offset half of the bending moment due to a uniform load along a simply supported beam:...

If you consider only the static forces then indeed the thickness might seem over-engineered. However, engine blocks are not statically loaded. They operate in the range of a few hundred to a few thousand rpm (Revolution Per Minute), so there are dynamic considerations here. Fatigue When materials are subjected to cyclic loading they exhibit a reduction in the allowable stresses. See below for an example: In general, BCC (body-centered cubic) materials (like steel) show a marked drop in strength (close to 50% or more depending on the steel). For these material there is stress (called the endurance limit), for which...

As with any new technology, the cost is the big driver here. In addition, these devices produce electricity which is a form of energy that a typical internal combustion automobile can only utilize for ancillary equipment. This would effectively improve fuel efficiency but the gain would be relatively minor. Engineers are generally reluctant to use expensive new technologies that are relatively untested when existing methods are sufficient for achieving the goal. In this case, most automobile manufacturers strive to produce a cost-competitive product. The people who are most concerned with fuel efficiency will tend to consider a hybrid (or all-electric)...


I've seen it in several data sheets - it is a measure of error of some kind, of course. The problem is I dont know the exact meaning. I've seen it in the context of repeatability, accuracy and linearity. An example is the following data sheet: smc data sheet (On page 3)

I will expand on DKNguyen answer, because to my knowledge also the two reasons are: reduce contact/bearing stresses (having a significant effect on thin finishes live galvanisation) change the joint tightening characteristics (see joint diagram). reduce contact stresses on surfaces. The basic idea is that since contact stress is defined as: $$\sigma = \frac{F}{A}$$ Obviously the larger the area the less the stress. Also, like Nuclear Hoagie pointed out the area changes with a square law of the diameter. UPDATE 2 - Calculation for M6 bolt (thanks to BenC) *The question gathered enough interest for me to carry out a...

Electricity production optimization is a very complex subject. It is also affected by many parameters , which I will try to outline below. TL;DR: Demand is constantly monitored and supply is constantly adjusted TL;DR 2: Lshaver's excellent post is a suggested reading after reading this, because it expands and explains what happens at timescales ranging from the micro-second to minutes timescales. Changes in energy demand during the day First of all, the energy demand during the day, week, month of year can change quite a lot. Below is a typical day in New England. Fluctuation in power energy consumption a...

FS = FULL SCALE = maximum reading. It means that the accuracy is such that the reading is probably within + or - 0.5% of the FULL SCALE reading. This is a very important and easily overlooked qualification of the result. If I have a reading of 1 Volt and the accuracy is +/- 0.5% it means that the actual result should lie in the range 1 - 0.5% x 1 to 1 + 0.5% of 1 = 0.995V to 1.005 V However - if I measure the result on the 10V range then 0.5% of 10V = 0.5% of...


At what point does an I-beam becomes a H-beam?

According to BS5950, a beam section can be classified as plastic, semi-compact, compact or slender. For the same section area, a H-beam can take axial compression (without buckling) better than an I-beam, and as such, uses a different strut curve in the code: Now, I understand that a H-beam has a wider flange compared to an I-beam, but at what point, precisely, does this transition from I- to H- occurs? For example, is a 400x300 (depth x width) beam considered a H- or an I-beam? Update: Extracted from BS5950 guide, the following table shows H-beams (also known as universal columns, some of which with depth greater than width. This is the reason why I don't believe the differentiation is so straight forward.

I'm going to set aside the potential legal liability aspects of your question. In part because you didn't ask about them, but also because liability will vary based upon jurisdiction. Obviously, consult an attorney familiar with the relevant law. Ethically, I think you've done everything that you're obligated to do. You have contacted the customer and notified them of an unsafe situation or configuration of the product. And you have (strongly) advised them that they need to discontinue using the older product in the unsafe configuration. If the customer remains insistent about using the product in an unsafe manner, you...

If you consider only the static forces then indeed the thickness might seem over-engineered. However, engine blocks are not statically loaded. They operate in the range of a few hundred to a few thousand rpm (Revolution Per Minute), so there are dynamic considerations here. Fatigue When materials are subjected to cyclic loading they exhibit a reduction in the allowable stresses. See below for an example: In general, BCC (body-centered cubic) materials (like steel) show a marked drop in strength (close to 50% or more depending on the steel). For these material there is stress (called the endurance limit), for which...

BS5950-1:2000 Clause 1.3.23 defines an H-section as having " an overall depth not greater than 1.2 times its overall width ", and Clause 1.3.25 defines an I section as having " an overall depth greater than 1.2 times its overall width ". Note that at exactly a ratio of 1.2, it would be an H section not an I section.

So there's an incorrect assumption underlying your question. In an ideal world the lifting capacity required of the jacks would be the self-weight of the bridge divided by the number of jacks (+ allowances for wind/snow, etc.). And the assumption there is that the lifting capacity is equivalent only to the weight of the bridge. The problem is that if anything goes wrong, you're likely to see a catastrophic failure of some sort which could lead to irreparable damage. Real world lifts don't operate in that "ideal" manner, and instead rely upon a safety factor in order to make sure...


Why are most standard bolt threads single start?

When looking at thread descriptions, one of the basic properties is always the number of thread starts. As far as I could tell, all of the major standard bolt threads are single-start. This includes: Unified Standard (UNC, etc.) National Pipe Thread (NPT, NPS) British Standard I only found one standard thread that can also come in a multiple-starts: ACME . What are the reasons why single-start threads are so common and multiple-start threads are rare? I am specifically interested in bolts and other fasteners.

If the receiver does not detect the sub-carrier for the "colour burst" signal which is transmitted during the horizontal blanking period the receiver switches on the "colour-killer" circuit so the set reverts to black and white mode. The colour-burst signal - 8 to 10 cycles of 3.85 MHz - is unlikely to be generated by random noise. Figure 1. The colorburst signal is transmitted on the "back porch" between the horizontal blanking pulse and the start of that line's luminance signal. The colorburst signal is used to synchronise the QAM (quadrature amplitude modulation) oscillator which can hold its frequency accurately...

Biggest advantage is that when connecting to trailers, there are no bleeding issues. Imagine having to connect hydraulic pipes and remove the air bubbles... As for the amount of air - the compressor and receiving tanks are designed for normal use. However if you wish to accompany AC/DC with the air brakes you will run out. Disc brakes already exist in an airbrake version for trucks - came out over 10 years ago IIRC. But one big difference is that if you lose hydraulics on a car braking system then you lose stopping power (except for handbrake etc) but with...

As Dave Tweed points out, the ratio of torque to tension is lower the lower the lead angle is. Since the important measure of bolt tightness is generally the tension in the bolt, we want to achieve that minimum pretension with the least effort possible. Assuming we have to maintain a certain shear area of the thread (so the the threads are stronger than the bolt when fully engaged) having two starts means we double the lead angle and greatly increase the amount of force required in the wrench to tighten the fastener appropriately. On its own though, this isn't...

The problem is that the formula $P=I\ V$ is correct when dealing with DC circuits or with AC circuits where there is no lag between the current and the voltage. When dealing with realistic AC circuits, the power is given by $$ P=I\ V\ \cos(\phi), $$ where $\phi$ is the phase difference between the current and the voltage. The unit kVA is a unit of what is called 'apparent power' whereas W is a unit of 'real power'. Apparent power is the maximum possible power attainable when the current and voltage are in phase and real power is the actual...


Is interference between aircraft an issue for fly-by-wireless technology?

I was reading up on fly-by-wire development, and I saw a short section about fly-by-wireless technology. It seems like a great idea, with the potential to lower costs, weight and complexity. I can see a possible scenario where it could be an issue, though: Two aircraft are very close together (e.g. on a runway or flying in formation). One pilot transmits commands through the aircraft's fly-by-wire system to other parts of the aircraft. The other aircraft accidentally receives the signal because it is so close. Things get very bad very quickly. The thing is, I haven't been able to find any technical specifications regarding fly-by-wireless systems, and I have no idea if the transmission would be powerful enough to reach the other craft, nor if it would then be interpreted as actual data sent from that aircraft's pilot. Is this cross-interference between fly-by-wireless systems possible? If so, how can it be mitigated?

electrical-engineering aerospace-engineering emc telecommunication product-testing

Cross-interference between aircraft is a high unlikely event because all commercial aircraft designs have to pass DO-160 environmental testing requirements. Among the DO-160 testing specification is EMI/EMC Testing. These tests include Radiated Emission, Interference and Immunity Testing. Part of these tests are to answer " Two aircraft are very close together " and " The other aircraft accidentally receives the signal because it is so close. " Below is a picture of an anechoic chamber used to test aircraft. Fly-by-wire allows the aircraft control system to access and command monitoring and control systems. The monitoring and control systems have a...

As it happens, I just recently went through that calculation myself for a different site. Given the following facts from a quick web search, it isn't difficult to work out the numbers. The maximum efficiency of a (large) windmill is about 40%. The density of air is 1.225 kg/m 3 You need about 50 mW (10 mA at 5V) to light up an LED First, we'll need about 50 mW / 0.40 = 125 mW of air power flowing through the windmill to create the electricity we need (ignoring other factors such as the actual efficiency of a small windmill...

I think you are talking about roundabouts, not traffic circles. It is baffling to those of us in the UK that Americans think roundabouts are a new idea. In the UK we have so many variants, from mini-roundabouts all the way up to full motorway junctions (a giant roundabout above or below the motorway). So do roundabouts take up more space? Not necessarily, this is a mini roundabout: It's nothing more than a slightly domed area of paint on the road, no lights are necessary, you can actually drive straight over the top of it rather than around it, its...


How to calculate lever force when lever has uniformed distributed load?

We have a simple class 1 lever: $$\begin {array}{c} \text {5,000 kg} \\ \downarrow \, \downarrow \, \downarrow \, \downarrow \, \downarrow \, \downarrow \, \downarrow \, \downarrow \, \downarrow \, \downarrow \, \downarrow \, \downarrow \, \downarrow \, \downarrow \, \downarrow \, \downarrow \, \downarrow \, \downarrow \, \downarrow \, \downarrow \, \downarrow \, \downarrow \, \downarrow \\ ==================== \\ \hphantom {==} \triangle \hphantom {==============} \\ \vdash \text{1 m} \dashv \vdash \hphantom {======} \text{4 m} \hphantom {======} \dashv \\ \end {array} $$ The lever ($===$) is 5 m long. The fulcrum ($\triangle$) is 1 m from one end of the lever. The lever has a object sitting uniformly upon it weighing 5,000 kg. How do I compute the upward force that needs to be exerted at the end of the 1 m side of the lever to keep the lever stationary? $F = (W \times X)/L$ is simple when the weight is applied at the very end of the lever. But what happens if the weight is distributed along the lever? Our final goal is to tether the free end (on the 1m side) to keep the lever level and we need to know how strong the tether should be.

Answer: Yes , this is exactly how it is done in the real world. What you have described is what I do in my job to check systems in CAD. Since you indicated you would like me to step through my design process, I have detailed it below. Note that most of this does not involve CAD. CAD is invaluable, but only if you are prepared to get out the pencil and paper first. Also note that this is just my design process, it is by no means the only way to go about things. Preparation When I begin any...

Since the mass is 5k kg and the lever is 5m, this makes it quite easy to simplify because it is exactly 1k kg per m. The leftmost 2k kg (2m) of the mass has its center of mass exactly above the fulcrum so can be ignored as it provides no contribution to the moment. This leaves 3k kg (3m) spread from 1m to 4m on the right side. The center of mass will therefore be at 2.5m. Now it's super-simple, assuming you want the moment when the lever is level (i.e. when gravity is pulling straight down, perpendicular to...

OP injection molding tag is correct. OBall uses injection molding and plastic welding. The OBall is the invention of David E. Silverglate. Toy Ball Apparatus with Reduced Part Count Reduced image from Kids II . It consists of four identical, flat, injection molded, pentagon and hexagon shapes with circular (or elipitical) holes, which are shaped and plastically welded into spheres. Pentagon and hexagon edges are the same size and individual connected circles are only connected along one edge. The four shapes are clearly shown in colors above and from the patent. Solid lines on each part are hard connections, while...

In the video you've linked to, the spheres are seen on both the leading and trailing edges of the propeller: I expect they are intentional - there are a number of ways to attach a propeller without having to disturb that surface, or using flush caps. Cavitation is caused by a drop in pressure. This would be seen on the trailing edges of the propeller, and is worse on the outer edge of the propeller which is moving faster through water than the inner area. I doubt these spheres have any effect on cavitation at all. It is either a...