# Tag Info

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None of the interesting equations in physics can be derived from simpler principles, because if they could they wouldn't give any new information. That is, those simpler principles would already fully describe the system. Any new equation, whether it's the Navier-Stokes equations, Einstein's equations, the Schrodinger equation, or whatever, must be ...

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They are derivable from classical mechanics using either the continuum or molecular points of view. Starting with a continuum view, one applies conservation of mass, momentum, and energy to a control volume and the result is the Navier Stokes equations. The Navier Stokes equations, in the usual form, apply to Newtonian fluids, that is fluids whose stress ...

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I once asked Putterman after a similar colloquium what he meant by this statement, and his answer was "long time tails". Long time tails are fractional powers that appear in the long time behavior of correlation functions, see, for example, here and here. These fractional powers are seen in molecular dynamics (they are more difficult to see experimentally), ...

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Best answer is given from xkcd's what-if: https://what-if.xkcd.com/124/. It's not space, but it describes the fluid flow in lower gravity - such as how you could jump out of the pool just by performing aquadynamic maneuvers, or walk on the water. It is really a cool read. As mentioned in the xkcd article - diving and floating, being primarily about ...

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Of course, conservation laws for particle number, momentum, and energy follow directly from the classical equations of motion. However, by fluid dynamics we mean more than that. We mean that the conservation laws can be expressed in terms of coarse grained, hydrodynamic variables, such as the density, the energy density, and the fluid velocity. For example, ...

3

The glue used on plastic bottles is usually based on polyisobutylene or something similar to it. This has long hydrocarbon chains in it, and when the material is at equilibrium the polymer chains form a tangled network much like a mass of tangled wool. If you quickly stretch the polyisobutylene then the chains cannot untangle themselves because the ...

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The physical absurdity - or at least highly hyperbolic situations - of most of Roald Dahl's scenarios is the essential Dahl - it's wholesale a part of his humor and his lack compliance with physical laws is, in this respect, quite deliberate. Having said this, the "Great Big Greedy Nincompoop" disappearing up the tube is wholly possible, given the right ...

2

Water stops draining from the jar into the dispenser once it forms an interface as draining of more water would result into the formation of a vacuum in the jar because no air can rush into the jar to displace the water as it has an interfacial-lock. Consider the water level above interface $= h$, water level below interface $= x$ now $$P_{surface}= ... 2 YES. It can "Laminarize" the flow. And this will reduce the friction too. If I think adding infinite number of infinitely thin dividers, we are then actually reinforcing the fluid like concrete is reinforced with steel. In praxis we are actually just changing the viscosity of the fluid, which -obviously- makes it less turbulent. Study hydraulic ... 2 Stokes Law is not going to apply in this situation because the water flow around the ball will be turbulent not laminar. The way to see this is to calculate the Reynold's number. For a sphere this is approximately given by:$$ Re \approx \frac{\rho_wdv}{\mu} $$If we feed in \rho_w = 1000 kg/m^3, d = 0.00317 m, v = 37 m/s and \mu = 0.001 Pa.s ... 2 This is a classic example, often used in fluid dynamics classes, of Bernoulli's principle. This is the principle which underlies the Venturi effect: increasing the flow speed leads to a drop in pressure. The governing equation for an flow of an incompressible fluid such as water is$$\frac{V^2}{2} + gh + \frac{P}{\rho} = \mathrm{constant}$$To answer your ... 2 Major classes of drag:Two main factors of drag are friction and flow separation. This friction drag is dominant in streamlined shape and pressure drag (drag due to flow separation) is dominant in bluff body. Ways to reduce friction and pressure drag: Turbulent flow has more momentum than laminar flow so they reduces flow separation so pressure drag is ... 2 If you drop a bottle without any residual motion (that is, it is not spinning etc) then everything inside that bottle will be in "free fall". The air and the water will attempt to fall at the same rate. There is a nice video of what happens to water when it "spills" in the International Space Station: it becomes a "blob" because of the surface tension. Add ... 2 Contrary to popular misconception, below a specific temperature, glasses do not flow. At all. A glass by definition is a solid sans repeating crystalline structure. Anything which flows (see "pitch-drop experiment which drops every 80 (or something) years") is a liquid, however viscous. Liquid glasses tend to have reasonably high viscosity, but once ... 2 I would go for this: Imagine the bottom of the cup as a saw. The noise or chattering of the spoon jumping on the sawteeth is higher the faster spoon moves. Those "sawteeth" on the cup bottom are very small, but the principle is the same. Therefore the faster stirring the higher pitch. 2 By Archimedes principle, the upward buoyancy force the water exerts on an object is equal to the weight of the fluid displaced by that object. Regardless of how you cut an object, in order for the object to sink, the weight of that object must exceed the upward buoyancy force. This therefore means that the weight of the displaced water must be less than ... 2 As Mews says, Archimedes principle applies to any shape so you can't make an object sink just by changing its shape. If you're interested Floris gives a simple proof of Archimedes principle here. But let me suggest an alternative sort of proof by pointing out that if your idea worked you could use it to make a perpetual motion machine. Suppose you take some ... 1 While in general I agree with other answers, there is some subtlety here. If you put your pyramid on the bottom of the liquid, and both the bottom of the liquid and the base of the pyramid are smooth enough, so the water (for example) cannot get under the pyramid (hydrophobic surfaces can help), the pyramid will stay at the bottom. The same would be true for ... 1 Hydrostatic pressure inside a pool on earth is given by: p=ρgh +p_{atm}, (g: gravity, h: depth, ρ: fluid density, p_{atm}: atmospheric pressure) Assuming 0 gravity and no atmosphere, there would be no pressure. You would feel no pressure at all whether you are on the surface or in the center of the sphere. Also, you wouldn't be able to float to the ... 1 It should be noted that the Water freezes on surface, cause the density of the Water is highest at 4 degrees, which makes the 0-degree water to float on the top. 1. What would eventually happen to the running water in the canal? Typically the running water simply is mixed, which means that the whole water mass must be cooled (and even the earth below it) ... 1 You can get a somewhat similar effect in a pot of water if you bring the water to a boil and then turn the heat down a bit. Do it just right and you'll see bubbles of steam form at the bottom of the pot, separate from the bottom, start to rise, only to vanish partway up. There's a vertical temperature gradient in that pot of simmering water. The water bottom ... 1 Water transitions from liquid to vapor when it hits the boiling point. With a pot of water approaching boiling, you'll see (and hear) boiling begin as small bubbles across the bottom of the pan, where the water is locally at the boiling point. The bubbles collapse, depositing their heat energy, when they reach cooler (higher) areas of the water. As the ... 1 It seems that the exact exit conditions of a Vortex doesn't influence too much on the Vortex functionality. For example a Vater Vortex; it doesnt matter if you take the water out from the top, or from the bottom. The basical funcionality of the Vortex remains very much the same. Please look this film Secondary flows. in 1:20-2:55 and 11:00-12:00 as a ... 1 Could the phenomenon of vortex bursting be exploited to reduce wake turbulence? Well, it's the only way to get rid of the Turbelence. Turbulence is caused by vortexes and they obviously must burst, before they completely stop. My question is, what are the physical variables which promote or inhibit vortex bursting and, if they can be controlled, can this ... 1 It depends on the type of pump. For a positive displacement pump (pistons, for example) a fixed volume is pumped per rotation. Pump speed and flow rate are directly proportional over a wide range. Eventually suction tries to cause negative pressure and you don't have a all-liquid system anymore. Things get a bit more complicated for a impeller type pump. ... 1 The volumetric flow rate has to stay the same, because the same amount of water flows out of the tube as flows into it. The only way for the volumetric flow rate to change along the tube would be if there was a leak. Friction (i.e. viscous drag) can't change the volumetric flow rate, all it can do is change the pressure gradient along the tube. So you are ... 1 Yes the impellor can agitate the fluid. When dealing with fluid flow there are two things to consider: viscous forces and inertial forces. By setting the viscosity to zero you make all the viscous forces zero, but you would still have inertial forces. As your impellor blade (or whatever) rotates it pushes the liquid. Even though the viscosity of the liquid ... 1 It is an implicit function which you have to solve numerically. Typically you would use "fixed point iteration". You can do this in Excel with some user defined functions where for a given geometry you start with f=1 and then use the above \frac{1}{\sqrt{f}} = L(f) a few times until in converges to a value$$f \rightarrow \frac{1}{L^2(f)}  In my ...

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There is no difference between free fall and say an aircraft wing moving horizontally, as regards the air molecules closest to the surface. Friction between the surface and the air will still cause the air molecules closest to the surface to be essentially stationary. Take the Blackbird SR-71 spy plane , it stretches a significant amount because of heat ...

1

Giving a full answer would take long, but here are a few steps to help you. The easiest is probably to start from the result, eq. (11). Multiply by a vector test function and integrate it over a given volume $V(t)$ within the solid phase, which is advected by the velocity $w$. Replace $w(x,t)$ by its value, defined in (3) -- note that $x_G$ has for ...

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