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For a single-component fluid, the conservation of mass follows $$ \left(\begin{array}{c}\text{mass of fluid } \\ \text{in volume }\Delta V\end{array}\right)=\left(\begin{array}{c}\text{flux of fluid } \\ \text{in/out of volume }\Delta V\end{array}\right)+\left(\begin{array}{c}\text{sources or} \\ \text{sinks in }\Delta V\end{array}\right) $$ In terms of a ...


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Speed of sound in water at 20 degrees Celsius is 1482 m/s., (2881 knots), just for comparison to current claimed achievable speeds. Small related fact: The pistol shrimp can create sonoluminescent cavitation bubbles that reach up to 5,000 K (4,700 °C) which are as loud as 218 decibels, breaking the sound barrier in water. Says Wikipedia YouTube video of ...


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The reason that the speed of sound is a well-defined quantity is that, for small pertubations, the equations which govern the fluid dynamics can be linearised. In that linearised form, the solution boils down to a simple wave ansatz with linear dispersion relation, i.e. constant velocity.Those are the sound waves. It so happens that in air, this linear ...


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Some dimensions I was able to dig up (mostly from Wikipedia). Draft of the Allure of the Seas: 31 ft (10 m) Length: 1181 ft (360 m) Beam at waterline: 47 m Height: 72 m above waterline Let's just draw the section based on these simple numbers: Now if the center of gravity were in the middle of the ship (31 m above the water line), it would indeed not be ...


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The method you are looking for is called corner transport upwind (CTU) (Google search). Typically, we get the finite difference schemes via Taylor expansion, keeping 1st order terms and ignoring the rest (as either small, or naturally via subtraction a la central difference). The CTU scheme keeps these 2nd order terms, so the expansion is \begin{align} ...


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Q: When we write that, do we suppose a collisionless or collisional nature of the fluids? A: It's the energy-momentum tensor for a perfect fluid Chapter 2.26 Q: If this description corresponds to collisional fluids, why cosmological simulations are N-body simulations (collisionless) and are not simply based on hydrodynamics? A: Cosmological simulations are ...


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An interesting limitation aside from the obvious practical ones being overlooked, is that eventually you would be moving quickly enough to bond your carbon atoms with oxygen in the air. If we put a lower limit of around 750 degrees F or about 673 Kelvin to start that fire, then you would have to move at about 1,300 meters per second.


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If the window is open just a crack, and then you open it wider, you expect this to make a difference. As the window gets larger the difference becomes less significant - and depends on whether it is diffusion or convection that is cause the cooling of air. Diffusion (no wind) depends directly on surface area: twice the area, twice the diffusion. For ...


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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 ...


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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 ...


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You are right, the two explanations are not mutually contradictory. There are two ways of caluclation the lift on an airplane. You can look at the total mass of air being deflected downward by the wing, and equate the rate of change of momentum of the air to the upward force on the airplane. This is exactly what is going on, and for my money it is the real ...


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Cavitation inception occurs when the local pressure is less than the vapour pressure of the liquid. In effect the liquid locally boils to form a bubble of vapour. But producing the pressure gradients required to boil the liquid require a non-zero stress, or more precisely the viscous stress tensor has to be non-zero. In a superfluid the stress is always ...


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I doubt it is all fluid dynamics. The have to stay upright even with dead engines. If the integral of the lever below the water line is bigger than above then it should stay upright. Ballast at the bottom goes a long way as it has a long lever. Stuff like engines below deck tends to be heavy anyway. Weight is not a big deal as they are not going up ...


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Depends on the Reynolds number. Stokes can be used for purely laminar flow. Complete answer to be found here.


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We know the general cause for turbulence: it is that inertial effects (mass wanting to keep going in the direction that it's going) grow so large that viscous effects cannot contain the system in the laminar flow regime anymore. When those viscous effects cannot slow down a whole chunk of fluid, they are forces acting off-center on a mass: hence they create ...


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So it's actually a really simple reason, but you're going to have to think a little bit about what's going on. The transport equation states that everything which is a "stuff" can be viewed in this way: "A small box flows downstream; the time rate of change of the stuff inside of the box is equal to the flow of stuff through the boundary of the box, plus ...


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I left this as a comment but I'll expand it here since it provides another viewpoint. Imagine you have a box of gas molecules bouncing around in them. Every molecule is identical so they have the same mass, temperature and pressure. Let's also say this box has a diaphragm in the middle separating the box into two. You now remove the diaphragm and start ...


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In the end this is physics, so maybe you should try it less formal? (and not confuse eulerian and langrangian methods) Initially the mass element at $a$ had mass ( I use $\delta$ to make clear that we really should consider finite differences and then perform a limit at the end) $$m = \rho(a,0) \delta a$$ now, we follow its motion and after some time t we ...


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According to the wiki page the 747 has a max takeoff "weight" of about 350,000 kg (depending on the model) and a wing surface of about 500 m2. That means that a force of 3.5 MN must be carried by 5 million square cm, or 0.7 N per square cm. If you can somehow split this evenly between the top and bottom surface, then you need to come up with a paper surface ...


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If you are above the water you will get accelerated down until the weight of the water you disperse is equal to your own weight (calling this level $x$). As soon as you are completely submerged the gravitational force downwards will be $\rho Vg$ and by Archimedes principle the force upwards will be $\rho_w V g$, where $\rho$ is your density, $V$ is your ...


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Mythbusters covered this one. They found significant fuel saving at constant speed. Assuming their findings are correct I can only guess that the technique is not used for cosmetic reasons ie few people would want to drive a car that looks like it has been in multiple accidents and covered in dents


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After you drain 4 liters, you have 3 liters old fluid left. When you add 4 new liters to make 7, you have a mix that is 3/7 old fluid, or 43% old fluid. If you repeat that, you wind up with a mix that is 3/7 old mix, where the old mix is 3/7 old fluid. 3/7 of 3/7 is $(3/7)^2$ = 18%. After 3 changes, you get 3/7 or 3/7 of 3/7 old fluid, or $(3/7)^3$ = 8%. ...


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There are lots of tried and tested methods for visualising flows, for example mica or aluminium flakes though these tend to settle fairly quickly. In days gone by I used zirconium phosphate that had been delaminated by titrating with tetramethyl ammonia. This gives very thin flakes that are stable to sedimentation for a day or so, though you have to prepare ...


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The liquid shooting upward from the pit of your vortex may be explained by at least two effects. The first effect was indirectly addressed by Albert Einstein in a 1926 paper he wrote on the erosion of river banks (http://people.ucalgary.ca/~kmuldrew/river.html). This effect is also called the tea leaves paradox, from an experiment Einstein performed in a ...


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An equivalent Ohms law can be applied to gas flow and pressure drop, but only for particular mechanical flow restrictions and limited to a range of flow. But more generally for orifices and tubes the relationship between pressure and flow is quadratic, explained predominantly by the energy equation for flow, also known as Bernoulli's equation. In the ...


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The Venturi effect is not specific to fluid flow in pipes but rather flow of fluid in general. The basis of the effect comes from the Bernoulli equation which accounts for the energy in a flowstream. Fluid which moves with a high velocity has high kinetic energy derived from a potential (pressure) energy. It's both the conservation and conversion of energy ...


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Conservation of energy is exactly how the venturi effect arises. In an incompressible fluid, conservation of energy states that $E = E_k + E_{p,pressure} + E_{p,gravity} = \frac{1}{2} mv^2 + PV + mgz = constant$ by dividing each term with volume, it becomes the Bernoulli Principle: $\frac{1}{2} \rho v^2 + P_{static} + \rho gz = anotherConstant$ So, how ...


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As posed there is no definite answer to your question. It is certainly possible for water to enter the well at a depth of 100 feet, and have sufficient pressure that it eventually rises to within 15 feet of the top. That just means that the "water table" in that area is 15 feet below the surface. If the sides of your well are reasonably well sealed so only ...


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Nice argument, Why opening windows in early morning reduces temperature? Every human body need energy to survive, That energy is covered into heat while doing work or for the operation of internal organs. For example carbohydrate in our body burns with oxygen and give heat and carbon-DI-oxide. If we do not open the windows , that heat will stagnate ...


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On the water-splash, here's a video that I think explains what happened. https://www.youtube.com/watch?v=2UHS883_P60 (the 3 balls, not the double bounce on the trampoline). The Newton law of conservation of energy says that energy is concerved, so a share of the energy of the drop transfers to the energy of the splash. Figure you drop it from 1/2 ...



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