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As mentioned by @Chester, Bernoulli isn't a good approximation for viscous flows which blood flow is. Instead you should use the Hagen-Poiseuille law which relates the average volumetric flowrate and the pressure gradient in the pipe. From it we find that the flowrate $Q$ is proportional to: $$Q \propto R^4 \Gamma$$ where $R$ is the radius of the pipe and ...


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The Bernoulli equation is a good approximation only if viscous flow resistance is not important. In blood flow through arteries, veins and (particularly) capillaries, viscous flow resistance is very important.


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I am not sure if the same laws apply to the heart as that of mechanical pump, but for a given flow rate, say X gallons per minute, the mechanical pump must develop a pressure P to overcome pipe friction and any other force trying to retard flow. If the pipe in a system is reduced in size, to pump the same flow rate a higher pressure will be required. The ...


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Because the sound is slowed down (or likewise sped up) only in the direction of flow. So in order to subtract (or add) the speed of sound and the speed of the media, both quantities need to be in the same direction. The cosine gives you the component of sound velocity in the flow direction. BTW time of flight is only one part of the equation to determine ...


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Let x be the instantaneous mass fraction of original water remaining in the lake at time t, w be the mass recharge/discharge rate, and M be the total mass of water in the lake (assumed constant). Also assume that the water in the lake is well-mixed. Then, for a mass balance on the original water, we have: ...


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Seventeen months later, I found the answer. What I described in the question is called choked flow. It means that, in the choke, fluid speed must be supersonic in order to "cut" disturbances coming from downstream. Ergo, fluid speed doesn't need to be supersonic in the entire pipeline. Also, it is achieved only for pure gas or multiphase (oil + gas) flow, ...


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A compression shock at subsonic flight speed only occurs when a supersonic pocket of air collapses downstream. Neither of your options is correct, and in that shock the speed drops from mildly supersonic (typically Mach 1.25) to the inverse of that Mach number (that would then be typically Mach 0.8). Acceleration into the supersonic regime is smooth and ...


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Bernoulli's equation, in the form you are applying it, ignores all friction in the pipe. That friction manifests itself as a pressure loss as given by the Darcy-Weisbach equation. If that pressure loss is called $\Delta P$ then the Bernoulli equation in your situation becomes simply: $$\Delta P=\rho gl$$ From it, using the pipe's characteristics and ...


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only if tenperatur is not 0K, any moleculus will move randomly ,it is so called thermal motion. when all moleculus is in one close capacity, they move to herr and there, so what you see is they are always uniform, since you open the capacity, it is obvious that they will move out


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See a vacuum chamber has no air inside it. So that is a low pressure region. But the capillary tube contains some pressure exerted by the air molecules on the walls of the tube. The fluid flows from a high pressure region to a low pressure region. So the air molecules spread out into the vacuum chamber filling the empty spaces. This continues as long until ...


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The battery sets up an electric field in the external circuit which all the mobile electrons feel in all the external circuit. This means that there is a force on all the mobile electrons in the external circuit. So these mobile electrons are accelerated by the electric field and gain kinetic energy from the electric field which is maintained by the battery. ...


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The electron gains potential energy in the battery; this is transformed to kinetic energy, which from time to time gets dissipated in the inelastic collisions with the lattice. It's quite analogous to a (semi-elastic) ball jumping down some stairs (and then, in the battery, taking the elevator to get up again). This might be more intuitive.


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A prop is actually a wing. If you've seen the shock wave of a supersonic jet you see how it actually comes at a higher degree away from the aircraft wing, like a 45+ degree angle. It seems like it would just flow along side the jet,but it's like trying to push too much water out of a dam, if the opening is too small the pressure of all the force balls up. ...



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