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An ideal gas or near-ideal gas such as air at about atmospheric pressure and room temperature has a bulk modulus which is the same as its pressure. That can be readily confirmed by taking the ideal gas equation $PV=nRT$ and substituting it into the equation for the bulk modulus $B=-V \frac{dP}{dV}$. Now for what P-V equations-of-state does the bulk modulus ...


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Concerning your wording "force is transmitted (and maybe decreases because of loss of energy)" - no, no, the decrease of force is not easily connected to the loss of energy. Force can be decreased because there is friction, but this does not imply a loss of energy (not if nothing moves). And also energy can be lost (plastic deformation of the rope) without a ...


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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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Your approach is along the right lines and you need to make use that $dp = \rho(z) \, g \, dz$ and use the relationship between pressure, volume and temperature for n moles of gas as $P V = n R T$, so that $P = \frac{n}{V} R T = \rho R T$, with $\rho$ the density. If you assume that the temperature of the atmosphere is uniform then the pressure varies as ...


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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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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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This has nothing to do with air pressure since the air pressure is exactly the same at all of the holes (including the top one). Regarding pressure only differences can cause stuff to move, the absolute pressure is only relevant for density and such. The concept you should read more about is called hydrostatic pressure and given by a very simple formula. ...


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A and C are not identical; that's where the thought experiment breaks down. Consider the pressure in the fluids around the opening between the long thin neck section and the wide base section. In C, you have one continuous fluid, and the pressure is the same both above and below the neck (and equal to $\rho g h$ where $h$ is the height of the next and ...


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If the pressure is uniform, there is no problem, because you just multiply the pressure by the total surface area of interest. However, if the pressure is varying on the surface, pressure should be regarded as a point function of location, and the contribution to the total force on the surface at a differential element of area on the surface dA is equal to ...


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A self-contained, careful derivation of (4.10): We consider a thermodynamic system whose state can be characterized by the macroscopic variables $(S, V, N)$, then starting with the fundamental relationship $\mathrm dU = T\,\mathrm dS -P\,\mathrm dV + \mu\,\mathrm dN$, and noting that $\beta = 1/(k T)$, one can deduce the following useful expression for the ...


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I think you misunderstand the definitions. The critical temperature is the temperature above which no amount of pressure will cause a gas to liquefy. The critical pressure is the pressure which will cause a gas to liquefy at its critical temperature. A supercritical fluid is another state of matter. A liquid and a gas phase have been subjected to ...


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Before valve-A is opened, the pressure in the tube is atm. Pressure since the top of the tube is opened. When the valve-A is opened, assumed instantaneously, the water will rush into the tube at: $$V = \sqrt{2gh}$$ where: $g$ = gravitation const (32.2 ft per sec per sec.), $h = 100\ \mathrm m$ = Height from bottom of tube to tank ...


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The real answer is quite complex; I think we should break it into a couple of different pieces. First - the static case. If you submerge an open pipe into water, the pressure inside and outside will be the same at a given height, and the water level inside the tube will settle at the same height as outside. If you add the effect of surface tension, it is ...


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The other answer that wrote earlier was wrong. Although there will be an unbalanced force, but due to restriction in movement, the pistons cannot move to the right. $$F_1 = A_1P_{atm}$$ $$F_2 = A_2P_{atm}$$ $$A_1 > A_2 \implies \ F_1 > F_2$$



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