Consider water fl owing by gravity through a short pipeconnecting two reservoirs whose surface levels differ by anamount D z . Why does the incompressible frictionless Bernoulliequation lead to an absurdity when the fl ow ratethrough the pipe is computed? Does the paradox havesomething to do with the length of the short pipe? Does theparadox disappear if we round the entrance and exit edgesof the pipe?

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Fluid Dynamics

The study of the flow of gases and liquids, usually in and around solid surfaces, is known as fluid dynamics in physics and engineering. Fluid dynamics, for example, can be used to evaluate the movement of air through an airplane wing or the surface of a vehicle. It can also be used in ship design to increase the speed at which ships pass through water.