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?

Question

Consider water fl owing by gravity through a short pipe
connecting two reservoirs whose surface levels differ by an
amount D z . Why does the incompressible frictionless Bernoulli
equation lead to an absurdity when the fl ow rate
through the pipe is computed? Does the paradox have
something to do with the length of the short pipe? Does the
paradox disappear if we round the entrance and exit edges
of the pipe?

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Fluid Mechanics

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