The discharge of liquids from vertical tubes with various contraction geometries was studied via the unsteady Bernoulli equation. The temporal variations of the exit velocity and fluid level in the tube were found from the numerical integration of nonlinear differential equations. Sudden, quadratic, and exponential contraction geometries were considered. For inlet to exit area ratios greater than two, the flow initially accelerates to a maximum speed and then it decelerates for the geometries studied. The exponential contraction has the shortest discharge time. The solutions also reveal that the largest possible velocity and the shortest discharge time are achieved in a non-converging tube.


Mechanical Engineering



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