A U shaped pipe with a uniform circular cross-section of area A is half submerge

Question

A U shaped pipe with a uniform circular cross-section of area A is half submerged in a tank of water and is traveling to the left as shown below with a constant velocity V. v = 5 ft/sec A = 4 inch2 p atm = 2100 lb/ft2 rho = 2 slugs/ft3 As the pipe scoops water from the tank it is ejected to the left out of the pipe. Compute the final velocity of the ejected water with respect to the tank. Also compute the force necessary to keep the pipe soving with a constant velocity V. (Assume inviscid flow and neglect body forces.)

Explanation / Answer

The velocity of the pipe flow equals V, from the conservation of mass.

Ignore gravity and without visccous fore, the pressure at the inlet equals the pressure at the exit, which is patm (this can be obtained from bernoulli equation).

Fx = R = (QV)out - (QV)in = (AV)(-V) - (AV)(V) = -2AV2

R = -2(2)(4/122)(52) = -2.78 lb

or R = 2.78 lb (leftward)

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