First slide

Fluid dynamics

Question

A liquid of density ρ comes out with a velocity V from a horizontal tube of area of cross - section A fitted at the bottom of a large tank. The reaction force exerted by the liquid on the tube is F.
a) F $\propto$ V b) F $\propto$ V²c) F $\propto$ A d) F $\propto$ ρ

Easy

A

a and b are correct
B

b,c and d are correct
C

a, c and d are correct
D

All are correct

Solution

Since the tank is large, velocity of liquid just before entering the pipe is zero. Rate of volume flow, Q=AV. Rate of mass flow m =ρAV. Rate of flow of momentum of the liquid just after entering the pipe, p_f = mV = ρAV². Rate of flow of momentum of liquid just before entering the pipe, p_i = 0
$∴$ Force exerted by the walls of the pipe on the liquid = p_f - p_i = ρAV². By Newton's Third Law of motion, magnitude of force exerted by the liquid on the pipe = ρAV²

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