Question

A tube of uniform cross-section $A$ is bent to form a circular arc of radius $R$, forming three quarters of a circle. A liquid of density $\rho$ is forced through the tube with a linear speed $v$ as shown in the figure. Find the net force exerted by the liquid on the tube.

Answer 1

Cross section A

Circular radius$=R$

Liquid of density $=\rho$

Linear speed$=V$

Net force exerted by the liquid on the tube$=?$

Change in momentum of the liquid$=m{v}^2=density\times volume$

$m=d\times A\times Hm=\left(\rho \right)A\frac{3}{4}\left(2\pi R\right)$

Therefore,

$F=\frac{changeinmomentum}{changeintime}F=\frac{\sqrt{2\pi R+\frac{3}{4}\left(\rho \right)A{V}^2}}{\frac{3}{4}2\pi R/V}F=\frac{1}{\sqrt{3}}\rho A{V}^2$