Question

A horizontal tube of uniform cross-sectional area $A$ is bent in the form of U as shown in figure. If the liquid of density p enters and leaves the tube with velocity $v,$ then the external force $F$ required to hold the bend stationary is

• A. $F=0$
• B. $\rho A{v}^2$
• C. $2\rho A{v}^2$
• D. $\frac{1}{2}\rho A{v}^2$

Answer 1

The correct option is C $2\rho A{v}^2$

$F=\frac{\Delta p}{\Delta t}=\left(\frac{\Delta m}{\Delta t}\right)\left(\Delta v\right)$
$=\rho \left(\frac{\Delta V}{\Delta t}\right)\left(2v\right)$
$=\rho \left(Av\right)\left(2v\right)=2\rho A{v}^2$