Question

An intense stream of water of cross-sectional area A strikes a wall at an angle $\theta$ with the normal to the wall and returns back elastically. If the density of water is $\rho$ and its velocity is $v$, then the force exerted on the wall will be :

• A. 2$Av\rho \cos \theta$
• B. 2$A{v}^2\rho \cos \theta$
• C. 2 $A{v}^2\rho$
• D. 2$Av\rho$

Answer 1

The correct option is B 2$A{v}^2\rho \cos \theta$

Impulse on wall due to $"dm"$ mass of the water is:

$I=\Delta P=dmvcos\theta -(-dmvcos\theta )$

$I=\Delta P=2dmvcos\theta$

Force =$\frac{dI}{dt}=\frac{dp}{dt}=2vcos\theta \frac{dm}{dt}$

$F=2vcos\theta (\rho .A\frac{dx}{dt})=2\rho A{v}^{2}cos\theta .$