Question

A flat plate moves normally with a speed $v_1$ towards a horizontal jet of water of uniform area of cross section.The jet discharges water at the rate of volume $Vpersecond$ at a speed of $v_2$.The density of water is $\rho$. Assume that water splashes along the surface of the plate at right angles to the original motion.The magnitude of the force acting on the plate due to jet of water is:

• A. $\rho V{v}_1$
• B. $\rho (\frac{V}{v_2}){(v_1+v_2)}^2$
• C. $\frac{\rho V}{v_1+v_2}{v}_1^2$
• D. $\rho V(v_1+v_2)$

Answer 1

Answer: (D)

$\rho V(v_1+v_2)$

$F=\frac{\Delta p}{\Delta t}=\frac{m(v_1+v_2)}{\Delta t}$

$\rho =\frac{m}{V}$

$m=\rho V$

$F=\rho V(v_1+v_2)$ (Since, $V$ is in $persecond$)