Question

A stream of water of density $\rho $ , cross-sectional area $A$ , and speed $u$ strikes a wall that is perpendicular to the direction of the stream, as shown in the figure below. The water then flows sideways across the wall. The force exerted by the stream on the wall is

• A. $\rho u^{2}A$
• B. $\rho u A / 2$
• C. $3\rho u^{2}A$
• D. $u^{2} A / \rho $

Answer 1

Answer: (A)

$F=\frac{dp}{dt}$
$F=\frac{d \left(mu\right)}{dt}=\frac{dm}{dt}u$
$\frac{dm}{dt}=\frac{d}{dt}\left(ρAx\right)=ρA\frac{dx}{dt}$
$=ρAu$
$F=\left(ρAu\right)u$
$F=ρAu^{2}$