Question

A hose ejects water at 80cl/s through a hole 2mm in diameter. The water impinged on a wall and drops off without rebounding. What is the force on the wall?

Answer 1

$$F= \frac{d(mv)}{dt}= v\frac{d(m)}{dt}=v\frac{d(\rho V)}{dt}=v\rho \frac{dV}{dt}$$

$$\frac{dV}{dt}=\frac{d(As)}{dt}= A \frac{ds}{dt}=Av=(0.25\pi d^2)v$$

$$F=\frac{4\rho (\frac{dV}{dt})^2}{\pi d^2}=\frac{4(1000)(0.0008)^2}{\pi (0.002 )^2}=200N$$