Question

An engine pumps water continuously through a hose pipe. If the water leaves the pipe with velocity $v$ and $m$ is the mass per unit length of the water in the pipe, then the rate at which kinetic energy is imparted to the water is:

• A. $\frac{1}{2} m v^3$
• B. $\frac{1}{2} m v^2$
• C. $m v^3$
• D. $\frac{3}{2} m v^2$

Hint:

Power can be represented as $F \cdot v$. The thrust force on a pipe discharging fluid is $F = v \frac{dM}{dt} = m v^2$. Thus, Power $= F \cdot v = (m v^2) v = m v^3$. However, only half of this work goes into the water's kinetic energy, yielding $\frac{1}{2} m v^3$.

Answer 1

The Correct Option is A