Q: A hose shoots water straight up to a height of 2.5 m. The opening end of the hose has an area of 0.75 cm^{2}. What is the speed of the water as it leaves the hose? How much water will come out in one minute?

Sol: Kinetic energy at bottom = Potential energy at the top

$\large \frac{1}{2} \rho v^2 = \rho g h $

$\large v = \sqrt{2 g h}$

$\large v = \sqrt{2 \times 9.8 \times 2.5 }$

v = 7 m/s

The rate of flow of water = Av.

So in one minute the volume of water that flows out

= Av × 60 = (0.75) × 700 × 60 = 0.75 × 42 × 10^{3}

= 3.15 × 10^{4} cm^{3} = 31.5 litre.