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 cm2…

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 cm2. 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 × 103

= 3.15 × 104 cm3 = 31.5 litre.