A pump lifts 200 litres of water per minute to height 10m — find power

Question

A pump lifts 200 litres of water per minute to a height of 10 m. Calculate the power of the pump. (Take $g = 10\text{ m/s}^2$, density of water = $1000\text{ kg/m}^3$.)

Solution — Step by Step

Why This Works

Power measures the rate of doing work. The pump continuously converts electrical energy into mechanical (potential) energy of the water. The faster you want to lift a given mass, the more power you need.

The formula $P = W/t = mgh/t$ can also be written as $P = \dot{m}gh$, where $\dot{m}$ is the mass flow rate (kg/s). Here $\dot{m} = 200/60 \approx 3.33\text{ kg/s}$, so $P = 3.33 \times 10 \times 10 = 333\text{ W}$ — same answer, cleaner for pipe-flow problems.

Alternative Method

Convert units first before calculating work:

Mass flow rate: $\dot{m} = \frac{200\text{ kg}}{60\text{ s}} = \frac{10}{3}\text{ kg/s}$

This approach directly gives power without calculating total work first — useful when the problem gives a flow rate rather than a total amount.

Common Mistake