Answer to Question #174501 in Physics for Sumeya Musa

Question

If a basement sump pump can empty a 5.0 gallon basin (approximately 19 kg) of water in 4.5 seconds and send the water out of a house through an outlet pipe 2.5 meter above the basin, how many watts must the pump motor minimally be rated at? (Assume frictionless pipes!) How many horse power is that?

Answer 1

Find the potential energy the water acquires:

$$E=mgh.$$

The work required to lift this mass of water:

$$W=\Delta E=E_f-E_i=E-0=E=mgh.$$

The power is how quickly the work can be done:

$$P=\frac Wt=\frac Et=\frac{mgh}{t},\\\space\\ P=\frac{19·9.8·2.5}{4.5}=103\text{ W}.$$

This is equivalent to 0.138 hp because 1 watt is 0.00134 horse power.