If a pump raises 650 tonnes of sea water a height of 55 m in 6 hours, what is the power required to drive the pump at 100% efficiency?

To determine the power required to drive the pump at 100% efficiency, we can use the formula for power, which is calculated as the work done over time. In this case, the work done is equal to the gravitational potential energy gained by the sea water when lifted to a height.

The formula for gravitational potential energy is given by:

[ \text{Work} = mgh ]

where:

• ( m ) is the mass (in kg),

• ( g ) is the acceleration due to gravity (approximately ( 9.81 , \text{m/s}^2 )),

• ( h ) is the height (in meters).

Given:

• The mass of the sea water is 650 tonnes, which is equivalent to 650,000 kg (since 1 tonne = 1,000 kg).

• The height ( h ) is 55 m.

Now we calculate the work done:

[ \text{Work} = 650,000 , \text{kg} \times 9.81 , \text{m/s}^2 \times 55 , \text{m} ]

Calculating this gives:

[ \text{Work} = 650