The diagram shows a pump called a hydraulic ram. In one such pump the long approach pipe holds 500 kg of water.

Question 10

The diagram shows a pump called a hydraulic ram.

In one such pump the long approach pipe holds 500 kg of water. A valve shuts when the speed of this water reaches 2.0 m s^-1 and the kinetic energy of this water is used to lift a small quantity of water by a height of 15 m.

The efficiency of the pump is 10%.

Which mass of water could be lifted 15 m?

A 0.15 kg                     B 0.68 kg                     C 1.5 kg                      D 6.8 kg

Reference: Past Exam Paper – June 2015 Paper 11 Q18

Solution:

Answer: B.

This question is on the conservation of energy. Energy is being transformed from one form to another.

The kinetic energy of the water is being converted into gravitational potential energy of the water.

However, since the efficiency of the pump is only 10%, only 10% of the kinetic energy is converted into GPE.

10 % of Kinetic energy of water = GPE of water lifted

0.10 × ½ × m × v² = m_l g h     where m_l is the mass of water lifted

0.10 × ½ × 500 × 2² = m_l × 9.81 × 15 

m_l = (0.10 × ½ × 500 × 2²) / (9.81 × 15) = 0.68 kg