The diagram shows a hydroelectric power station. The reservoir is linked to the turbines by a pipe of uniform cross-sectional area.

Question 32

The diagram shows a hydroelectric power station.

The reservoir is linked to the turbines by a pipe of uniform cross-sectional area.

Water flows from X to Y at constant speed. Which statement about the change of energy of the water as it moves from X to Y is correct?

From June 2015:

A It gains both gravitational potential energy and kinetic energy.

B It loses both elastic potential energy and kinetic energy.

C It loses both elastic potential energy and gravitational potential energy.

D It loses gravitational potential energy and gains elastic potential energy.

From November 2012:

A It gains both gravitational potential energy and kinetic energy.

B It loses gravitational potential energy and gains elastic potential energy.

C It loses gravitational potential energy and gains kinetic energy.

D It loses both elastic potential energy and gravitational potential energy.

Reference: Past Exam Paper – November 2012 Paper 13 Q21 & June 2017 Paper 12 Q16

Solution:

Answer: D. [referring to June 2015 options]
For Nov 2012 P13 Q21: Answer: B.

The water flows between X and Y at constant speed, so its kinetic energy does not increase. The loss of potential energy must be balanced by an increase in elastic potential energy.

X is at a higher position than Y – as the water moves from X to Y, it is losing gravitational potential energy (E_P = mgh). [A is incorrect – referring to June 2015 options]

The kinetic energy of the water cannot increase as the pipe is sealed and full of water, and it is stated that the water flows at constant rate along the pipe. This means that its speed is constant, and hence its kinetic energy is constant (E_K = ½ mv²). [A is incorrect – referring to June 2015 options]

The water is gaining elastic potential energy as its pressure increases between X and Y. The pressure at any point in the pipe depends on the length of the column of liquid ABOVE that point. From the diagram, it can be observed that there are more water above point Y than above point X. This means that the pressure at Y is greater than at X.

Under normal conditions, we can assume that water cannot be compressed. However water may be compressed under very high pressure, as in this case. (Note that water also contains some air and so, can be compressed.) The molecules get closer to each other under the high pressure. Any object that is being compressed has elastic potential energy.

Choice B goes against the law of conservation of energy. [referring to June 2015 options]