Question

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

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

Answer 1

Hint: Remember the formulae of gravitational potential energy, elastic potential energy, and kinetic energy. Use those formulae to find out the factors that influence these energies, and check for any change in those factors. Then choose the right option accordingly.

Complete step by step solution:
The figure shows that X is at a higher position than Y. Thus, as water moves from X to Y, its height decreases and it is losing gravitational potential energy.
The kinetic energy of the water is going to remain constant. This is because the pipe is sealed and full of water. It is stated that the water flows at a constant rate. Thus, its speed is constant, and its kinetic energy will remain unchanged.
Since the pressure increases between X and Y, the water is gaining elastic potential energy.
By the above reasons, we can conclude that options A, B, and C are incorrect.
Hence, option D is the correct answer.

Note:
Gravitational Potential Energy is only affected by the height and the mass of an object at a given moment. In most cases, the mass of an object doesn’t increase. In this question, the gravitational potential energy was determined by height.
Normally, as Gravitational Potential Energy of an object decreases, its Kinetic Energy increases, due to the law of conservation of Energy.
Elastic Potential Energy varies with the pressure being applied.