Question

What is the relationship between height and gravitational potential energy of water behind a dam?

Water is contained in a tidal basin behind a dam. The water has a depth h at high tide and zero at low tide. The gravitational potential energy of the water stored in the basin between a high tide and a low tide is proportional to

1. h^(1/2)
2. h
3. h^2
4. h^3

Answer 1

3.
`h^2`

Step-by-step explanation:

Energy of volume contained in a dam is given by

`E=(1)/(2)A\rho gh^2`

where,

A = Horizontal surface area of the barrage

`\rho` = Density of water

g = Acceleration due to gravity = 9.81 m/s²

h = Vertical tidal range,

It can be seen that

`E\propto h^2`

Hence, the energy is proportional to
`h^2`