Question

Hydroelectric power plants convert the gravitational potential energy of falling water into electrical power, typically by allowing the water to flow through a pipe called a penstock to rotate a generator located below it. Let the bottom of the penstock be the origin of a Cartesian coordinate system and the point at which the gravitational potential energy is zero.

a) Consider a penstock that is vertical and has a height of h = 61 m. How long, t in seconds, does it take water to fall from the top of the penstock to the bottom? Assume the water starts at rest.

Answer 1

3.527 seconds

Step-by-step explanation:

The height of the falling water, assuming no friction or air resistance, is given by ...

h(t) = -(1/2)gt² +61

where g is the standard gravity value, 9.80665 m/s².

The the time required for h(t) = 0 is ...

1/2gt² = 61

t² = 2·61/g

t = √(2·61/9.80665) ≈ 3.527 . . . . seconds