EnergySmart School Inventors

Miniature Hydroelectric Power Plant

Prologue:

Engineer L.A. Pelton started developing what is now known as the Pelton wheel in 1881. The first wheel was sold in 1884. In contests against other wheels of the time, the Pelton was the most efficient, extracting the most power from a given water source. The Pelton Water-Wheel Company was founded in 1888 in San Francisco and produced wheels up into the 1920s.

The purpose of the nozzle feeding water to a Pelton wheel is to convert the water's pressure into velocity. A Pelton wheel wants fast-moving water.

The Pelton wheel has buckets around its outside. The purpose of a bucket is to reverse the direction of the water jet coming out of the nozzle and hitting the bucket. In other words, the bucket makes the water do a U-turn.

In this way, the water hitting the bucket is somewhat like a light-weight rubber ball bouncing off of a heavy object where the ball represents the water and the heavy object represents the bucket.

How fast should the bucket move to recover all the energy in the jet of water that comes from the nozzle?

In Figure 1, we see that if the heavy object (bucket) is not moving, the ball (water jet) reverses direction but it loses no speed. If it loses no speed, then it hasn't given its energy to the heavy object.

Figure 1.

In Figure 2, we see the heavy object moving the same speed as the ball. Since the ball's speed is not changed, it again hasn't given its energy to the heavy object.

Figure 2.

In Figure 3, we see the heavy object moving half as fast as the ball. Now the ball hits the object at half speed (relative to the object), and when it bounces off, it is still going half speed relative to the object, but in the opposite direction. This speed is zero speed relative to us, so the rubber ball has given up all of its energy (relative to us). The energy added to the heavy object would normally make it go faster, but the generator immediately takes that energy away from the Pelton wheel and uses it to make electricity.

Figure 3. When the closing velocity is half the ball's restframe velocity, the ball's velocity after impact is zero. All of the ball's energy has been added to the block's energy.