Lectures on Physics has been derived from Benjamin Crowell's Light and Matter series of free introductory textbooks on physics. See the editorial for more information....

# A Turbine

In a hydroelectric plant, water flowing over a dam drives a turbine, which runs a generator to make electric power. The figure shows a simplified physical model of the water hitting the turbine, in which it is assumed that the stream of water comes in at a 45 °angle with respect to the turbine blade, and bounces off at a 90 °angle at nearly the same speed. The water flows at a rate R, in units of kg/s, and the speed of the water is v. What are the magnitude and direction of the water's force on the turbine?

In a time interval Δt, the mass of water that strikes the blade is RΔt, and the magnitude of its initial momentum is mv = vRΔt. The water's final momentum vector is of the same magnitude, but in the perpendicular direction. By Newton's third law, the water's force on the blade is equal and opposite to the blade's force on the water. Since the force is constant, we can use the equation

Choosing the x axis to be to the right and the y axis to be up, this can be broken down into components as

and

The water's force on the blade thus has components