Question

To approximate the speed of the current of a river, a circular paddle wheel with radius6 feet is lowered into the water. If the current causes the wheel to rotate at a speed of 15revolutions per minute, what is the speed of the current?

Answer 1

Given,

The radius of the wheel, r=6 ft=1.83 m

The angular speed of the wheel, ω=15 rev/min=1.57 rad/s

The speed of the current will be equal to the linear speed of the wheel.

The linear speed of the wheel is given by,

`v=r\omega`

On substituting the known values,

`\begin{gathered} v=1.83*1.57 \\ =2.87\text{ m/s} \end{gathered}`

Thus the speed of the river currents is 2.87 m/s