## Drag Force When Flow is Turbulent

The drag force acting on an object moving through a fluid depends on whether the flow is smooth or turbulent.

If the flow is smooth, the drag force is proportional to the relative speedof object and fluid.

(1)

whereis the drag coefficient. Stoke's Lawis an example of this.

The flow is smooth when the speedis small. Ifincreases, the flow becomes turbulent. At higher speed, the drag force depends on

(2)

This means that at higher speeds the drag force increases very rapidly.

Both of these expressions are approximations. The drag force may be more accurately described as a sum of expressions (1) and (2).

At higher speeds still, even this expression becomes inadequate, and higher powers ofmust be taken into account.

In general the coefficientsare decreasing, so that each term becomes important only as increases sufficiently.