Viscosity and Turbulence (Problem 95)

A skydiver will reach a terminal velocity when the air drag equals their weight. For a skydiver with a large body, turbulence is a factor at high speeds. The drag force then is approximately proportional to the square of the velocity. Taking the drag force to be $F_{\text{D}}=\frac{1}{2}\text{rhoA}{v}^2,$ and setting this equal to the skydiver’s weight, find the terminal speed for a person falling “spread eagle.”