The fluid dynamic characteristics of a golf ball are to be tested using a model in a wind tunnel. The dependent parameters of interest, the drag force, FD is dependent on the velocity of the ball, V, diameter of the ball, D, air density and viscosity (? and µ), as well as angular rotational speed of the golf ball, ?, and a dimple depth, d.
(a) Use dimensional analysis and determine the relevant Pi terms, there will be 4 total. For simplicity of solution, choose ?, V and D as the repeating variables.
(b) A pro golfer can hit a ball at V=240 ft/s and ? = 9000 RPM. To model these conditions in a wind tunnel which has a maximum speed of 80 ft/s, what diameter model must be used? How fast must the model rotate? A standard diameter for a golf ball is 1.68 inches.