A pitcher throws a baseball at 85 miles per hour. The flow field over the baseball moving...

A pitcher throws a baseball at 85 miles per hour. The flow field over the baseball moving through the stationary air at 85 miles per hour is the same as that over a stationary baseball in an airstream that approaches the baseball at 85 miles per hour. (This is the principle of wind tunnel testing, as will be discussed in Chap. 4.) This picture of a stationary body with the flow moving over it is what we adopt here. Neglecting friction, the theoretical expression for the flow velocity over the surface of a sphere (like the baseball) is. Here V∞ is the airstream velocity (the free-stream velocity far ahead of the sphere). An arbitrary point on the surface of the sphere is located by the intersection of the radius of the sphere with the surface, and ᶿ is the angular position of the radius measured from a line through the center in the direction of the free stream (i.e., the most forward and rearward points on the spherical surface correspond to ᶿ = 0° and 180°, respectively). The velocity V is the flow velocity at that arbitrary point on the surface. Calculate the values of the minimum and maximum velocity at the surface and the location of the points at which these occur.