he surface; rather it is at rest relative to the surface of the ball. Momentum is transferred across this boundary layer from the flowing air to the surface of the ball. The force on the ball is determined by the rate of this momentum transfer. A feeling for what is happening in the boundary layer may be had by imagining the stirring of a kettle of some viscous fluid, such as molasses, with a spoon. As the spoon stirs the fluid, the kettle will turn along with the fluid unless the kettle is held fixed. A torque must be applied to the kettle to keep it from turning. The tangential force of the fluid on the inner surface of the kettle results from the internal viscous effects in the fluid. A similar tangential force on the surface of the ball results from the internal viscous effects in the boundary layer at the surface of the ball. The force on the ball is proportional to the relative velocity of the air past the ball at this low velocity. In the case under discussion, the air flowing from A to B outside the boundary layer is going from a high pressure region to a low pressure region and we may look upon this pressure difference as helping to increase the air velocity. However the air in flowing from B to C moves from a low pressure region to a high pressure region and loses velocity in going against this pressure difference. When the viscous effect in the boundary layer becomes large enough so that the air near the surface of the ball is stopped before it reaches C, turbulent motion takes the place of the streamline flow. This happens sooner or later as the air velocity increases. The velocity of the air past a well hit golf ball in flight is much greater than that at which streamline flow will occur. Figure 8.1(b) shows flow lines for small masses of air past a smooth ball without spin when the air velocity is such that extensive turbulence occurs. From A to B the flow is very similar to that in the previous example. At B or a little b...
