Chapter 14, Problem 14.113RP

An airplane with a weight W and a total wing span b flies horizontally at a constant speed v. Use the airplane as a reference frame: that is, consider the airplane to be motionless and the air to flow past it with speed v. Suppose that a cylinder of air with diameter b is deflected downward by the wing (the cross section of the cylinder is the dashed circle in the figure). Show that the angle through which the cylinder stream is deflected (called the downwash angle) is determined by the formula sin $\theta =4W(\pi b^2\rho v^2)$, where $\rho$ is the mass density of the air.