We've all seen (in movies, newscasts, or perhaps in person) the violent effect of the downwash that occurs when a helicopter hovers over the ground. Leaves, grass, and debris are dramatically blown about. We've also sat in front of circulating room fans and felt a large draft, whereas there seems to be very little air movement behind the fan. The cause of this is a delightful manifestation of Bernoulli's principle. The fan blades, or helicopter rotor blades, produce a pressure differential as air passes through them—let us say p1 before and p2 after, as shown in Fig. 1, with p2 greater than p1. If p0 is the ambient pressure, Bernoulli's equation gives
where v1 is the velocity of the air entering the fan. Continuity requires that v2 leaving the fan must equal v1 entering the fan for an incompressible fluid, approximately true here (Av1 = Av2, where A is the area swept out by the blades, the “rotor disk area”). However, some distance below the rotor (or in front of the fan) the velocity is vd (vdowndraft in the figure) and the pressure again p0, so Bernoulli gives us
This content is only available via PDF.
AAPT members receive access to The Physics Teacher and the American Journal of Physics as a member benefit. To learn more about this member benefit and becoming an AAPT member, visit the Joining AAPT page.