Fluid Reaction Force on Solids

Abstract

Steady flow past a circular arc wing produces a vertical lift force, which has been calculated before, but it also causes two horizontal reaction forces, equal and opposite, due to Newton’s third law: the accelerated and decelerated flows act back on the top surfaces of the wing. Reaction forces are computed here and compared with the lift force. The magnitude of the two perpendicular forces are equal when the ratio of the maximum thickness of the wing is about 1/5 the length of the wing’s flat bottom surface. An example of an asymmetric wing is discussed and the net reaction force is calculated, which is always directed horizontally away from the top surface of the wing that has the greater mean slope. Based on these results,it is predicted that a surface ship should go more easily through the water if the bow were blunt and the stern pointed, just the opposite configuration of what is commonly found traversing lakes and oceans. Surface gravity waves are argued not to change this conclusion in general.