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.
Highlights
When a fluid accelerates along the smooth surface of a solid body, due to the presence of the body in a steady flow, there is an equal but opposite “reaction” force of the fluid back on the body, in accordance with Newton’s third law of motion
To attempt a physical explanation for why a surface ship with a blunt front would not be inconvenienced by encountering waves in most cases, remember the fact that the net reaction force on an asymmetric solid in a uniform flow is the same, in magnitude and direction, for either way the flow passes by it: the net force always points away from the blunt front [1]
Reaction forces of fluids passing by solid bodies are brought into focus by means of calculations in a specific model and a comparison with the better known lift force
Summary
When a fluid accelerates along the smooth surface of a solid body, due to the presence of the body in a steady flow, there is an equal but opposite “reaction” force of the fluid back on the body, in accordance with Newton’s third law of motion. The assumption was made that the perturbed velocity decays exponentially with distance from the bump such that the e-folding scale is only proportional to the bump’s length for a thin bump: height over length of the bump is much less than one. For comparison the reaction force on both front and back top faces of the circular arc wing are computed and it will be seen under what conditions the two different (perpendicular) forces can be equal in magnitude
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