Page:Aerial Flight - Volume 1 - Aerodynamics - Frederick Lanchester - 1906.djvu/168

§ 112 of the earth, and that the transmission of the stress is effected by the communication of momentum from part to part, and is thereby distributed over a considerable area as a region of increased pressure. But, as is usual in fluid dynamics, there is a certain ambiguity in the application of the principle of the continuous communication of momentum, and we as yet lack some definite statement as to the application of the principle to the case in point.

In Fig. 62 $$A\ B$$ represents an aerofoil, supporting weight, $$W$$, dynamically, under the conditions of the hypothesis. Consider a fluid prismatic column formed by imaginary vertical surfaces touching the edges of the aerofoil and continued downwards to the earth's surface and upwards indefinitely. Adopting the hypothesis that the fluid is inviscid, all forces acting on the column from the surrounding fluid must be normal to its surface, and have no vertical component. The only vertical forces acting on the column are therefore the weight of the loaded aerofoil, $$W,$$ acting downwards, and the pressure on the base of the column $$C\ D,$$ due to the distribution of the weight W on the earth's surface. Let this latter equal $$w;$$ there is then a downward resultant $$W\ \boldsymbol{-}\ w$$ acting on the column. (The weight of the column itself and the pressure produced