Page:Aerial Flight - Volume 1 - Aerodynamics - Frederick Lanchester - 1906.djvu/211

Rh force acting rearward on the dead-water as a whole, the reaction of which appears as a region of decreased pressure (a partial vacuum) on the rear face of the plane.

Dines has investigated this point experimentally, and has found that for a one foot square plane in air at 60 m/h., the deficit of pressure on the rear face is approximately one-half the excess pressure on the front of the plane, the measurement being made in the centre of the plane. A similar proportion was found to obtain when the pressure on the mouth of a tube was measured pointed towards and away from the relative wind direction.

Lord Kelvin has pointed out (Nature, p. 597, 1894) that the pressure recorded by Dines in the above experiment, i.e., 1.82 inches of water, corresponds exactly to that given by the Torricellian method, that is to say, that the excess pressure that occurs at the centre of a normal plane for any given velocity is that of the corresponding hydrostatic head. This fact is fully consistent with hydrodynamic theory. If the stream lines could be plotted it is evident that at the point on the face of the plane where the stream divides, the velocity of the fluid will be nil, therefore by § 82 the pressure at this point will be in excess of that at a distance away by an amount corresponding to the head due to the relative velocity of the fluid.

We have here a definite proof that the Torricellian method is inapplicable in the determination of the constant $$C,$$ for at every other point on the face of the plane than that at which the stream divides the fluid is possessed of velocity, and consequently its pressure is less than that given by the calculation on the basis in question.

There may be a small departure from the maximum pressure law due to viscosity, but there is every reason to suppose that in fluids of moderate viscosity such error may be ignored; the