Page:Aerial Flight - Volume 1 - Aerodynamics - Frederick Lanchester - 1906.djvu/147

$.44\ \rho \ V^{2}\ l$, where $\rho$ is density, $V=$ velocity, and $l=$ width of lamina in absolute units. The expression for mean pressure will therefore be:—

$P=.44\ \rho \ V^{2}$

Similarly the case of an inclined lamina has been investigated by Kirchhoff and Rayleigh, and the following are the expressions obtained:—

${\frac {P}{\beta }}={\frac {\pi \ \sin \beta }{4+\pi \ \sin \beta }}\ \rho \ V^{2},$

(1)

where $\beta$ is the angle of inclination.

For the position of the centre of pressure:—

$x={\frac {3}{4}}\times {\frac {\cos \beta }{4+\pi \sin \beta }}\times l,$

(2)

where $l$ is the width of the plane and $x$ the distance forward of the geometric centre.

The following Table gives the result for different values of $\beta$
(1) pressure on plane in terms of normal pressure, and (2) the proportionate distance of the centre of pressure from the central line:—

$\beta$	(1)	(2)
90° 70° 50° 30° 20° 10°   0°	1.000   .965   .854   .641   .481   .273   .000	.000 .037 .075 .117 .139 .163 .187

§ 98. Deficiencies of the Eulerian Theory of the Perfect Fluid.—The deficiencies of hydrodynamic theory have already been pointed out in several instances and partially discussed. The forms of flow that result from the assumption of continuity' and the equations of motion bear in general but scant resemblance to those that obtain in practice, and it is not altogether easy to account for the cause of the failure.

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