R = P (sin φ)1.842 cos φ.

A simpler and more convenient expression given by Colonel Duchemin is

R = 2P sin2 φ / (1 + sin2 φ).

Consequently, the total pressure between the fluid and plane is

N = 2P sin φ / (1 + sin2 φ) = 2P / (cosec φ + sin φ),

and the lateral force is

L = 2P sin φ cos φ / (1 + sin2 φ).

In 1872 some experiments were made for the Aeronautical Society on the pressure of air on oblique planes. These plates, of 1 to 2 ft. square, were balanced by ingenious mechanism designed by F. H. Wenham and Spencer Browning, in such a manner that both the pressure in the direction of the air current and the lateral force were separately measured. These planes were placed opposite a blast from a fan issuing from a wooden pipe 18 in. square. The pressure of the blast varied from 6⁄10 to 1 in. of water pressure. The following are the results given in pounds per square foot of the plane, and a comparison of the experimental results with the pressures given by Duchemin’s rule. These last values are obtained by taking P = 3.31, the observed pressure on a normal surface:—

Angle between Plane and Direction of Blast15°20°60°90°
Horizontal pressure R0.40.612.733.31
Lateral pressure L1.61.961.26..
Normal pressure √ (L2 + R2)1.652.053.013.31
Normal pressure by Duchemin’s rule1.6052.0273.2763.31

Water Motors