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 Blast | 15° | 20° | 60° | 90° |
| Horizontal pressure R | 0.4 | 0.61 | 2.73 | 3.31 |
| Lateral pressure L | 1.6 | 1.96 | 1.26 | .. |
| Normal pressure √ (L2 + R2) | 1.65 | 2.05 | 3.01 | 3.31 |
| Normal pressure by Duchemin’s rule | 1.605 | 2.027 | 3.276 | 3.31 |
Water Motors