§ 162. Direct Action distinguished from Reaction (Rankine, Steam Engine, § 147).
The pressure which a jet exerts on a vane can be distinguished into two parts, viz∴—
(1) The pressure arising from changing the direct component of the velocity of the water into the velocity of the vane. In fig. 153, § 154, ab cos bae is the direct component of the water’s velocity, or component in the direction of motion of vane. This is changed into the velocity ae of the vane. The pressure due to direct impulse is then
P1 = GQ (ab cos bae − ae) / g.
For a flat vane moving normally, this direct action is the only action producing pressure on the vane.
(2) The term reaction is applied to the additional action due to the direction and velocity with which the water glances off the vane. It is this which is diminished by the friction between the water and the vane. In Case 2, § 160, the direct pressure is
P1 = Gbt (v − u)2 / g.
That due to reaction is
P2 = −Gbt (v − u)2 cos φ / g.
If φ < 90°, the direct component of the water’s motion is not wholly converted into the velocity of the vane, and the whole pressure due to direct impulse is not obtained. If φ > 90°, cos φ is negative and an additional pressure due to reaction is obtained.