P2 = -Gbt(v - u)² cos [phi]/g.
If [phi] < 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 [phi] > 90°, cos
[phi] is negative and an additional pressure due to reaction is
obtained.
[Illustration: FIG. 164.]
§ 163. _Jet Propeller._--In the case of vessels propelled by a jet of
water (fig. 164), driven sternwards from orifices at the side of the
vessel, the water, originally at rest outside the vessel, is drawn
into the ship and caused to move with the forward velocity V of the
ship. Afterwards it is projected sternwards from the jets with a
velocity v relatively to the ship, or v - V relatively to the earth.
If [Omega] is the total sectional area of the jets, [Omega]v is the
quantity of water discharged per second. The momentum generated per
second in a sternward direction is (G/g)[Omega]v(v - V), and this is
equal to the forward acting reaction P which propels the ship.