Hence the efficiency of the jet propeller is
PV/W = 2V / (v + V).
(3)
This increases towards unity as v approaches V. In other words, the less the velocity of the jets exceeds that of the ship, and therefore the greater the area of the orifice of discharge, the greater is the efficiency of the propeller.
In the “Waterwitch” v was about twice V. Hence in this case the theoretical efficiency of the propeller, friction neglected, was about 2⁄3.
| Fig. 165. |
§ 164. Pressure of a Steady Stream in a Uniform Pipe on a Plane normal to the Direction of Motion.—Let CD (fig. 165) be a plane placed normally to the stream which, for simplicity, may be supposed to flow horizontally. The fluid filaments are deviated in front of the plane, form a contraction at A1A1, and converge again, leaving a mass of eddying water behind the plane. Suppose the section A0A0 taken at a point where the parallel motion has not begun to be disturbed, and A2A2 where the parallel motion is re-established. Then since the same quantity of water with the same velocity passes A0A0, A2A2 in any given time, the external forces produce no change of momentum on the mass A0A0A2A2, and must therefore be in equilibrium. If Ω is the section of the stream at A0A0 or A2A2, and ω the area of the plate CD, the area of the contracted section of the stream at A1A1 will be cc(Ω − ω), where cc is the coefficient of contraction. Hence, if v is the velocity at A0A0 or A2A2, and v1 the velocity at A1A1,
vΩ = ccv (Ω − ω);
∴ v1 = vΩ / cc (Ω − ω).
(1)