480 APPLIED MECHANICS 
bal eae , and this requires that a force Pale 
v2 : 
shall act on the jet 
a4 the direction of its motion. As a consequence of this there must be — 
another force F equal and opposite to P acting on 
the vessel, as shown in Fig. 777, and unless an 
external force be applied to the vessel the latter will 
move under the action of the force F. 
If the vessel moves under the action of the 
force F in the direction of that force with a velocity 
v,, the magnitude of F and P remain the same, 
namely Pape wav Fig. 777. 
J 
2 
Useful work done per second = Fv, = peli 
Total energy = useful work + lost work | 
2, 2 
CAO py) = Ant 3. 
29 29 
Ge at + Oy fe” 
299 Ut v2 
418. Deviation of a Jet in one Direction by a Vane without 
Shock.—In the examples on the impact of a jet on a vane which have — 
hitherto been considered, the jet has struck the vane and been deviated — 
abruptly. A consequence of this abrupt deviation is a shock, and there-_ 
fore a loss of energy in agitating the water. The full force of the 
impact may, however, be obtained and the shock avoided by so shaping — 
the vane that the jet on meeting it glides along its surface and is 
deviated gradually. 
Case I. Vane at rest (Fig.778).—At B, where the jet first meets the vane, 
the direction of the surface of the vane coincides with the direction of the jet, 
that is, the jet meets the vane tangentially. 
The jet is then gradually deviated by the 
curved surface of the vane, and leaves 
it in a direction tangential to the vane 
at C. 
The velocity of the water at B is equal 
to v in the direction BD, and the velocity 
at C is equal to v in the direction of the 
tangent to the vane at C. Draw BE 
parallel to the tangent to the vane at C, 
and make BE and BD each equal to ». 
Join DE. Then DE is the change in the 
velocity of the water, in magnitude and direction, while it passes over — 
the vane. If 6 is the interior angle between the tangents to the vane at 
B and C, then DE=2 vcos . The change in the momentum of the 
2 
a 6 : 
water per second in passing from B to C is had *DE= a 008 3 3? and this" 
wAv Oy 
Efficiency = 
Fig. 778. 
is equal to R, the resultant force on the vane due to the impact of 
