. The steam-engine and other heat-motors . quan-tities are to be added. w Hence F=—(V— v)(l+ cos a). In Fig. 236 let the bucket move in the direction F with the velocityv. If the absolute velocity of entrance of the stream be Ve, itsvelocity relative to the bucket section on entrance is V{ in thedirection shown and, on departure, the relative velocity is Vf=V{,neglecting frictional and other resistances. Resolve the relativevelocities along the direction of F and obtain W F = —Vf (cos a + cos /?) Vf equals V* since there is no friction, v is the velocity ofthe bucket and V2 is the absolute fin
. The steam-engine and other heat-motors . quan-tities are to be added. w Hence F=—(V— v)(l+ cos a). In Fig. 236 let the bucket move in the direction F with the velocityv. If the absolute velocity of entrance of the stream be Ve, itsvelocity relative to the bucket section on entrance is V{ in thedirection shown and, on departure, the relative velocity is Vf=V{,neglecting frictional and other resistances. Resolve the relativevelocities along the direction of F and obtain W F = —Vf (cos a + cos /?) Vf equals V* since there is no friction, v is the velocity ofthe bucket and V2 is the absolute final velocity of the stream. From the velocity diagrams, other equivalents may be obtainedfor F W F = —(Vt cos A-v + 7,cos/?), W F =—(Vecosk±V2cosd). 454 THE STEAM-ENGINE AND OTHER HEAT-MOTORS. Blade Angles.—If the entering stream struck the back of arevolving blade the motion of the latter would be impeded andthe efficiency would be lowered. The angle a of the backof the blade on the entering side in Fig. 236 is determined by. Fig. relations that exist between Ve, v and X. Hence a can bedetermined from the relation found as follows: v sin (a— X) sin a cos X— cos a sin X Ve sin awhence sin acot a= cot X— cos X—cot a sin X, VK sin X Shock is avoided, then, by having the entering angle of theback of the blade parallel to the relative motion of theentering stream. On the other hand, the angle of leaving isone of the principal factors in determining the efficiency of themechanism. The difference in the energy of a stream on enteringand on leaving a blade must appear either as friction or as usefulwork. Efficiency is increased by making the energy rejected assmall as possible. If a stream has an absolute velocity, V», before it meets aresistance and an absolute velocity of V2 afterwards the loss of SUPERHEATED STEAM AND STEAM-TURBINES. 455 energy of the stream is W(V2- V22) wAeVE(V2- V22) This 2g 2g loss of energy may appear as the work of friction, usefu
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