. The steam-engine and other heat-motors . te.—The above formulas may be gotten more simply thus: If the stream is turned through 90° and the velocity in the original WVdirection becomes zero the force is . Hence for any other angle, WV WV 2# = 0and SF = 0, we have Fx = (1 — cos a) and Fy = sin a. 9 9 SUPERHEATED STEAM AND STEAM-TURBINES- 451 The values of F given for the angles 90° and 180° may be ob-tained from these general equations by making a = 90° or 180°.The value of cos a is additive if the angle through which thestream is turned is greater than 90° and subtractive if it be lessthan 9
. The steam-engine and other heat-motors . te.—The above formulas may be gotten more simply thus: If the stream is turned through 90° and the velocity in the original WVdirection becomes zero the force is . Hence for any other angle, WV WV 2# = 0and SF = 0, we have Fx = (1 — cos a) and Fy = sin a. 9 9 SUPERHEATED STEAM AND STEAM-TURBINES- 451 The values of F given for the angles 90° and 180° may be ob-tained from these general equations by making a = 90° or 180°.The value of cos a is additive if the angle through which thestream is turned is greater than 90° and subtractive if it be lessthan 90°. In the derivation of the formula a indicated the angle throughwhich the stream is turned. Frequently, however, the supple-mentary angle or the angle beween the entering and departingstreams is used. Hence the preceding formulas often appear as WVFx=—(1+cosa), v WV • Fv = sin a. y g Fr = V2(l+cosa)._ A modification of the preceding lines of motion is seen inFig. 171, where the entering and leaving streams are inclined at. Fig. 234. angles a and /? with F, the line of action of the required a stationary and frictionless vane the entering and departingvelocities must be equal since there can be no loss of energy. The 452 THE STEAM-ENGINE AND OTHER HEAT-MOTORS. WVe impulse due to V, in its line of action is . The reaction due to WV2 V2 in its line of action is . Resolving these forces along the line of action of F and we have p w WV< Pi = r e cos a = cos a, 9 WV9P2 = F2 cos p = cos/?. WV,As Ve = V2, P = (cos a + cos /?). The action or the impulse of the stream against the bucket whenstationary, as in the preceding examples, or when moving, as inthe examples that follow, and whether friction is regarded or dis-regarded, may be found by the application of the following rule. Draw the line of motion of the vane or bucket. Find thevelocities of entrance and departure of the stream relative to thebucket section. Resolve these velocities along the line of
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