. Applied thermodynamics for engineers. Fig. 249. Arts. 527, 532, 534. — VelocityCorrected for Friction. 374 APPLIED THERMODYNAMICS 528. Bucket Angles and Work Done. In Fig. 250, the absolutevelocities v and Y may be resolved into components ab and db in thedirection of rotation, and ae and de at rightangles to this direction. The former compo-nents are those which move the wheel; the lat-ter produce an end thrust on the shaft. Nowab 4- bd (Jyd being negative) is the change invelocity of the fluid in the direction of rotation ;it is the acceleration; the force exerted perjjound is then (ab ^bd
. Applied thermodynamics for engineers. Fig. 249. Arts. 527, 532, 534. — VelocityCorrected for Friction. 374 APPLIED THERMODYNAMICS 528. Bucket Angles and Work Done. In Fig. 250, the absolutevelocities v and Y may be resolved into components ab and db in thedirection of rotation, and ae and de at rightangles to this direction. The former compo-nents are those which move the wheel; the lat-ter produce an end thrust on the shaft. Nowab 4- bd (Jyd being negative) is the change invelocity of the fluid in the direction of rotation ;it is the acceleration; the force exerted perjjound is then (ab ^bd)-^g= (ab ^ bd) -r- = (vcos a+ I^cos^) -V- This force is exerted through the distance u the work done 2jer pound of steam is then This, from Art. 526, equals. Fig. 250. Arts. 528, 529.—Rotative and ThrustComponeuts. feet per second ; u(v COS a -\- Ycos g) -j- foot-pounds. 778 E (q— Q) whence E= u(v cos a + Zcos^) -- (^ - $). The efficiency is thus directl}^ related to the bucket angles. To avoid splashing, the entrance angle of the bucket is usuallymade equal to the relative entering angle of the jet, as in Fig. 251.(These formulas hold only when the sides of thebuckets are enclosed to prevent the lateralspreading of the stream.) In actual turbines,bd (Fig. 250) is often not negative, on accountof the extreme reversal of direction that wouldbe necessary. With positive value.^ of bd^ themaximum work is obtained as its value ap-proaches zero, and ultimately it is uv cos «^
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