F.yp?F1.yp1?F2'.yp2'?F2''.yp2''?17640?1.5?23520?0.5?9800?0.333?41483.441483.441483.4yp???0.814(m)F50960
22. A diverging nozzle that discharges an 8-in-diameter water jet into the air is on the right end of a horizontal 6-in-diameter pipe. If the velocity in the pipe is 12fps, find the magnitude and direction of the resultant axial force the water exerts on the nozzle. Neglect fluid friction. (10分) Solution:
A162v2?v1?2?12?6.75(ft/s)A282 p1v12p2v2??z1???z2?
?2g?2g
?262.4 ?p1?(v2?v12)?(6.752?122)??95.38(lb/ft2)2g2?32.2
?Fx??Q(V2?V1)?P1A1?Fbx
?F??F?PA??Q(V?V)??95.38???(6)2?62.4?12???(6)2?(6.75?12)xbx112141232.2412
? 5 . 24 ( lb ) to the right
23. A horizontal 100-mm-diameter pipe (f=0.027) projects into a body of water (ke=0.8) 1m below the surface. Considering all losses, find the pressure at a point 5 m from the end of the pipe if the velocity is 4 m/s and the flow is (a) into the body of water; (b) out of the body of water. (10分)
Solution: (a) 2p1v12p2v2 ?z1???z2??hL?2g?2g
p1v12v12lv12
??z2?z1?f?(k') ?2gd2g2g p1542?1?0.027?
98000.12?9.8
p1?20.6(kN/m2)
2(b) p1v12p2v2?z1???z2??hL ?2g?2g
p1v12v12lv12??z2?z1?f?ke
?2gd2g2g
?p154242?1?0.027??1.8?98000.12?9.82?9.8p1??15.4(kN/m2)
24. A rectangular plate 5 ft by 4 ft is at an angle of 30°with the horizontal, and the 5-ft side is horizontal. Find the magnitude of the force on one side of the plate and the depth of its center of pressure when the top edge is (a) at the water surface; (b) 1 ft below the water surface. (10分)
Solution:
4(a)
F??hcA?62.4??sin30??(5?4)?1248(lb) 222
hp?h??4?sin30??1.333(ft) 334(b)
F??hcA?62.4?(1??sin30?)?(5?4)?2496(lb) 2131bl?5?43
Ic1412?(?)??4?12?4.333(ft) yp?yc?14ycAsin30?24?(4?5)(?)A
sin30?2
hp?ypsin30??4.333?0.5?2.17(ft)
1. 25. Water in a reservoir is discharged from a vertical pipe. If a=25 ft, b= 60 ft, c=40 ft, d= 2ft. All the losses of energy are to be ignored when the stream discharging into the air at E has a diameter of 4 in. What are pressure heads at B, C and D, if the diameter of the vertical pipe is 5 in? (10分)
22 pAvApEvE??zA???zE? ?2g?2g2 vE0?(25?60?40)?0?0?0? 2g
?vE?2?32.2?125?89.72(ft/s)
AE42?vB?vC?vD?vE?2?89.72?57.42(ft/s) AB5 22pAvApBvB ??zA???zB??2g?2g
2 PBvB57.422??a??25???26.2(ft) ?2g2?32.2
22 pCvCpBvB??zB???zC? ?2g?2g
PP ?C?B?(zB?zC)??26.2?60?33.8(ft)?? 22pBvBpDvD ??zB???zD??2g?2g
PP ?D?B?(zB?zD)??26.2?60?40?2?71.8(ft)??
26. A nozzle that discharges a 60-mm-diamater water jet into the air is on the right end of a horizontal 120-mm-diameter pipe. In the pipe the water has a velocity of 4 m/s and a gage pressure of 400 kPa. Find the magnitude and direction of the resultant axial force the water exerts on the nozzle, and the head loss in the nozzle. (10分)
Solution:
A11202v2?v1??4?16(m/s)A2602 ?Fx??Q(V2?V1)?P1A1?Fbx
?F??F?PA??Q(V?V)?400000???0.122?1000?4???0.122?(16?4)xbx112144
?4523.9?542.9?3981(N)
to the right
2 p1v12p2v2??z1???z2??hL
?2g?2g
2222pvv40000416112 ?hL???????28.57(m)?2g2g98002?9.82?9.8
?
27. A 450-ft-long pipeline runs between two reservoirs, both ends being under water, and the intake end is square-edged and nonprojecting. The difference between the water surface levels of the two reservoirs is 150ft. (a) What is the discharge(流量) if the pipe diameter is 12 in and f = 0.028? (b) When this same pipe is old, assume that the growth of tubercles has reduced the diameter to 11.25 in and that f=0.06. What will the rate of discharge be then? (10分)
Solution: (a) 22pvpv1 ?z1?1?2?z2?2?hL?2g?2g
2v2 lvz1?z2?f?(ke?k') d2g2g
450v2150?(0.028?0.5?1)
122?32.2
12
v?26.2(ft/s)
12 ??()212?20.6(cfs) Q?v.A?26.2?4
2(b) p1v12p2v2?z1???z2??hL ?2g?2g 2v2lv z1?z2?f?(ke?k')d2g2g
450v2
150?(0.06?0.5?1)11.25 2?32.2 12 v?17.8(ft/s) 11.252??() 12Q?v.A?17.8??12.32(cfs) 4