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HW_SET_5.soln

# HW_SET_5.soln - Solution The CV encloses the inlet and...

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Solution: The CV encloses the inlet and outlet and is just inside the walls of the tube. We don’t need to establish a relation between umax and Uo by integration, because the results for these two profiles are given in the text. Note that Uo uav at section (2). Now use these results as needed for the balance of forces: R 2 2 ) 22 x1 2 d r a g 2 2 o o o 2 0 F( pp ) RF u ( u 2 r d r ) U (R U ) R U ( 1   We simply insert the appropriate momentum-flux factors from p. 136 of the text: (a) Laminar: . (a) Ans 2 drag 1 2 o p p ) R ( 1 / 3 ) R U  Turbulent, 1.020: F (p p ) R 0.02 R U (b) 2 . (b) Ans 2 drag 1 2 o P3.54 For the pipe-flow reducing section of Fig. P3.54, D1 8 cm, D2 5 cm, and p2 1 atm. All fluids are at 20°C. If V1 5 m/s and the manometer reading is h 58 cm, estimate the total horizontal force resisted by the flange bolts. Fig. P3.54 Solution: Let the CV cut through the bolts and through section 2. For the given manometer reading, we may compute the upstream pressure: 12 m e r cw a t e r p p ( )h (132800 9790)(0.58 m) 71300 Pa (gage)  Now apply conservation of mass to determine the exit velocity: 2 2 Q Q , or (5 m/s)( /4)(0.08 m) V ( /4)(0.05) , solve for V 12.8 m/s   ) , Finally, write the balance of horizontal forces: x bolts 1,gage 1 2 1 FF p A m ( V V bolts or: F (71300) (0.08) (998) (0.08) (5.0)[12.8 5.0] . 44 Ans 163 N P3.55 In Fig. P3.55 the jet strikes a vane which moves to the right at constant velocity Vc on a frictionless cart. Compute (a) the force Fx required to restrain the cart and (b) the power P

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P3.57 Water flows through the duct in Fig. P3.57, which is 50 cm wide and 1 m deep into the paper. Gate BC completely closes the duct when 90°. Assuming one- dimensional flow, for what angle will the force of the exit jet on the plate be 3 kN? Solution: The steady flow equation applied to the duct, Q1 Q2, gives the jet velocity as V2 V1(1 – sin ). Then for a force summation for a control volume around the jet’s impingement area, Fig. P3.57      2 11 1 1 (s i n ) ( ) ( 1s i n xj j FF m V h h D V 2 )   2 2 (998)(0.5)(1)(1.2) sin 1 sin 1 3000 hDV Ans. F 49.5 P3.58 The water tank in Fig. P3.58 stands on a frictionless cart and feeds a jet of diameter 4 cm and velocity 8 m/s, which is deflected 60° by a vane. Compute the tension in the supporting cable. Solution: The CV should surround the tank and wheels and cut through the cable and the exit water jet. Then the horizontal force balance is Fig. P3.58 22 x cable out out j j F T m u ( AV )V cos 998 (0.04) (8) cos60 .
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HW_SET_5.soln - Solution The CV encloses the inlet and...

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