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418 Chapter 8 ■ Viscous Flow in Pipes Separated flow Vena contracta V 1 = 0 x (1) (2) V 2 > V 3 (3) Flow separation at corner (a) p 1 p 3 p ____ ρV 2 2 2 Ideal full recovery of kinetic energy Actual ____ ρV 2 3 2 ____ ρV 2 3 K L 2 x 1 x 2 x 3 x (b) Flow pattern and pressure distribution for a sharp- F I G U R E 8.23 edged entrance. 0.5 0.4 r 0.3 K L F I G U R E 8.24 0.2 D 0.1 0 0 0.05 0.1 0.15 0.20 0.25 r __ D Entrance loss coefficient as a function of rounding of the inlet edge (Ref. 9). V8.10 Entrance/exit flows A head loss 1the exit loss2 is also produced when a fluid flows from a pipe into a tank as is shown in Fig. 8.25. In these cases the entire kinetic energy of the exiting fluid 1velocity V 1 2 is dissipated through viscous effects as the stream of fluid mixes with the fluid in the tank and eventually comes to rest 1V 2 02. The exit loss from points 112 and 122 is therefore equivalent to one velocity head, or K L 1. Losses also occur because of a change in pipe diameter as is shown in Figs. 8.26 and 8.27. The sharp-edged entrance and exit flows discussed in the previous paragraphs are limiting cases of this type of flow with either A 1A 2 q, or A 1A 2 0, respectively. The loss coefficient for a sudden contraction, K L h L1V 2 22g2, is a function of the area ratio, A 2A 1 , as is shown in Fig. 8.26. The value of K L changes gradually from one extreme of a sharp-edged entrance 1A 2A 1 0 with K L 0.502 to the other extreme of no area change 1A 2A 1 1 with K L 02. In many ways, the flow in a sudden expansion is similar to exit flow. As is indicated in Fig. 8.28, the fluid leaves the smaller pipe and initially forms a jet-type structure as it enters the larger pipe. Within a few diameters downstream of the expansion, the jet becomes dispersed across the pipe, and fully developed flow becomes established again. In this process [between sections 122 and 132] a portion of the kinetic energy of the fluid is dissipated as a result of viscous effects. A squareedged exit is the limiting case with A 1A 2 0. A sudden expansion is one of the few components 1perhaps the only one2 for which the loss coefficient can be obtained by means of a simple analysis. To do this we consider the continuity
8.4 Dimensional Analysis of Pipe Flow 419 (2) (1) (a) (b) (c) (d) F I G U R E 8.25 Exit flow conditions and loss coefficient. (a) Reentrant, K L 1.0, (b) sharp-edged, K L 1.0, (c) slightly rounded, K L 1.0, (d) well-rounded, K L 1.0. 0.6 A 1 A 2 h L = K 2 ___ V 2 L 2g 0.4 K L F I G U R E 8.26 0.2 0 0 0.2 0.4 0.6 0.8 1.0 A 2 /A 1 Loss coefficient for a sudden contraction (Ref. 10). 1.0 0.8 A 1 A 2 hL = K 2 ___ V 1 L 2g 0.6 K L 0.4 F I G U R E 8.27 0.2 0 0 0.2 0.4 0.6 0.8 1.0 A 1 /A 2 Loss coefficient for a sudden expansion (Ref. 10).
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Achieve Positive Learning Outcomes
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Sixth Edition F undamentals of Flui
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About the Authors vii Bruce R. Muns
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P reface This book is intended for
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Preface xi Life Long Learning Probl
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Preface xiii WileyPLUS offers today
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Featured in this Book xv LEARNING O
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C ontents 1 INTRODUCTION 1 Learning
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Contents xix 6.4.3 Irrotational Flo
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12.6 Axial-Flow and Mixed-Flow Pump
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10 8 Jupiter red spot diameter 2 Ch
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4 Chapter 1 ■ Introduction and do
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6 Chapter 1 ■ Introduction up the
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8 Chapter 1 ■ Introduction the SI
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10 Chapter 1 ■ Introduction E XAM
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12 Chapter 1 ■ Introduction TABLE
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14 Chapter 1 ■ Introduction TABLE
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16 Chapter 1 ■ Introduction Crude
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18 Chapter 1 ■ Introduction Visco
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20 Chapter 1 ■ Introduction Kinem
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22 Chapter 1 ■ Introduction As th
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24 Chapter 1 ■ Introduction Boili
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26 Chapter 1 ■ Introduction E XAM
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28 Chapter 1 ■ Introduction The r
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30 Chapter 1 ■ Introduction fluid
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32 Chapter 1 ■ Introduction Secti
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34 Chapter 1 ■ Introduction avail
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36 Chapter 1 ■ Introduction compr
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2 Fluid Statics CHAPTER OPENING PHO
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40 Chapter 2 ■ Fluid Statics in a
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42 Chapter 2 ■ Fluid Statics p Fo
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44 Chapter 2 ■ Fluid Statics the
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58 Chapter 2 ■ Fluid Statics Free
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60 Chapter 2 ■ Fluid Statics The
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66 Chapter 2 ■ Fluid Statics SOLU
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92 Chapter 2 ■ Fluid Statics 2.12
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94 Chapter 3 ■ Elementary Fluid D
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100 Chapter 3 ■ Elementary Fluid
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148 Chapter 4 ■ Fluid Kinematics
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264 Chapter 6 ■ Differential Anal
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7 Dimensional Analysis, Similitude,
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334 Chapter 7 ■ Dimensional Analy
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468 Chapter 9 ■ Flow over Immerse
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∋ 530 Chapter 9 ■ Flow over Imm
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10 Open-Channel Flow CHAPTER OPENIN
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646 Chapter 12 ■ Turbomachines Ex
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702 Appendix A ■ Computational Fl
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A ppendix B Physical Properties of
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Answers to Selected Even-Numbered H
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I ndex Absolute pressure, 13, 48 Ab
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Index I-5 hydrostatic: on curved su
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Index I-13 Weber, M., 29, 350 Weber
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■ TABLE 1.4 Conversion Factors fr
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■ TABLE 1.7 Approximate Physical
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