8 equation 109 is therefore the correct solution for

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Unformatted text preview: 2)1/2 1 (1 (10.43) With y2 thus known, V2 follows from the wide-channel continuity relation V1y1 y2 V2 (10.44) Finally, we can evaluate the dissipation head loss across the jump from the steady-flow energy equation hf E1 E2 y1 V2 1 2g V2 2 2g y2 Introducing y2 and V2 from Eqs. (10.43) and (10.44), we find after considerable algebraic manipulation that hf (y2 y1)3 4y1y2 (10.45) | v v Equation (10.45) shows that the dissipation loss is positive only if y2 y1, which is a requirement of the second law of thermodynamics. Equation (10.43) then requires that | e-Text Main Menu | Textbook Table of Contents | Study Guide 10.5 The Hydraulic Jump 681 Fr1 1.0; that is, the upstream flow must be supercritical. Finally, Eq. (10.44) shows that V2 V1 and the downstream flow is subcritical. All these results agree with our previous experience analyzing the normal-shock wave. The present theory is for hydraulic jumps in wide horizontal channels. For the theory of prismatic or sloping channels see advanced texts [for example, 3, chaps. 15...
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This note was uploaded on 10/27/2009 for the course MAE 101a taught by Professor Sakar during the Spring '08 term at UCSD.

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