7 this is analogous to eq 910 the velocity change v

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Unformatted text preview: nduced by a surface wave is small if the wave is “weak,” y y. If we neglect bottom friction in the short distance across the wave in Fig. 10.4b, the momentum relation is a balance between the net hydrostatic pressure force and momentum 1 2 | v v or | e-Text Main Menu y)2 gb[(y g1 | y2] 1 2 y y Textbook Table of Contents cby(c y V c) cV | Study Guide (10.8) 664 Chapter 10 Open-Channel Flow ;;; Sluice gate Hydraulic jump Subcritical yc = Fig. 10.5 Flow under a sluice gate accelerates from subcritical to critical to supercritical flow and then jumps back to subcritical flow. Q2 b2g Subcritical 1/ 3 Supercritical This is analogous to Eq. (9.12). By eliminating V between Eqs. (10.7) and (10.8) we obtain the desired expression for wave propagation speed c2 gy 1 y y 1 2 1 y (10.9) y The “stronger” the wave height y, the faster the wave speed c, by analogy with Eq. (9.13). In the limit of an infinitesimal wave height y → 0, the speed becomes c2 0 gy (10.10) This is the surface-wave equivalent of fluid sound speed a, and thus th...
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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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