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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  eText 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 OpenChannel 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 surfacewave 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.
 Spring '08
 Sakar

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