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b0Q2
g Ac
Vc Q
Ac 1/3 (10.37a) gAc
b0 1/2 (10.37b) For a given channel shape A(y) and b0(y) and a given Q, Eq. (10.37) has to be solved by
trial and error or by EES to find the critical area Ac, from which Vc can be computed.
2  v v This is the basis of the waterchannel analogy for supersonic gasdynamics experimentation [14, chap. 11].  eText Main Menu  Textbook Table of Contents  Study Guide 674 Chapter 10 OpenChannel Flow By comparing the actual depth and velocity with the critical values, we can determine the local flow condition
y Vc: subcritical flow (Fr y Critical Uniform Flow:
The Critical Slope yc, V 1) yc, V Vc: supercritical flow (Fr 1) If a critical channel flow is also moving uniformly (at constant depth), it must correspond to a critical slope Sc, with yn yc. This condition is analyzed by equating Eq.
(10.37a) to the Chézy (or Manning) formula:
gA3
c
b0 Q2
or 2
2
C2Ac RhSc n 2 4/3
Ac Rh Sc n2g P
2 1/3
Rhc b0 n2gAc
4/3
2
b0Rhc Sc 2 fP
8 b0 (10.38) where 2 equals 1.0 for SI units and 2.208 for BG units. Equation (10...
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 Spring '08
 Sakar

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