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Slowly changing cross section
Onedimensional velocity distribution
Pressure distribution approximately hydrostatic The flow then satisfies the continuity relation (10.1) plus the energy equation with bottom friction losses included. The two unknowns for steady flow are velocity V(x) and
water depth y(x), where x is distance along the channel. Basic Differential Equation Consider the length of channel dx illustrated in Fig. 10.13. All the terms which enter
the steadyflow energy equation are shown, and the balance between x and x dx is
V2
2g y S0 dx
dy
dx or V2
2g S dx
d
dx V2
2g d S0 V2
2g y dy S (10.46) where S0 is the slope of the channel bottom (positive as shown in Fig. 10.13) and S is
the slope of the EGL (which drops due to wall friction losses).
To eliminate the velocity derivative, differentiate the continuity relation
dQ
dx 0 A dV
dx V dA
dx (10.47) 3  v v This section may be omitted without loss of continuity.  eText Main Menu  Textbook Table of Contents  Study Guide 10.6 Gradually Varied Flow 683 Horizontal
slope S
V2
2g EGL V2
V2
+...
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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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