G the dissipation is large but the temperature rise

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Unformatted text preview: mps) Slowly changing cross section One-dimensional 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 steady-flow 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. | e-Text 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.

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