Question 12.8: The channel in Fig. 12–20 is made of finished concrete, and ......

Fluid Mechanics [1012629]

The channel in Fig. 12–20 is made of finished concrete, and the bed drops 2 m in elevation for a horizontal stretch or reach of 1000 m. Determine the steady uniform flow when the depth of the water is 2 m. Take n = 0.012.

fig 12-20

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Fluid Description. The flow is steady and uniform, and the water is assumed to be incompressible and flows with an average velocity V.
Analysis. Here we will use the Manning equation, with k = 1, for SI units. The slope of the channel is $S_0$ = 2 m/1000 m = 0.002. Also, for a 2-m depth of water, the hydraulic radius is

R_h  =  \frac{A}{P}  =  \frac{(3  m) (2  m)}{2 (2  m)  +  3  m}  =  0.8571  m

Applying Eq. 12–18,

V  =  \frac{kR_h^{2/3} S_0^{1/2}}{n}

\frac{Q}{(3  m)(2  m)}  =  \frac{(1)(0.8571  m)^{2/3}(0.002)^{1/2}}{0.012}

Q = 20.18 m^3/s = 20.2 m^3/s

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