Chapt10

# 101 23 however the practical engineering approach used

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Unformatted text preview: approach, used here, is to make a one-dimensional-flow approximation, as in Fig. 10.2. Since the liquid density is nearly constant, the steady-flow continuity equation reduces to constant-volume flow Q along the channel Q V(x)A(x) const (10.1) where V is average velocity and A the local cross-sectional area, as sketched in Fig. 10.2. A second one-dimensional relation between velocity and channel geometry is the energy equation, including friction losses. If points 1 (upstream) and 2 (downstream) are on the free surface, p1 p2 pa, and we have, for steady flow, V2 1 2g V2 2 2g z1 z2 hf (10.2) where z denotes the total elevation of the free surface, which includes the water depth y (see Fig. 10.2a) plus the height of the (sloping) bottom. The friction head loss hf is analogous to head loss in duct flow from Eq. (6.30): hf f x2 x1 V2v a Dh 2g Dh hydraulic diameter 4A P (10.3) where f is the average friction factor (Fig. 6.13) between sections 1 and 2. Since channels are irregular in shape, their “...
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