Question 12.10: The triangular flume in Fig. 12–22a is used to carry water o......

Fluid Mechanics [1012629]

The triangular flume in Fig. 12–22a is used to carry water over a ravine. It is made of wood and has a slope of $S_0$ = 0.001. If the intended flow is to be Q = 3 m³/s, determine the depth of the flow. Take n = 0.012.

fig 12-22a

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Fluid Description. We assume steady uniform flow of an incompressible fluid.
Analysis. If y is the depth of the flow, Fig. 12–22b, then

$P = 2\sqrt{2}y$ and $A = 2[\frac{1}{2}(y)(y)] = y^2$

For SI units,

Q  =  \frac{kA^{5/3}S_0^{1/2}}{nP^{2/3}};               3  m^3/s =  \frac{(1)(y^2)^{5/3}(0.001)^{1/2}}{0.012 (2\sqrt{2} y)^{2/3}}

y = 1.36 m

fig 12-22b

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