p0790

# p0790 - viz S 1 2 c = nQ χ by c X b 2 y c by c ~ 2 3 = ⇒...

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7.90. CHAPTER 7, PROBLEM 90 893 7.90 Chapter 7, Problem 90 By definition, the critical depth, y c , is y c = X Q 2 gb 2 ~ 1 / 3 Also, the Ch´ezy-Manning equation tells us u = χ n S 1 / 2 o R 2 / 3 h , χ = 1 . 49 ft 1 / 3 / sec while the hydraulic radius for a rectangular channel is R h = by b + 2 y Since the volume-flow rate is Q = uA = uby , we can rewrite the Ch´ezy-Manning equation at critical conditions as follows. Q by c = χ n S 1 / 2 c X by c b + 2 y c ~ 2 / 3 For the given values, y c = p 600 ft 3 / sec Q 2 p 32 . 174 ft / sec 2 Q (10 ft) 2 1 / 3 = 4 . 82 ft Now, the critical slope is given by the Ch´ezy-Manning equation with the critical depth,
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Unformatted text preview: viz., S 1 / 2 c = nQ χ by c X b + 2 y c by c ~ 2 / 3 = ⇒ S c = X nQ χ by c ~ 2 X b + 2 y c by c ~ 4 / 3 Then, since n = 0 . 025 , we have S c = . 025 p 600 ft 3 / sec Q p 1 . 49 ft 1 / 3 / sec Q (10 ft)(4 . 82 ft) 2 ^ 10 ft + 2(4 . 82 ft) (10 ft)(4 . 82 ft) ± 4 / 3 = 0 . 0132 Finally, the critical angle, θ c , is θ c = tan − 1 S c = 0 . 75 o...
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