1.) A 40-ft wide rectangular channel carries 950 ft3/sec at a depth of 6 ft. If n = 0.025, what must the channel slope be in order to produce uniform flow at the 6-ft depth? Is this flow subcritical or supercritical? What is the critical slope that would cause the flow to just flip to the other flow profile (subcritical → supercritical or supercritical → subcritical)?2.) Continuing with Problem 1:a. What is the alternate flow depth? (hint: in Problem 1 you should have found that flow was subcritical, so now you're finding the supercritical flow depth)b. What is the critical rise of the surface bed (Δzcrit) that would just cause the flow to flip to supercritical?c. What is the critical width (bcrit) of a throat in a contraction of the channel that would just cause the flow to switch to supercritical?

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Asked Nov 16, 2019
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1.) A 40-ft wide rectangular channel carries 950 ft3/sec at a depth of 6 ft. If n = 0.025, what must the channel slope be in order to produce uniform flow at the 6-ft depth? Is this flow subcritical or supercritical? What is the critical slope that would cause the flow to just flip to the other flow profile (subcritical → supercritical or supercritical → subcritical)?

2.) Continuing with Problem 1:
a. What is the alternate flow depth? (hint: in Problem 1 you should have found that flow was subcritical, so now you're finding the supercritical flow depth)
b. What is the critical rise of the surface bed (Δzcrit) that would just cause the flow to flip to supercritical?
c. What is the critical width (bcrit) of a throat in a contraction of the channel that would just cause the flow to switch to supercritical?

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Expert Answer

Step 1

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Given:

Width of the rectangular channel=40ft

Discharge, Q= 950 ft3/sec

n= 0.025

Depth = 6ft

To find: channel slope

Step 2

to find the slope of bed :

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area, A widthx depth A 40 ftx 6 ft A 240 t wetted perimeter, P = B + 2y P 40+2x6 P 52 ft hydraulic meanradius, R = P 240 - 4.615 54 R = discharge, is given by: 2 1 Q =AR S S = bed slope Qxn S = AXR3 950 x0.025 240x 4.615 S 1.274x10 001274

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Step 3

to determine if the flow is sub c...

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critical depth is given by: У, g where q is discharge per unit width.q= b 950 = 23.75 40 g acceleration due to gravity 32.1741ft / sec 23.752 У. 32.1741ft/sec2 y3 17.531 ye 2.6ft yyimplies that flow is sub critical

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