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Open Channel Problem 1 - Determine depth of flow and subcritical or supercritical flow:
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Find the flow depth for a trapezoidal channel with a 12' bottom, 3/1 side slopes, slope of energy grade line at 0.5% carrying 1500 cfs. What is the critical depth of the channel? Is the channel flow subcritical or supercritical? |
1. From the channels submenu open the flow (Q) calculation for a trapezoidal channel, ChannelQTrap.aspx. Input the "Title" of the calculation, the "Designer/Checker" information and the variables. For the iterative design, guess at a depth of 4 feet.
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2.
For the manning's roughness coefficient open up the coefficient table and look up the correct manning's coefficient.
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3. Put in the manning's coefficient and click on the "Calculate" button. Review the results. A depth of 4' gives a flow of 541 cfs.
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4.
Try the calculation again using a depth of 6 feet. Review the results. A depth of 6 feet gives a flow of 1270 cfs.
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5.
Try the calculation again using a depth of 6.5 feet. Review the results. A depth of 6.5 feet gives 1511 cfs. The flow depth is 6.5 feet.
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6.
To determine the critical depth from the channels menu, open the critical depth for trapezoidal channel calculation, DcTrapezoid.aspx. Input the "Title" information, "Designer/Checker" information and the input variables. Click on the "Calculate" button and review the results. The Critical Depth, Dc is 4.5 feet.
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7.
From the critical depth we know that if the critical depth is less than the flow depth that the flow is subcritical. We can also check the Froude number to validate that the flow is subcritical. If the Froude number is less than 1 then the flow is subcritical.
From the Channels submenu open the Froude number calculation, FroudeOther.aspx. Input the "Title", "Designer/Checker" and variable information. Click on the "Calculate" button and review the results. The Froude number is 0.64. Therefore the flow is subcritical.
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8. Summary
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The depth of flow in the channel at 1500 cfs is 6.5 feet. The critical depth is 4.5 feet. The flow is subcritical since the critical depth is less than the flow depth and the Froude number is 0.64 which is less than 1.
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