Civil Engineering Hydraulics. Backwater Profile Nonrectangular Section. Backwater Profile

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Dorthy Stevens
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the universe is that none of it has tried to contact us.

1 Civil Engineering Hydraulics Backwater Profile Nonrectangular Section Sometimes I think the surest sign that intelligent life exists elsewhere in the universe is that none of it has tried to contact us. Backwater Profile This expression is consistent across any type of channel section. S0 Sf ( 1 Fr 2 2 ) dz dx 1

2 Backwater Profile The changes will come in the expressions for Sf and Fr. S0 Sf ( 1 Fr 2 3 ) dz dx Backwater Profile The slope of the channel will still be approximated by tanθ sinθ θ S0 Sf (1 Fr ) 2 () sin θ Sf (1 Fr ) 2 dz dx dz dx 2

3 Backwater Profile Sf can be expressed as The hydraulic radius will be dependent on the channel geometry It will still be the ratio of the flow area divided by the wetted perimeter () sin θ Sf (1 Fr ) 2 Sf n 2v 2 Rh 3 () sin θ n 2v 2 Rh 3 (1 Fr ) 2 5 dz dx dz dx Backwater Profile The Froude number is The subscript on the z denotes that the mean depth is used This is the ratio of the top width to the area of the flow () sin θ n 2v 2 Rh 3 (1 Fr ) 2 Fr () dz dx v gzm sin θ n 2v 2 Rh 3 dz 2 dx v 1 gz m 6 3

4 Backwater Profile To utilize this method for any type of channel, be sure to use the zm () sin θ n 2v 2 Rh 3 (1 Fr ) 2 Fr dz dx v gzm () sin θ n 2v 2 Rh 3 dz dx v2 1 gz m 7 Backwater Profile 8 We will still use this expression, but we will need to have expression reflect the channel geometry for the hydraulic radius and the mean depth () sin θ n 2v 2 Rh 3 Δz Δx v2 1 gz m

5 Backwater Profile 9 A triangular channel is made of concrete (m1:1) and conveys water at a flow rate of 20 m3/s. A dam in the channel is used to contain the flow; the water depth at the dam is 6.2 m. The channel slope is Determine the shape of the backwater curve () sin θ n 2v 2 Rh 3 Δz Δx v2 1 gz m Backwater Profile 10 A triangular channel is made of concrete (m1:1) and conveys water at a flow rate of 20 m3/s. A dam in the channel is used to contain the flow; the water depth at the dam is 6.2 m. The channel slope is Determine the shape of the backwater curve We can work from the worksheet we developed in the previous class and see what changes we need to make. () sin θ n 2v 2 Rh 3 Δz 2 Δx v 1 gz m 5

6 To start, I just made a copy of the worksheet we developed previously. 11 The known values are entered. In this case, we cannot enter the width because it is a function of the depth of flow in the channel. The known values are entered. In this case, we cannot enter the width because it is a function of the depth of flow in the channel. 12 6

Since a number of these formulas were based on the channel width, errors will appear now that we have removed the

7 The known values are entered. In this case, we cannot enter the width because it is a function of the depth of flow in the channel. Since a number of these formulas were based on the channel width, errors will appear now that we have removed the width variable. 13 The known values are entered. In this case, we cannot enter the width because it is a function of the depth of flow in the channel. With a 1:1 slope the Top Width will be equal to twice the depth. 1 7

9 Since the mean depth is used for the Fr calculation, this is the value that we need to match

21 Homework A trapezoidal channel is brick-lined with b m, side slope of 1:0.8, and S The water depth over a dam placed at the downstream end is 7.2 m. For a volume flow rate over the dam of 100 m3/s, calculate and plot the backwater curve upstream of the dam until the depth of flow is approximately normal depth. 21

Civil Engineering Hydraulics. Backwater Profile

Civil Engineering Hydraulics. Backwater Profile Civil Engineering Hydraulics God put me on this earth to accomplish a certain number of things. Right now I am so far behind that I will never die. Last class, we derived an expression for the change in