Open Channel Flow (mannings equation)

[Stacyg]

A trapezoidal channel with side batters 1:1 and Manning's n value of 0.025 has a bed slope of 0.0045 m/m. When the depth is equal to the bottom width the discharge is 7.5 m^3/s. Calculate the bottom width to the nearest 0.01m.

Using mannings equation

V= 1/n.R^2/3.S^1/2

S=0.0045 n=0.025 Q=7.5

Q=V.A V=Q/A

I don't know where to start I know how to use the equation and we have been shown how to use some graphs for the solution of mannings formula but I'm not sure on using them.
Any help would be great thanks

 

[civilGuy20]

Hey,

I guess you may have found the answers you are looking for. But just in case you are still searching go to http://flowsizer.com" they have a nice clean mannings calculator that will get you the answers to those equations

 

[Mene]

I can provide some guidance on how to solve this problem using Manning's equation. First, let's define the variables in the equation:

V = velocity of the flow (m/s)
n = Manning's roughness coefficient
R = hydraulic radius (m)
S = bed slope (m/m)
Q = discharge (m^3/s)
A = cross-sectional area of the channel (m^2)

We are given the values for S, n, and Q, and we want to find the bottom width (B) of the channel. To do this, we need to rearrange the equation to solve for A:

Q = V*A

A = Q/V

Next, we can substitute in the values for Q and V:

A = 7.5/1.45 = 5.17 m^2

Now, we can use the formula for the cross-sectional area of a trapezoidal channel:

A = (B + z)*z

Where B is the bottom width and z is the depth of flow. Since we are given that the depth is equal to the bottom width, we can rewrite the equation as:

A = (B + B)*B

Simplifying:

A = 2B^2

Now, we can substitute in the value for A that we found earlier and solve for B:

5.17 = 2B^2

B^2 = 2.585

B = 1.61 m

Therefore, the bottom width of the channel is approximately 1.61 m. Keep in mind that this is only an approximation, as the given values may not be exact. To get a more precise answer, you can use the graphs that you mentioned or use a numerical method, such as the Newton-Raphson method, to solve for B. I hope this helps!