Civil engineering - manning's equation through channel

[Dawei]

civil engineering -- manning's equation through channel

Homework Statement

I'm given the slope S, the flow Q, the n value, and the diameter of the pipe. I am asked if the channel can handle a certain depth D of water.

Homework Equations

V = (1/n)*R^(2/3) x S^(1/2)

The Attempt at a Solution

I don't understand what I need to do. R is the hydraulic depth which is defined as the cross sectional flow divided by the wetted perimeter. Do I use the depth in question, D, and convert this into a hydraulic radius? How? I don't know how to calculate the area of a circle filled to just above half of its radius...

 

[mark726]

Thank you for your post. It seems like you are trying to use Manning's equation to determine if a channel can handle a certain depth of water. Manning's equation is commonly used in civil engineering to calculate the flow of water in open channels, such as rivers or pipes.

To answer your question, yes, you will need to use the depth in question, D, and convert it into a hydraulic radius. This can be done using the formula for the area of a circle (πr^2), where r is the radius of the pipe. However, in this case, the radius will not be the full radius of the pipe, but rather the hydraulic radius, which is defined as the cross-sectional flow area divided by the wetted perimeter. The wetted perimeter is the perimeter of the pipe that is in contact with the water.

Once you have calculated the hydraulic radius, you can plug it into Manning's equation along with the other given parameters (slope, flow, and n value) to determine the velocity of the water. If the velocity is within the acceptable range for the channel, then it can handle the given depth of water. If the velocity is too high, then the channel may not be able to handle the depth and could potentially overflow.

I hope this helps to clarify the steps you need to take to solve this problem. If you need further assistance, please don't hesitate to ask. Keep up the good work in your studies!