Calculating pipe diameter for half-flow condition/mannings equation

In summary, the conversation is about a student struggling to understand fluid mechanics and needing help with a specific problem involving Manning's equation and velocity calculations. They are also confused about how to find the diameter of a channel for a half-flow condition and whether the calculated velocity is suitable. The conversation also includes the necessary equations and an example slide for reference.
  • #1
kachi
9
0
Hello,

My knowledge on fluid mechanics is on a introductory level. When explaining, it would be great if you could explain in simple English and also like teaching to a student who isn't very good at the subject area!
I've been reading a lecture slide and have been trying to follow the example to solve my given problem. I don't really understand how the lecturer got certain parts of the solution though (equation hasn't been explained/defined on any of the slides). I don't understand how the lecturer found the diameter or the suitable velocity is for half-flow.

EDIT: The question doesn't require me to find whether the calculated velocity is suitable, but I would like to know how you do find it.

I have attached the slide that I'm using as an example below.

I used A = pi*D^2/8 and P = pi*D/2 as my problem is for half flow condition.

What is wrong? How do I do this correctly?

Thank you for reading. Any help would be appreciated, thank you.

Homework Statement



If water flows from Point D at Kinglake to Point E at Sugarloaf in a lined circular channel laid on a slope of 0.001. If Manning’s n = 0.013 and if the design discharge is 0.07 m^3/s, what diameter channel should be designed for a half-flow condition? What will be the mean velocity in the channel for this condition?

Manning’s n = 0.013
Slope = 0.001
Q, Discharge = 0.03m^3/s

Find diameter of channel for half flow condition.
Find mean velocity of channel in half flow condition.

Homework Equations



Mannings equation:[/B]

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Velocity equation:

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The Attempt at a Solution



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A = pi*D^2/8 and P = pi*D/2
Diamter, D = 0.53m^(8/3)

How do I find the diameter required for the channel from this? Is this (above) the diameter? I don't understand on the attachment below, how 0.52m^(8/3) becomes a diameter of 1.21 metres?

------

gif.gif

V = 0.07m^3/s/((pi*(0.53)^2)/8) = 0.634 m/s

How do I find whether the velocity I calculated is suitable?
 

Attachments

  • manningseq.png
    manningseq.png
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  • #2
You can't change the formula for the perimeter and/or area of a circle. If you want a half flow condition than divide the flow by 2.
 
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  • #3
Ok thank you.
 

Related to Calculating pipe diameter for half-flow condition/mannings equation

1. How do I calculate the diameter of a pipe for half-flow condition?

The diameter of a pipe for half-flow condition can be calculated using the Manning's equation, which is expressed as Q = (1.486/n) * A * R2/3 * S1/2, where Q is the flow rate, n is the Manning's roughness coefficient, A is the cross-sectional area of the pipe, R is the hydraulic radius, and S is the slope. To calculate the diameter, you need to set the flow rate to half of the maximum flow rate and solve for A. Once you have A, you can use the formula D = 2 * (A/π)1/2 to calculate the diameter of the pipe.

2. What is the Manning's roughness coefficient and how do I determine it?

The Manning's roughness coefficient is a measure of the resistance to flow in a channel or pipe. It takes into account the roughness of the channel walls, debris, and other obstructions that can affect the flow. The value of n varies depending on the type of material and condition of the channel. It can be determined through field measurements or by consulting engineering handbooks that provide typical values for different materials.

3. What is the hydraulic radius and how is it calculated?

The hydraulic radius is a measure of the efficiency of a channel or pipe in carrying water. It is defined as the cross-sectional area of the flow divided by the wetted perimeter. In other words, it is the average distance from the center of the channel to the surface of the water. It can be calculated using the formula R = A/P, where A is the cross-sectional area and P is the wetted perimeter.

4. Can I use the Manning's equation for any type of pipe material?

Yes, the Manning's equation can be used for any type of pipe material as long as you have the appropriate value of n for that material. However, it is important to note that the equation is derived based on the assumption of a smooth and uniform flow, so it may not be accurate for pipes with significant roughness or irregularities.

5. How do I account for changes in slope when calculating the diameter for half-flow condition?

The Manning's equation takes into account the slope of the channel or pipe. Therefore, if there are changes in slope, you need to calculate the average slope for the entire length of the channel or pipe and use that value in the equation. If there are significant changes in slope, it is recommended to divide the channel into smaller segments and calculate the diameter for each segment separately, then choose the largest diameter as the final result.

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