Calculating pipe diameter for half-flow condition/mannings equation

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The discussion focuses on calculating the pipe diameter and mean velocity for a half-flow condition using Manning's equation. The user is struggling to understand the derivation of certain equations and how to apply them correctly, particularly in determining the diameter and suitable velocity for the given discharge. They have attempted calculations using specific formulas for area and perimeter but are confused about how to arrive at the correct diameter. The user seeks clarification on whether their calculated velocity is appropriate and how to properly assess it. Overall, the thread emphasizes the need for clear explanations in fluid mechanics concepts.
kachi
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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

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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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Ok thank you.
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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