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Old   February 7, 2010, 09:18
Default Dimensional Analysis question
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Hi there,

Flow over a weir in an open rectangular channel is given by the relationship:[latex]Q=\phi(H,V,g,B)[/latex] where:

Q is the flowrate (m^3/s),
B width of the weir (m),
Hthe height of the water above the weir(m),
V the mean velocity of water (m/s),
g gravity (m/s^2)

Would you help me find a relationship between Q and these variables please? I keep getting really stuck because I know the equation is actually: [latex]Q=KB\sqrt{\dfrac{2}{3g}}(H+\dfrac{v^2}{2})^{3/2}[/latex]
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Old   February 7, 2010, 17:28
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The forum cannot render latex. You will have to insert images of the equations.

But I can't see your point. You just stated the equation so why do you need to find the relationship? Is there something wrong with the equation you stated? These questions are best answered by you in your work anyway as they are specific to your work.
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Old   February 8, 2010, 09:19
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Quote:
Originally Posted by ghorrocks View Post
The forum cannot render latex. You will have to insert images of the equations.

But I can't see your point. You just stated the equation so why do you need to find the relationship? Is there something wrong with the equation you stated? These questions are best answered by you in your work anyway as they are specific to your work.
I'm demonstrating the usefulness of weirs to undergraduates and would like to be able to show the relationship between flow rate and head height can be deduced through dimensional analysis. What I'd like the students then to do is carry out an experiment to find the constants of proportionality and the exponents. Thing is I can't seem to prove it myself. Do you see what I'm after?
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Old   February 8, 2010, 18:15
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Quote:
Do you see what I'm after?
I do not see what you are after yet. Do you want to so a series of simulations at various head heights, obtain the flow rates and then use the dimensional analysis relationship to curve fit the constants and exponents?
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Old   February 9, 2010, 06:59
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Quote:
Originally Posted by ghorrocks View Post
I do not see what you are after yet. Do you want to so a series of simulations at various head heights, obtain the flow rates and then use the dimensional analysis relationship to curve fit the constants and exponents?
Thank you for making it concise and simple . Yes that is what I'd like to accomplish. The exercise in doing the simulations and calculating the line of best fit and hence coefficients and exponents is pretty straight forward. What I'm having trouble with at the moment is actually finding the relationship ( priori) between the variables by means of dimensional analysis to get them started. Does that make more sense?

Best regards,
kingjewel1
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Old   February 9, 2010, 07:41
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So your question is about dimensional analysis, not CFD.

Here's how I would do it:
http://en.wikipedia.org/wiki/Buckingham_%CF%80_theorem
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