How Does Dimensional Analysis Relate Flow Rate to Propeller Speed in a Pipe?

AI Thread Summary
Dimensional analysis can relate flow rate to propeller speed by utilizing the Buckingham Pi Theorem. The expression for volume flow rate, Q, incorporates the pipe diameter (D), propeller rotational speed (N), and a dimensionless function of density and viscosity. Understanding how these variables interact is crucial for deriving the relationship. The discussion highlights the importance of familiarizing oneself with the Buckingham Pi Theorem to clarify the derivation process. Engaging with these concepts will aid in resolving the confusion surrounding the topic.
kris
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I have this queston:

The flow rate in a pipe is assessed by measuring the speed of rotation of a propeller having its axis along the pipe centre-line. Show by dimensional analysis that the volume flow rate, Q, is given bu the expression:

Q=(D^3).N.Phi.(d/D,(density.(D^2).N)/viscosity)

where D= diameter of the pipe,
d=diameter of the pipe
N=the rotational speed of the propeller

I'm very confused as to how to go about this, any help would be appreciated.
 
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Have you read up on the Buckingham Pi Theorem?
 
Have you read up on the Buckingham Pi Theorem?
 
no i haven't but i will now, thank you
 

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