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

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Discussion Overview

The discussion revolves around the relationship between flow rate and propeller speed in a pipe, specifically through the lens of dimensional analysis. Participants are exploring how to derive an expression for volume flow rate using relevant parameters such as pipe diameter, propeller speed, and fluid properties.

Discussion Character

  • Exploratory, Technical explanation, Homework-related

Main Points Raised

  • One participant presents a question regarding the derivation of a volume flow rate expression using dimensional analysis, citing specific parameters like pipe diameter and propeller speed.
  • Another participant suggests looking into the Buckingham Pi Theorem as a potential method for addressing the problem.
  • A subsequent reply indicates that the participant has not yet reviewed the Buckingham Pi Theorem but intends to do so.

Areas of Agreement / Disagreement

There is no consensus yet, as participants are still in the early stages of exploring the topic and have not yet engaged in detailed discussion or analysis.

Contextual Notes

Participants have not yet established any assumptions or definitions that may be critical for the dimensional analysis, and there are unresolved steps in the derivation process.

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.
 
Engineering news on Phys.org
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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