Volume Flow Rate in a Pipe for Viscous Fluid

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Discussion Overview

The discussion revolves around calculating the volume flow rate of glycerine in a circular pipe under different conditions of inclination and verifying whether the flow is laminar. The context includes a homework problem related to thermodynamics and fluid mechanics.

Discussion Character

  • Homework-related
  • Technical explanation

Main Points Raised

  • One participant presents a problem involving the flow of glycerine through a pipe and seeks assistance in calculating the volume flow rate under various conditions.
  • The participant uses the equation Q = (∏d^4 / 128μ) * (ΔPloss / length) but expresses uncertainty about the correctness of their approach.
  • Another participant suggests using Bernoulli's equation as an alternative method for solving the problem.
  • A different participant confirms that the original formula provided works for part (i) of the problem, questioning whether the poster is confusing gauge pressure with absolute pressure.
  • The original poster acknowledges the potential mix-up between gauge and absolute pressure, indicating a moment of realization about their error.

Areas of Agreement / Disagreement

Participants appear to agree that the formula can be used to solve the problem, but there is uncertainty regarding the correct interpretation of pressure types, indicating a lack of consensus on that aspect.

Contextual Notes

The discussion does not resolve the specific calculations or assumptions regarding the pressure types, and the implications of using gauge versus absolute pressure remain unclear.

jde23
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Homework Statement



Hi, my first post here! I have a Thermodynamics resit over the summer and I'm trying to get my head around viscous flow, I'm stuck at a question and need help! Thanks :)

Glycerine discharges to the atmosphere through a circular pipe 100mm in diameter. The gauge pressure 50m from the exit is 458 kPa. Data for glycerine: ρ=1260 kg/m^3, μ=0.9 kg/ms.

Determine the volume flow rate Q for the following cases:
(i) a horizontal pipe (verify the flow is laminar!) (Ans: 25 litres/s)
(ii) a pipe inclined upwards by 20° (Ans: 13.5 litres/s)
(iii) a pipe inclined downwards by 20° (Ans: 36.5 litres/s)

Homework Equations



I thought this equation was the right one to use but my answer is totally wrong when I plug the numbers in, it's not a units thing either...

Q = (∏d^4 / 128μ) * (ΔPloss / length)

The Attempt at a Solution



I assumed the gauge pressure at the pipe exit is equal to atm pressure, so 100kPa - is this correct? The rest is just plugging numbers in. Am I missing something obvious here...?
 
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Have you tried using Bernoulli's equation?
 
Your formula works. I get 25 for part i. Are you mixing gauge pressure and absolute pressure?
 
Hi LawrenceC, yes I think I am! Embarrassing moment, whoops...

Thanks!
 

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