Volume Flow Rate in a Pipe for Viscous Fluid

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SUMMARY

The discussion focuses on calculating the volume flow rate (Q) of glycerine through a circular pipe with a diameter of 100mm under different conditions. The gauge pressure at 50m from the exit is 458 kPa, with glycerine properties defined as ρ=1260 kg/m³ and μ=0.9 kg/ms. The correct volume flow rates are established as 25 litres/s for a horizontal pipe, 13.5 litres/s for a pipe inclined upwards by 20°, and 36.5 litres/s for a pipe inclined downwards by 20°. The formula used for these calculations is Q = (∏d^4 / 128μ) * (ΔPloss / length), emphasizing the importance of distinguishing between gauge and absolute pressure.

PREREQUISITES
  • Understanding of fluid dynamics principles, specifically viscous flow.
  • Familiarity with the Hagen-Poiseuille equation for laminar flow.
  • Knowledge of pressure measurements, including gauge and absolute pressure.
  • Basic thermodynamics concepts related to fluid behavior.
NEXT STEPS
  • Study the Hagen-Poiseuille equation in detail to understand laminar flow calculations.
  • Learn about Bernoulli's equation and its applications in fluid dynamics.
  • Research the effects of pipe inclination on flow rates in viscous fluids.
  • Explore the properties of glycerine and how they affect flow characteristics in pipes.
USEFUL FOR

Students studying thermodynamics, engineers working with fluid systems, and anyone involved in the analysis of viscous fluid flow in pipes.

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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