Hagen–Poiseuille equation for pipe flow

SingleRain · December 12, 2011, 01:38

Hi All

I have a simple question, but it has confused me for a long time.

Why velocity equation of pipe flow (Hagen–Poiseuille equation) be related with pressure gradient and fluid viscosity, but without fluid density?

When I run numerical simulation case of pipe flow by FLUENT, the velocity will change if I only changed the value of density.

Any comments are very welcome! Thanks in advance!

Sincerely,

teopetre · December 12, 2011, 12:20

The Hagen-Poiseuille equation or law, is very often written in term of kynematics viscosity which is in fact the dynamic viscosity over fluid density. Making a paranthesis, the Reynolds number is the ratio of inertial to viscous forces, and the inertial ones are linked to density(the specific mass), so density should have influence upon your calculations. This law describes the pressure loss along a constant cross section pipe. Beneath, a more relevant measure of pressure loss could be deducted from pressure loss form of Darcy-Weisbach law which explicitely comprises the density(see wiki).

SingleRain · April 18, 2012, 21:41

Thank you very much!

vut · February 12, 2014, 10:52

Hi all,

This topic interest me. I have to prepare a mesh in Gambit for the Hagen-Poiseille flow through a cylindrical tube (length/diamter = 100).

How can I estimate the size of the mesh a long the length of the tube (length) and over its section?

Let's consider that at the inlet, there is a potential flow, no turbulence and the injection pressure is about 4bar?

Thank you very much,

December 12, 2011, 01:38	Hagen–Poiseuille equation for pipe flow	#1
SingleRain New Member SingleRain Join Date: Oct 2009 Posts: 5 Rep Power: 16	Hi All I have a simple question, but it has confused me for a long time. Why velocity equation of pipe flow (Hagen–Poiseuille equation) be related with pressure gradient and fluid viscosity, but without fluid density? When I run numerical simulation case of pipe flow by FLUENT, the velocity will change if I only changed the value of density. Any comments are very welcome! Thanks in advance! Sincerely,

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December 12, 2011, 12:20		#2
teopetre New Member Petrut Teodor Join Date: Feb 2010 Location: Romania Posts: 12 Rep Power: 16	The Hagen-Poiseuille equation or law, is very often written in term of kynematics viscosity which is in fact the dynamic viscosity over fluid density. Making a paranthesis, the Reynolds number is the ratio of inertial to viscous forces, and the inertial ones are linked to density(the specific mass), so density should have influence upon your calculations. This law describes the pressure loss along a constant cross section pipe. Beneath, a more relevant measure of pressure loss could be deducted from pressure loss form of Darcy-Weisbach law which explicitely comprises the density(see wiki).

April 18, 2012, 21:41		#3
SingleRain New Member SingleRain Join Date: Oct 2009 Posts: 5 Rep Power: 16	Thank you very much!

February 12, 2014, 10:52		#4
vut Member Join Date: Feb 2014 Posts: 57 Rep Power: 12	Hi all, This topic interest me. I have to prepare a mesh in Gambit for the Hagen-Poiseille flow through a cylindrical tube (length/diamter = 100). How can I estimate the size of the mesh a long the length of the tube (length) and over its section? Let's consider that at the inlet, there is a potential flow, no turbulence and the injection pressure is about 4bar? Thank you very much,