Talk:Poiseuille's law

Could somebody add how it's the name pronounced? (IPA code) 213.98.180.215 14:17, 21 August 2007 (UTC)

Should merge this with Hagen-Poiseuille_flow article. 194.171.252.100 10:23, 14 September 2007 (UTC)

The article should make use consistent symbols. L and $$\Delta x$$ both refer to the length of the tube. Also, is it really necessary to introduce the variable s when we are just going to call it r later on.

The article should also stop referring to 'mathematical tricks'. This makes the deriviation sound more hand-wavy than necessary. —Preceding unsigned comment added by 129.112.109.251 (talk) 19:39, 17 January 2008 (UTC)

=
=== I think it's pronounced approximately pwah-zoy.

I agree with the comments about L, s, and "tricks".

The derivation given here seems to me unnecessarily complicated. It proceeds by equating to zero the net force on a thin cylindrical shell of radius r. This necessitates computing the viscous force of the fluid both inside and outside the shell, and yields a second order differential equation for the velocity as a function of radius v(r). A simpler way to proceed is to equate to zero the net force on a SOLID cylinder of radius r, on the grounds that in steady flow the center of mass of this cylinder is not accelerating. (The fact that there are internal viscous forces in this cylinder is irrelevant, since they cancel thanks to Newton's third law.) Then the only viscous force on the cylinder is from the fluid outside it. This yields directly a first order differential equation for v(r). The derivation goes like this, using the same notation as the present article:

The net pressure force is -(Delta p)(pi r^2), while the next viscous force is eta v'(r) 2pi r Delta x. The sum must vanish, so v'(r) = (1/2 eta)(Delta p/Delta x) r. Viola! The solution is v(r) = -(1/4 eta)|Delta p/Delta x| r^2 + v(0), where I took into account the fact that p is decreasing with x to replace (Delta p/Delta x) by -|Delta p/Delta x|. Setting v(R)=0 then yields v(0)=(1/4 eta)|Delta p/Delta x| R^2, so v(r) = (1/4 eta)|Delta p/Delta x| (R^2 - r^2). —Preceding unsigned comment added by 216.164.50.50 (talk) 07:56, 16 February 2008 (UTC)