# Poiseuille’s equation

QUESTION
I’m working on some design and I needed to evaluate volume flow rate. Tried to use Poiseuille’s equation but was suspicious about results so I made simple test and measured flow rate of water and compared it to Poiseuille’s equation results, they were very different.

Test setup is simple, water pressure reducer and after it 1m hose opened to atmosphere. I measured

• water flow rate of 480 lit/h,
• inlet pressure P1=0.2 bar = 20 000 Pa
• Outlet pressure P2=0 bar - opened to atmosphere
• Hose internal diameter 1/4" => radius r= 3.175 mm = 0,003175m
• Hose length L = 1 m
• Viscosity of water n = 0,001 Pa.s

So when I used Poiseuille’s equation
Q= PI * dP * r^4 / 8 * n * L

I get ridiculous results:

Q = ( 3.14 * 20000 * 0.003175^4 ) / ( 8 * 0.001 * 1) = 0.0008 m3/s that would be 47 lit/min which is impossible as I get 8 lit/min on test. So I am confused and would appreciate any help

I don’t have fully developed flow I understand that, but results are far to different, so I assume I made some mistake. Any idea on what I did wrong?

REPLIES

katmar
Poiseuille’s equation applies to laminar flow, but your Reynolds number at 8 litre/minute is nearly 27 000 and the flow regime will definitely be turbulent. You need to have a Reynolds number below 2000 for Poiseuille’s equation to apply.

SOURCE