How this calculator works
Fully developed laminar flow has a parabolic velocity profile in a circular tube with no slip at the wall. Balancing viscous shear against pressure gradient gives Poiseuille law. It assumes a Newtonian fluid, a rigid straight tube and constant viscosity. Entrance effects, turbulence, compressibility and non-Newtonian behaviour are excluded. Check Reynolds number separately; satisfying this formula does not establish that flow is laminar.
Formula
Q = pi r^4 delta p/(8 mu L). Hydraulic resistance Rh = delta p/Q = 8 mu L/(pi r^4), measured in Pa s/m3, not Pa s.
Worked example
For r = 0.001 m, L = 1 m, mu = 0.001 Pa s and delta p = 100 Pa, Q = 3.926990817e-8 m3/s. Doubling radius increases flow sixteenfold to 6.283185307e-7 m3/s.
Advertisement
Frequently asked questions
Can I enter diameter in the radius field?
Divide diameter by two first. Using diameter directly would overestimate flow by a factor of sixteen.
Is hydraulic resistance a viscosity?
No. Resistance also includes tube geometry and has units Pa s/m3.
Does the equation work for turbulent flow?
No. Use Darcy-Weisbach with an appropriate friction factor when the laminar assumptions fail.