# Hagen–Poiseuille Equation

on . Posted in Fluid Dynamics

Hagen–Poiseuille equation, also called Hagen–Poiseuille Law, Poiseuille equation, or Poiseuille law, gives the pressure loss in a fluid flowing through a long cylindrical pipe.

## Hagen–Poiseuille Equation formula

$$\large{ \Delta p = \frac { 8 \; \mu \; l \; Q }{ \pi \; r^4 } }$$
Symbol English Metric
$$\large{ \Delta p }$$ = pressure loss $$\large{\frac{lbf}{in^2}}$$  $$\large{Pa}$$
$$\large{ \mu }$$  (Greek symbol mu) = dynamic viscosity $$\large{\frac{lbf-sec}{ft^2}}$$ $$\large{Pa-s}$$
$$\large{ l }$$ = length of pipe $$\large{ft}$$ $$\large{m}$$
$$\large{ \pi }$$ = Pi $$\large{3.141 592 653 ...}$$
$$\large{ r }$$ = pipe inside diameter $$\large{in}$$ $$\large{mm}$$
$$\large{ Q }$$ = volumetric flow rate $$\large{\frac{ft^3}{sec}}$$ $$\large{\frac{m^3}{s}}$$