# Poiseuille's Equation for Compressible Fluids

Written by Jerry Ratzlaff on . Posted in Fluid Dynamics

## Poiseuille's Velocity Equation for Compressible Fluids formula

 $$\large{ v = \frac{ r^2 }{ 16 \; \eta \; l } \; \frac{ p_1^2 \;-\; p_2^2 }{ p_1 } }$$

### Where:

 Units English Metric $$\large{ v }$$ = velocity of fluid $$\large{\frac{ft}{sec}}$$ $$\large{\frac{m}{s}}$$ $$\large{ l }$$ = length of tube $$\large{ft}$$ $$\large{m}$$ $$\large{ p_i }$$ = input pressure $$\large{\frac{lbf}{in^2}}$$ $$\large{Pa}$$ $$\large{ p_o }$$ = output pressure $$\large{\frac{lbf}{in^2}}$$ $$\large{Pa}$$ $$\large{ r }$$ = radius of tube $$\large{in}$$ $$\large{mm}$$ $$\large{ \eta }$$  (Greek symbol eta) = viscosity of fluid $$\large{\frac{lbf - sec}{ft^2}}$$ $$\large{ Pa - s }$$