# Poiseuille's Equation for Compressible Fluids

Written by Jerry Ratzlaff on . Posted in Fluid Dynamics

## Poiseuille's Velocity Equation for Compressible Fluids formula

$$\large{ v = \frac{ r^2 }{ 16 \; \eta \; l } \; \frac{ p_1^2 \;-\; p_2^2 }{ p_1 } }$$
Symbol 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 $$\large{\frac{lbf - sec}{ft^2}}$$ $$\large{ Pa - s }$$