The Hagen number is a dimensionless number used in forced flow calculations. It is the forced flow equivalent of the Grashof number.

It is defined as:

$$

mathit{Hg} = -frac{1}{rho}frac{mathrm{d} p}{ mathrm{d} x}frac{L^3}{nu^2}

where:

• $frac\{mathrm\{d\}\; p\}\{mathrm\{d\}\; x\}$ is the pressure gradient
• L is a characteristic length
• $rho$ is the fluid density
• $nu$ is the kinematic viscosity

For natural convection

$$

frac{mathrm{d}p}{mathrm{d}x} = rho g beta Delta T,

and so the Hagen number then coincides with the Grashof number.

See also