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Hagen number

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:

• $frac\left\{mathrm\left\{d\right\} p\right\}\left\{mathrm\left\{d\right\} x\right\}$ 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.