Hagen Number

The Hagen number is a dimensionless number used in forced flow calculations. It is the forced flow equivalent of the Grashof number and was named after the German hydraulic engineer G. H. L. Hagen.

It is defined as:

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

where:

  • is the pressure gradient
  • L is a characteristic length
  • is the fluid density
  • 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.

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