Hagen number

It is defined as:

: $$

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

where:

• $\backslash frac\{\backslash mathrm\{d\}p\}\{\backslash mathrm\{d\}x\}$ is the pressure gradient
• L is a characteristic length
• ρ is the fluid density
• ν 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.

Awad:{{cite journal |first=M.M. |last=Awad |title=Hagen number versus Bejan number |journal=Thermal Science |volume=17 |issue=4 |year=2013 |pages=1245–1250 |doi=10.2298/TSCI1304245A |doi-access=free }} presented Hagen number vs. Bejan number. Although their physical meaning is not the same because the former represents the dimensionless pressure

gradient while the latter represents the dimensionless pressure drop, it will be

shown that Hagen number coincides with Bejan number in cases where the characteristic

length (l) is equal to the flow length (L). Also, a new expression of Bejan

number in the Hagen-Poiseuille flow will be introduced. In addition, extending the Hagen number to a general form will be presented. For the case of Reynolds analogy (Pr = Sc = 1), all these three definitions of Hagen number will be the same. The general form of the Hagen number is

: $$

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

where

: $\backslash delta$ is the corresponding diffusivity of the process in consideration

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Category:Dimensionless numbers of physics

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