The Hagen number (Hg) is a

dimensionless number A dimensionless quantity (also known as a bare quantity, pure quantity, or scalar quantity as well as quantity of dimension one) is a quantity to which no physical dimension is assigned, with a corresponding SI unit of measurement of one (or 1) ...

used in forced flow calculations. It is the forced flow equivalent of the Grashof number and was named after the German

hydraulic Hydraulics (from Greek: Υδραυλική) is a technology and applied science using engineering, chemistry, and other sciences involving the mechanical properties and use of liquids. At a very basic level, hydraulics is the liquid counter ...

engineer G. H. L. Hagen. It is defined as: :

\mathrm = -\frac\frac\frac

where: *

\frac

is the pressure gradient *''L'' is a characteristic length *''ρ'' is the fluid

density Density (volumetric mass density or specific mass) is the substance's mass per unit of volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' can also be used. Mathematical ...

*''ν'' is the

kinematic viscosity The viscosity of a fluid is a measure of its resistance to deformation at a given rate. For liquids, it corresponds to the informal concept of "thickness": for example, syrup has a higher viscosity than water. Viscosity quantifies the inter ...

For natural convection :

\frac = \rho g \beta \Delta T,

and so the Hagen number then coincides with the Grashof number. Awad: 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 = -\frac\frac\frac

where :

\delta

is the corresponding diffusivity of the process in consideration

References

{{NonDimFluMech Dimensionless numbers