Hagen Number

Hagen number, abbreviated Hg, a dimensionless number, is used in fluid dynamics to describe the relative importance of viscous forces to surface tension forces in a liquid flow.  The Hagen number is particularly relevant in capillary flow and other situations where both viscous and surface tension effects play a role.  It helps characterize the behavior of a liquid as it moves through a narrow conduit or capillary.

Hagen Number Interpretation

Hg < 1  -  Viscous forces dominate over surface tension forces.  In this case, the flow is typically smooth and well behaved, similar to a viscous flow in a larger conduit.
Hg > 1  -  Surface tension forces dominate over viscous forces.  This can lead to the formation of menisci and capillary effects that significantly influence the flow pattern, particularly in narrow passages.

The Hagen number is crucial in understanding fluid flow in microfluidics, capillary tubes, and porous media, where the interaction between viscous and surface tension forces becomes important.  It's also relevant in applications involving liquid transport, such as in certain medical devices, inkjet printing, and oil reservoir modeling.

 

Hagen number formula
\( Hg \;=\; (1 \;/\; \rho) \; (d p \;/\; d x) \;  (l^3  \;/\; \nu^2)  \)
Symbol	English	Metric
\( Hg \) = Hagen Number	\( dimensionless \)	\( dimensionless \)
\( \rho \)  (Greek symbol rho) = Fluid Density	\(lbm\;/\;ft^3\)	\(kg\;/\;m^3\)
\( d p \) = Pressure Differential	\(lbf\;/\;in^2\)	\(Pa\)
\( \frac {d p}{d x}  \) = Pressure Gradient	\(psi\;/\;ft\)	\(Pa\;/\;m\)
\(  d x  \) = Distance Between Pressure Centers	\(t\)	\(m\)
\( l \) = Length	\(ft\)	\(m\)
\( \nu \)  (Greek symbol nu) = Kinematic Viscosity	\(ft^2\;/\;sec\)	\(m^2\;/\;s\)