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:
where:
For natural convection
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 is equal to the flow length. 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, all these three definitions of Hagen number will be the same. The general form of the Hagen number is
where