For the case of Reynolds analogy (Le = Pr = Sc = 1), it is clear that all three definitions of Bejan number are the same.
Also, Awad and Lage: obtained a modified form of the Bejan number, originally proposed by Bhattacharjee and Grosshandler for momentum processes, by replacing the dynamic viscosity appearing in the original proposition with the equivalent product of the fluid density and the momentum diffusivity of the fluid. This modified form is not only more akin to the physics it represents but it also has the advantage of being dependent on only one viscosity coefficient. Moreover, this simple modification allows for a much simpler extension of Bejan number to other diffusion processes, such as a heat or a species transfer process, by simply replacing the diffusivity coefficient. Consequently, a general Bejan number representation for any process involving pressure-drop and diffusion becomes possible. It is shown that this general representation yields analogous results for any process satisfying the Reynolds analogy (i.e., when Pr = Sc = 1), in which case the momentum, energy, and species concentration representations of Bejan number turn out to be the same.
Therefore, it would be more natural and broad to define Be in general, simply as:
is the fluid density
is the corresponding diffusivity of the process in consideration.
In addition, 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).
In the field of fluid mechanics the Bejan number is identical to the one defined in heat transfer problems, being the dimensionless pressure drop along the fluid path length in both external flows and internal flows:
is the dynamic viscosity
is the momentum diffusivity (or Kinematic viscosity).
A further expression of Bejan number in the Hagen-Poiseuille flow will be introduced by Awad. This expression is
The above expression shows that the Bejan number in the Hagen-Poiseuille flow is indeed a dimensionless group, not recognized previously.
The Bhattacharjee and Grosshandler formulation of the Bejan number has large importance on fluid dynamics in the case of the fluid flow over a horizontal plane  because it is directly related to fluid dynamic drag D by the following expression of drag force
which allows expressing the drag coefficient as a function of Bejan number and the ratio between wet area and front area :
where is the Reynolds Number related to fluid path length L. This expression has been verified experimentally in a wind tunnel.
^Bhattacharjee, S.; Grosshandler, W. L. (1988). "The formation of wall jet near a high temperature wall under microgravity environment". ASME 1988 National Heat Transfer Conference. 96: 711-716. Bibcode:1988nht.....1..711B.
^Herwig, H., and Schmandt, B., 2014. How to determine losses in a flow field: A paradigm shift towards the second law analysis." Entropy 16.6 (2014): 2959-2989. DOI:10.3390/e16062959 https://www.mdpi.com/1099-4300/16/6/2959