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). Fluid mechanics 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: where 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 where is the Reynolds number is the flow length is the pipe diameter 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. This equation represents the drag coefficient in terms of second law of thermodynamics: where is entropy generation rate and is exergy dissipation rate and ρ is density. The above formulation allows expressing Bejan number in terms of second law of thermodynamics: This expression is a fundamental step toward a representation of fluid dynamic problems in terms of the second law of thermodynamics. See also Adrian Bejan Entropy Exergy Thermodynamics Constructal theory References Dimensionless numbers of thermodynamics Dimensionless numbers of fluid mechanics Convection