Small or large sizes of certain dimensionless parameters indicate the importance of certain terms in the equations for the studied flow.
Further, non-dimensionalized Navier–Stokes equations can be beneficial if one is posed with similar physical situations – that is problems where the only changes are those of the basic dimensions of the system.
[3] Scaling helps provide better understanding of the physical situation, with the variation in dimensions of the parameters involved in the equation.
This allows for experiments to be conducted on smaller scale prototypes provided that any physical effects which are not included in the non-dimensionalized equation are unimportant.
The incompressible Navier–Stokes momentum equation is written as: where ρ is the density, p is the pressure, ν is the kinematic viscosity, u is the flow velocity, and g is the body acceleration field.
The non-dimensionalized Euler equation for an inviscid flow is Density variation due to both concentration and temperature is an important field of study in double diffusive convection.
Non dimensionalizing using the scale: we get where ST, TT denote the salinity and temperature at top layer, SB, TB denote the salinity and temperature at bottom layer, Ra is the Rayleigh Number, and Pr is the Prandtl Number.