The flow profile correction factor, β, accounts for the ratio of the integrated local square velocity field to the square of the integrated local velocity field (see Equation 9-3). It is defined in terms of the total velocity field (background plus acoustic variations).

In the case of no-background flow (u0 = 0) β is 1 in the absence of a wall drag coefficient, as only plane wave modes propagate. If a wall drag force is introduced, to model some loss mechanism, β starts to differ slightly from 1. This can for example be losses introduced to model viscous and thermal effects in narrow pipes.

In the presence of a background u0 the factor β can be set different 1 in order to model a nonflat velocity profile inside the tube. The value of b (and the actual shape of the background field) influences the convective momentum transfer balances. The places where β enter the governing equations are multiplied with either the Mach number or the Mach number squared, indicating that the effects become important for an increasing background flow.