where [c.sub.0] and M(x) = [v.sub.0](x)/[c.sub.0] represent the adiabatic sound speed and the local Mach number, respectively.
As the local Mach number near the wall is smaller than that near the pipeline center, the contribution of the flow profile on the propagation speed is slight in the downstream propagation.
As a result, in the downstream propagation, the local Mach number near the pipeline wall slightly accelerates the propagation speed compared with that near the pipeline center.