Compressible Navier–Stokes flow with pressure-dependent viscosity and Navier-slip.

Second-order perturbation solution with compressibility as perturbation parameter.

Viscosity–density parameter at second order for axial velocity, density, flow rate.

Viscosity–density parameter at first order for pressure, Darcy friction factor.

Darcy friction factor, pressure drop may increase due to viscosity–pressure dependence.