I'd like to perform some calculations on adiabatic compressible pipe flow as I'm starting a project with pneumatic transport.

I came across a few different approaches:

1) The Fanno relations, which seem to be a more generally accepted approach, e.g. Fundamentals of Compressible Flow, by Brian J. Cantwell

2) Richard Turton, “A new approach to non choking adiabatic compressible flow of an ideal gas pipes with friction”, The Chemzcal Engzneerzng Journal, 30 (1985) 159 - 160 However I have some difficulty with the equation 5) that has units of [s/m] instead of [kg/s]

3) Fucheng Teng, Pedro Medina and Mark Heigold, Compressible Fluid Flow Calculation Methods, Chemical Engineering www.che.com february 2014. I do like this approach although I believe there are a few mistakes in the equations. Did anybody ever check if this approach agrees with the Fanno equations?