Viscous gas flow through a nozzle treated as an exponential function

Exact solutions for quasi-one-dimensional compressible viscous flows in conical nozzles

“…Instead, there are no available solutions for the steady-state problem, in closed form, for a compressible viscous flow through a variable cross-section pipe: the generally adopted methodology involves calibrating the isentropic model using empirical factors for a given viscous gas, or applying other empirical models (Senftle et al. 2003). In fact, exact solutions can only be determined for a variable area Fanno flow if an additional function, which relates the change in pressure to the change in area, is hypothesised for the pipe (Loh 1970), but such a function is generally unknown a priori .…”