The entrance region has been divided into two parts, the inlet region and the filled region. At the end of the inlet region, the boundary layers meet at the pipe axis but the velocity profiles are not yet similar. In the filled region, adjustment of the completely viscous profile takes place until the Poiseuille similar profile is attained at the end of it. The boundary-layer equations in the inlet region and the Navier-Stokes equations with order-of-magnitude analysis in the filled region are solved using fourth-degree velocity profiles. The total length of the entrance region so obtained is ξ = x/R Re = 0·150, whereas the boundary layers are observed to meet at approximately one-quarter of the entrance length, i.e. at ξ = 0·036. Experiments reported in the paper corroborate the analytical results.
The boundary layer form of the conservation equations for supersonic flow of a perfect gas in the inlet region of a smooth circular pipe are solved numerically using the Von Karman-Pohlhausen integral technique. The wall condition is adiabatic, and the thermal and hydrodynamic boundary layers are considered to be of equal thickness. Details of boundary layer development, choking condition, pressure gradient, wall shear stress and temperature are presented for different inlet Mach number values. The trend of results is in agreement with one-dimensional Fanno line predictions.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.