Numerical solutions of the simplified Navier-Slokes and continuity equations applicable to the laminar vapor flow in slender cylindrical heal pipes are presented. The number of unknowns is reduced to two by eliminating the pressure gradient term. A numerical marching procedure is used to solve the governing nonlinear differential equation. The effect of fractional and momentum pressure drops on the static pressure is studied for values of the wall Reynolds number in the range 2 to −5.