Jets manifest in a wide variety of astrophysical phenomena. We study them using a semi-analytical model of the General Relativistic Magnetohydrodynamic (GRMHD) equations in Kerr metric that describes the jet near the rotation axis, assuming steady state, and axisymmetry. The model is constructed by expanding the rotating black hole metric and the forces, with respect to the polar angle about the rotation axis. This results in all the physical quantities being expressed as functions of the radial distance. The goal is to solve for the bulk acceleration, the shape of the jet, and understand how these depend on the magnetic field. The addition to the previous semi-analytical models that expand the metric around the rotation axis, is that the flow is governed by a polytropic equation of state. The solutions in this presentation start from a stagnation surface very close to the event horizon and become highly relativistic at large distances.