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This study presents a semi analytical solution for the transient weakly underexpanded jet. Different polytropic processes are compared with available experimental data in the literature to assess the best process for steady and transient weakly underexpanded jets. The steady state results agree reasonably well with the experimental and analytical data. It is also shown that isentropic process evaluates steady injection better than other processes. Tip penetration of transient results was compared with available data in literature, and no exact agreement for isothermal and isentropic is observed. This appears due to the linearization of equation of state. It is suggested that more accurate linearization with a combination of process should be used for transient injection. Effects of pressure ratio and exit velocity on the pressure profile are shown. It is also concluded that during injection locations of shock cells do not vary with pressure ratios while are affected by exit velocity.

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