Problem#$4(8$ marks$)$

The thrust force of a jet engine, $$ depends on the flight speed, ambient pressure and temperature, $V_a,p_a$ and $T_a,$ respectively. In addition, it also depends on the maximum turbine inlet temperature $T_{\text{m}\text{a}\text{x}}$ and the compressor's rotational speed $,$ tip radius $R,$ maximum stagnation pressure, $p_0,$ fluid density, $$ and viscosity $.$ Obtain all non$-$dimensional groups necessary to test the engine's performance.