Question

action and reaction are not balance in working principle of rocket.why?

Answer 1

I'm not really sure what you are asking, but I'll try to explain how rockets generate thrust and maybe you can draw the answer you want from my answer.

At a very high level, rockets accelerate gases to hypersonic velocities in a nozzle. This fast moving gas follows Newton's third law. As the gas is accelerated from the rocket nozzle it pushes back against the rocket, accelerating the rocket upwards.

Outside of Newton's third law, this flowing gas has a dynamic pressure. In the combustion chamber of the rocket, the fuel and oxidizer are mixed and combusted. This combustion generates large amounts of pressure. The gas is accelerated through a diverging nozzle until the flow reaches a speed of Mach 1. Then the sonic flow is expanded to further increase the speed. (Super sonic flow is accelerated by EXPANSION, while subsonic flow is accelerated by COMPRESSION.) As the gas expands through the diverging portion of the nozzle, the pressure decreases. Necessarily, for flow to occur through the nozzle, the pressure at the nozzle exit must be greater than ambient pressures. At sea level this ambient pressure 14.7 psi. Remember that fluids cannot flow from lower pressure regions to higher pressure regions. Since the pressure at the nozzle exit is greater than ambient pressure, there is a pressure gradient at the nozzle exit. This pressure gradient add to our total thrust.

Therefore, the net thrust generated by a rocket is expressed as\[F_n = \dot m v_e + A_e(P_e - P_{amb})\] where \(\dot m\) is the mass flow rate of the gasses through the nozzle, \(v_e\) is the velocity at the exit of the nozzle, \(A_e\) is the cross sectional area of the nozzle exit, \(P_e\) is the pressure of the gasses at the nozzle exit, and \(P_{amb}\) is the ambient pressure of the environment that the nozzle is in.

Perhaps, it is this extra pressure term that you are seeking.