The general thrust equation for rockets is: F=mdot*V_{e} + (P_{e} - P_{a})*A_{e} where,

F=thrust,

mdot=mass flow rate,

V_{e}=velocity of the exhaust at the nozzle exit,

P_{e}=exhaust pressure at the nozzle exit,

P_{a}=ambient pressure, and

A_{e}=area of the nozzle exit.

When considering the P_{a} term during the low altitude segment of the flight, is that very strictly the general atmospheric pressure at the rocket's altitude? I believe the forward travel of the rocket and backward travel of the high velocity exhaust gasses creates a localized low pressure at the base of the rocket (this causes the plume recirculation seen on some launches, right?). Does this area's lowered pressure need to be taken into account for a higher accuracy calculation of the thrust?

I imagine this could come down to a matter of definition. What really matters is the total force on the rocket, and how that's divided up between thrust and drag may be a little bit arbitrary. However, I am inclined to use atmospheric pressure in calculating the pressure term in the thrust equation. That equation is typically derived by noting that if a rocket engine imparts momentum to its exhaust at a rate

The usual way of deriving the thrust equation quoted above is to argue that if the rocket engine imparts momentum at a rate mdot*V

_{e}, then by Newton's third law momentum in the opposite direction is imparted to the engine. Then the back-pressure term is rather artificially, in my view, tacked on.

However, the equation can also be derived by considering nothing but the pressure forces on the engine. As one proceeds aft from the forward dome of the combustion chamber, diverging sections (including the forward dome itself) exert forward forward on the engine wherever the internal pressure exceeds ambient, and converging sections exert rearward force. Where internal pressure is lower than external, diverging sections exert rearward force and converging sections exert forward force. Add up all of those forces (i.e., integrate from the top of the combustion chamber to the nozzle exit), and you get the usual expression for thrust.

If you look at thrust this way, then it's natural that the general ambient pressure appears in the equation.

EDIT: "thats" -> "that's"