Aerospace/Aviation/Rocket engine nozzle pressure
While reading about the Saturn F1 engine, I read that nozzles are optimized when Pa = Pe at the plane where the thrust exits the nozzle. So if a nozzle is optimized when the pressure of the thrust at the exit plane = atmospheric pressure, where is that pressure measured? Are they measuring the thrust stream? Or are they measuring pressure perpendicular to the thrust stream at the boundary of the stream? I am sure any rocket scientist just plain knows how pressure is measured, but I cannot find a single layman's explanation. I really want to know for sure. Thank you!!!!
When it is said that a nozzle is optimized when the exit pressure matches the ambient pressure that simply means that the nozzle is designed for that condition... The walls of a (bell-shaped) nozzle, not the ambient pressure determine how the gases within the nozzle expand and what velocity the gases achieve (and to some extent how much thrust the rocket will produce). Atmospheric pressure varies as you increase altitude (it goes down), so a bell-shaped nozzle will only be operating at its design condition (most efficient production of thrust) at the moment the rocket passes through the altitude where the atmospheric pressure equals the exit pressure. There is no specific measurement going on and ideally the pressure is uniform across the exit plane, but that is not necessarily true in the real case. The rocket will produce more thrust after it passes through that particular altitude, it's just not as efficient. The flow coming out of a bell-shaped nozzle is supersonic so ultimately I would say the pressure at the boundary of the hot gases exiting the rocket would be the most critical location for the pressures to match...
Hope this helps some...