Rocket engine nozzle physics

[txsgrl]

While researching the Space Shuttle Main Engines, I read that the nozzles are optimized when Exit Pressure of the thrust is the same as Ambient Pressure (Pa = Pe) but this is confusing because I can't find an explanation of where that pressure is measured.

It can't possibly be the thrust itself but I have read many articles and nobody talks about where the pressure is being measured.
Are they talking about the pressure of the thrust stream? Or are they measuring pressure perpendicular to the thrust stream at the boundary of the stream?

I really want to know how to get this correct. Thank you!!!!

[theborg]

txsgrl,

Thank you for the question and welcome to science buddies. Sorry for the delay in getting an answer to you. The parameter you are referencing can be kind of confusing. If you think of the combustion chamber as a closed container containing a gas under pressure, you can imagine that the gas exerts pressure on the walls of the tank equally in all directions. When the tank is "opened" on one side the gas exits through the opening, or nozzle. As it is doing so, it expands outward until it reaches equilibrium with the ambient conditions, like the local atmospheric pressure, which decreases as a function of altitude until you reach space in which case the atmospheric pressure is essentially zero. As the plum expands outward, it exerts a force on the inner walls of the nozzle. If Pa is greater than Pe, then the plum will cease to expand before it fully exits the nozzle and there is then extra physical structure that is not being utilized for the production of thrust. This is known as overexpansion. If on the other hand, Pe is greater than Pa, then once the gas exits the end of the nozzle (and the rocket system altogether) it will continue to expand outward and so the energy in that expanding gas is not captured and utilized for the production of thrust (known as underexpansion). In both cases, the engine is less efficient than it could be than if at the very moment it left the nozzle it was already at equilibrium and all the energy of expansion had been captured. To answer your question, where is this pressure measured. It is the pressure of the jet stream. That pressure acts equally in all directions. don't confuse the thrust, which is the force imparted due to the mass of the particles being thrown out the back of the rocket (known as mass flow rate). Pe is the pressure of the fluid/gas pressure of the jet stream at the nozzle exit plane...if it is greater than the ambient pressure then it is still expanding and there is energy in the stream not being used by the rocket system. The point where this pressure interacts with nozzle and, after exiting, the atmosphere is along the boundary of the stream.