# How is chamber pressure determined for rocket engines?

I've been looking for this for quite some time now, and I can't find anything other than calculations where they already assume a chamber pressure. So my questions are two:

• What are the equations for calculating the chamber pressure for a bipropellant engine? In case it's the opposite, how do you find out the needed propellant flow rate so that you achieve the design chamber pressure?

• When you have a pressurized gas thruster, that is, with no combustion, what do you have to take into account in order to calculate the parameters of the injector?

• Your second question is already answered at space.stackexchange.com/questions/21577/… – Nathan Tuggy Jun 2 '17 at 15:10
• No, it's not. That's why I am asking again. Yes, you have a regulator that you can control, but you should be able to calculate before even running the engine how much feed pressure you need. And I doubt you would feed it with the chamber pressure you want, cause the chamber is open, therefore you won't achieve as much pressure. – mariohm1311 Jun 2 '17 at 19:16
• If you're not satisfied with the answer(s) because you think they're wrong, asking a new question isn't the way to handle it. With more rep you can add a bounty for better answers, or you can edit the question to be clearer. Otherwise, we're just going to give the same answers again, or nothing. – Nathan Tuggy Jun 2 '17 at 19:19
• What else can I do? It's not like I can add a bounty, and I don't really understand what's not clear about the question. – mariohm1311 Jun 2 '17 at 19:22
• With no combustion there's no point to having a combustion chamber and as result no combustion chamber pressure. The pressure fed from the regulator IS the pressure reaching the nozzle, directly. – SF. Mar 18 '20 at 13:49

I can only answer your first question. You can use the following equation:

$$\dot{m} = \frac{P_{c}A_{t}}{C^*}$$ where $$C^* = \frac{\sqrt{RT_{c}}}{\sqrt{\gamma}(\frac{2}{\gamma+1})^\frac{\gamma+1}{2(\gamma-1)}}$$

• Could you give a source and/or define the variables? – Steve Linton Jun 1 '18 at 13:11
• link. Here you can find the notation I use. Also the main source for introduction to rocket propulsion is Sutton's Rocket Propulsion Elements. You can find the same formula if you check equation 3-32. – Kaan Güven Jun 1 '18 at 13:37

By chamber Pressure, you mean stagnation/Steady state Pressure.

Here's the Equation

$$P_0 = p\left[1 + \frac{1}{2} \left(k - 1\right)M^2\right]^{\frac{k}{k-1}}$$

$$P_0$$ = Stagnation Pressure or Steady-state Pressure your chamber Pressure

$$p$$ = let's call it environmental pressure (Atmospheric pressure, but it changes with altitude)

$$k$$ = ratio of specific heat at constant pressure to specific heat at constant volume

$$M$$ = is the Exit velocity in Mach number

The equation above assumes that the Mach of the chamber/before the nozzle throat is negligible

Ask me more if you still confuse