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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?

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    $\begingroup$ Your second question is already answered at space.stackexchange.com/questions/21577/… $\endgroup$
    – Nathan Tuggy
    Jun 2, 2017 at 15:10
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    $\begingroup$ 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. $\endgroup$
    – mariohm1311
    Jun 2, 2017 at 19:16
  • $\begingroup$ 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. $\endgroup$
    – Nathan Tuggy
    Jun 2, 2017 at 19:19
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    $\begingroup$ 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. $\endgroup$
    – mariohm1311
    Jun 2, 2017 at 19:22
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    $\begingroup$ 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. $\endgroup$
    – SF.
    Mar 18, 2020 at 13:49

2 Answers 2

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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

You might ask me what is Stagnation Pressure and Steady-state Pressure?

And you might question me why I used the word Environmental pressure?

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

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

Edit: Okay, since a lot of people ask I will try to explain this a bit better.

1_ By the assumptions of isentropic flow and choked throat conditions, you get a relationship between mass flow rate, and pressure/temperature/throat area/ratio of specific heats. Chamber temperature is the adiabatic flame temperature of the gas mixture. This also changes with pressure. You can use Gaseq or NASA CEA package, or Canterra. There, you will also see the ratio of specific heats change.

When you make a design, you should define your criterias. For example you may want to start making a safe, and relatively cheap rocket. In that case the clever thing to do is to pick a pressure, and throat area. Then, you can easily calculate the required mass flow rate for the conditions that you first assumed. Or, maybe you are a student and want to make some measurements on a small engine. Then your professor might say, our laboratory can tolerate a mass flow rate of 1 kg/s. Then you fix mass flow rate and iteratively find the other parameters.

2_ It is the same principle. You are trying to use the pressure as much as you can. So, you need a throat section first. There you accelerate your gas up to sonic speed. If the pressure is still enough you need a nozzle and further expand your gas, and decrease the pressure. But be careful. Your gas was cold in the first place. So when you decrease its pressure it gets cold. You don't want your gas to condensate. Then expand it until it reaches the condensation temperature. There you will take all you can take from a cold gas thruster. N.B. cold here, in the jargon, referes to non combustive propellant flow.

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    $\begingroup$ Could you give a source and/or define the variables? $\endgroup$
    – Steve Linton
    Jun 1, 2018 at 13:11
  • $\begingroup$ 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. $\endgroup$
    – Kaan Güven
    Jun 1, 2018 at 13:37
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    $\begingroup$ Temporary, reversible -1 until the source cited is added back into the answer and the variables explained within the answer post. In Stack Exchange answers need to be fairly stand-alone so that if links break the answer does not loose value, and not everybody has a copy of Sutton in their back pocket. Thanks! $\endgroup$
    – uhoh
    Jun 1, 2021 at 23:51
  • $\begingroup$ -1 (Also temp/rev) This answer doesn't say what any of that stuff means, as @uhoh says. Without that, it's a bit useless, sorry. $\endgroup$
    – SusanW
    Aug 16, 2021 at 11:56

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