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In a compressed-tank LOX+ethanol (or similar liquid fuel) rocket:

How much should the tank or combustion chamber pressure (which should be the same) be to have a significant exhaust velocity increase due to combustion and for the de-laval nozzle to work as expected (high temperature high pressure-subsonic flow to lower temperature lower pressure supersonic flow)

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    $\begingroup$ @OrganicMarble Which is one of the top destructive rules of the SE. $\endgroup$
    – peterh
    Sep 10, 2020 at 22:18
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    $\begingroup$ @OrganicMarble its just an example, i am not asking whether the rocket will work or not, its just about the pressure ratio at which a de Laval nozzle starts working as expected $\endgroup$
    – Sartem Cacartem
    Sep 10, 2020 at 22:26

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The critical pressure ratio for a de Laval nozzle is

$$\left(\frac{P_0}{P_{atm}}\right)_{crit} = \left(\frac{\gamma+1}{2}\right)^{{\gamma}/({\gamma-1})}$$

Where

  • $P_0$ = stagnation pressure in chamber

  • $P_{atm}$ = atmospheric (back) pressure

  • $\gamma$ = ratio of specific heats for the gas

$(P_0 / P_{atm})$ must exceed this critical value in order for a de Laval nozzle to achieve supersonic exhaust velocity.

Reference: Sonic Flow Through a Nozzle equation 14.75

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