# At which pressure does a liquid fueled rocket start producing supersonic flow?

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)

• @OrganicMarble Which is one of the top destructive rules of the SE. – peterh - Reinstate Monica Sep 10 '20 at 22:18
• @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 – Sartem Cacartem Sep 10 '20 at 22:26

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