I am trying to build a rocket with liquid fuel and oxidizer that is being pumped to the injectors/combustion chamber using electric motors/pumps. Assuming that the oxidizer and fuel are liquid, wouldn't the tanks need an inert gas to be put back in? I don't believe this diagram shows this. If anyone can explain how this process would take place, or can provide another diagram it would be greatly appreciated. Thank you!
There are a few ways to do this:
Using an inert gas (helium is often used). This is carried in a separate high-pressure tank and fed into the oxidizer/fuel tanks as they are depleted. The ox/fuel tanks are kept at a pressure of a few bar to help the pumps draw in the liquids.
Autogenous pressurization: some of the fuel/ox is warmed up (by running it through a hot part of the engine) and evaporated, and fed back into the tank as a gas.
Before a rocket takes off you can see gas coming off the side. This is excess fuel and oxidiser from the tank which has evaporated and must be let out to ensure stable pressure. If you balance it right, you can let out just enough gas whilst still keeping pressure in the tanks. While use of something like a helium pressurisation system may work, you could get away with using the natural fuel evaporation to provide pressure.