system
Given the following post, respond as if you're commenting on Reddit:
human
Once a rocket reaches space and goes in to free fall, how do they get fuel/oxidant to flow downward towards the nozzle without thrust or gravity pulling it downward?

There has to be some simple mechanism that pushes the fuel and oxidant out of the fuel tanks once they've cut their initial thrust. What is it?
gpt
In the simplest tank design, the propellant is at the bottom, separated by a diaphragm from an ullage volume where a pressurizing gas pushes the diaphragm.

Pros: very simple and cheap design

Cons: you lose pressure as the propellant is consumed and the gas expands on an every time larger volume. This can be mitigated if the ullage volume is initially very large, so the gas won't have expanded a lot, but then you'll have the problem that big tanks are massive (in space, you want things to be as light as possible so they can be accelerated easily with little propellant).

A better design is to keep the gas in a separate small container at high pressure, with a pressure regulator feeding the gas gradually into the tank. Then as the propellant is consumed, more gas flows into the ullage volume and pressure is kept nearly constant without the need for a very large tank.

Pros: less massive, nearly constant pressure

Cons: more complex and expensive

In simple rocket engines (e.g. for attitude control), sometimes these approaches suffice. But when high thrust is required (i.e. high mass flow rate), then the pressure from the gas and diaphragm may not enough to ensure a good flow into the combustion chamber. Then you need turbopumps. They can be powered by the same fuel and oxidizer with a pre-burner.