Watched an Apollo Saturn launch. Why is a stage allowed to separate/drop with residual fuel?

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Watched the Apollo 11 famous footage of the launch and the camera perspective was from the ground focused on the ascending rocket. When it came time for staging and dropping the first stage, we can clearly see cutoff of rocket motors, separation and ignition of the second stage.

One thing that puzzled me always was the first stage as it falls away is seen trailing vapor, residue from its shut off engines. This reasonably has to be residual unburned oxidizer/propellant. its enough of a plume to be visible even 30+ seconds later it is still leaking away as the second stage carries the rocket further away and away.

Im asking bc every ounce, every bit of weight is calculated for and certainly fuel is no exception. Why lug the fuel up there just to shut the engines off presumably early and not burn it. Any reason for this inefficiency?

EDIT: Including link to video. [https://www.youtube.com/watch?v=dhTvadtW2dc](https://www.youtube.com/watch?v=dhTvadtW2dc) Begin watching at time 36:38

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Anonymous 0 Comments

The first stage is pushing you up right up until it’s not. Once it’s out it’s slowing you down.

If you wait until you’re sure it’s 100% completely empty to ditch it, you’re liable to lose delta V.

Much of the fuel systems for the early stages also run via pressure, so you have to keep a certain level of positive pressure in the fuel tanks in order to keep the stage going. Once that pressure drops below a certain point it’s time to separate.

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