Thrust in a Water rocket (or any rocket?)

[Swamp Thing]

I was debating with a friend, who insisted that the thrust in a rocket is merely due to the fact that a force PxA would have acted on a plate that sealed the nozzle. This force would have exactly balanced its counterpart "disk" on the other side of the chamber. After removing the seal, we are left with an unbalanced force PxA.

A bit of internet research - for example, https://www.ohio.edu/mechanical/programming/rocket/nielsen_rocket.pdf
shows that the actual force is twice the value predicted by my friend's naive reasoning. The result is derived from momentum balance and Bernoulli's theorem, but I'm wondering if there is a direct and intuitive way to prove this. I'm looking for something that would be as easy to understand as my friend's logic.

For example, can we split the 2PA into one PA term that corresponds to the "unbalanced disk forces" and another term that can be explained in some simple way?

 

[mfb]

For example, can we split the 2PA into one PA term that corresponds to the "unbalanced disk forces" and another term that can be explained in some simple way?

Loss of mass? You increase the total momentum of your rocket and decrease its mass at the same time.