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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?