# What is the optimal diameter for the exhaust hole in a pressurized vessel to deliver highest acceleration ?

Imagine you have a sealed cylindrical vessel with a given radius with a compressed gas inside. Let's give some numbers, 5 cm radius and 100 atm pressure. You poke a hole in the vessel and the gas will flow out, propelling the vessel in the opposite direction with a given force. Intuition tells me that this force depends on the hole size. Suppose the pressure does not change as time goes by, what's the optimal hole size to deliver the best acceleration ?

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"Highest acceleration" probably isn't the metric you want. You can get the maximum momentary acceleration by making the "hole" the whole half the vessel away from the direction you want to go, but of course, you are done almost instantly (and it breaks your claim about the pressure not changing). Perhaps maximum $\Delta v$ is a better metric? – dmckee Jul 4 '13 at 15:54
@dmckee: maximum delta v – Stefano Borini Jul 4 '13 at 19:55
Theoretically you want the largest hole, with the shortest duration impulse to get you going as soon as possible. – ja72 Jul 4 '13 at 21:31