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I'm trying to do my homework in physics but here I have found something that I am not understanding.

It says:

Define analytically the terms that should stationary flow accomplish.

I know that in a stationary flow the velocity, pressure, and density don't change, but I don't understand what "define analytically" means.

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Well, the word analytic means different things, depending on the context. Here it probably means Write down a mathematical model for the physical system at hand. – Qmechanic Sep 23 '13 at 15:22
To repeat something I said about this in chat, the sentence is poorly constructed, but it probably means to associate the name of each condition with a mathematical expression. For example "irrotational" goes with \nabla \cross v = 0. – dmckee Sep 23 '13 at 18:50

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