I would like to calculate the energy need for move in the black volume in gas (move in from r2 to r1), when gas is under rotating movement. The black volume turn at the same speed than gas. The weight of black volume is considered like 0. Like rotating create centripetal force, the pressure at external circle is more important than at internal, so it's not easy. Is it possible to calculate function of Gas, T, P, r1, r2, h, p, W and how can I do ? Consider "torus" like a square section and close. At first, my idea is to say the temperature of gas don't change because gas rotating, so if the temperature don't change it's like put volume in gas without rotating but I'm not sure, could you help me ?