Is bernoulli in contradiction with pascal?

Question

Bernoulli equation says that the total work is (P1 - P2) * V, where P1 is the pressure in one end of a tube filled with a fluid, P2 is the pressure in the other end, and V is the volume of fluid displaced, which is the same in both ends of the tube. That implies that there's a difference in pressure between the ends of the tube.

But pascal law states that the pressure must remain constant, which is what drives hidraulic lifts for car repairs. The pressure must remain constant, and since P = F/A, the smaller the cross-sectional area of a tube, the smaller the force required.

I've already read the explanations on the internet but they don't address this issue. Thank you.

Answer 1

Pascal's principle is for static fluids. By using a term for volume displacement, Bernoulli's equation is explicitly for dynamic fluids.

Answer 2

> "pascal law states that the pressure must remain constant..."



That's not what Pascal's Law says. It says that a _change_ in pressure is transmitted uniformly to all parts of the fluid. For example, if the pressure in one part of the fluid is 100 Pa and the pressure in another part is 150 Pa, then if you increase the pressure of the first part to 102 Pa, the pressure at the second part will increase to 152 Pa.

Answer 3

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