Bernoulli theorem is based on conservation of

Consider the situation of the previous problem. Let the water push the left wall by a force F₁ and the right wall by a force F₂.

Water enters through end A with a speed u₁ and leaves through end B with a speed u₂ of a cylindrical tube AB. The tube is always completely filled with water. In case I the tube is horizontal, in case II it is vertical with the end A upward and in case III it is vertical with the end B upward. We have v₁ = v₂ for

Water is flowing through a long horizontal tube. Let P_A and P_B be the pressures at two points A and B of the tube.

Water and mercury are filled in two cylindrical vessels up to same height. Both vessels have a hole in the wall near the bottom. The velocity of water and mercury coming out of the holes are u₁ and u₂ respectively.