A fluid flows in a pipe with a sudden increase in its cross section, as shown in the sketch. Assume that the pressure in the wider section right after the jump, P2, equals P1. Using a control volume where stations 1 and 3 are the inlets and outlets, respectively, apply conservation of mass and momentum to find expressions for the average velocity at station 3, the pressure at station 3 and the head loss associated with the sudden expansion. Express your results in terms of diameters d and D, the average inlet velocity v1 and the pressure at station 1.