The pressure rise, p, across a centrifugal pump of a given shape can be expressed as p=f(D,,,Q) where D is the impeller diameter, the angular velocity of the impeller, the fluid density, and Q the volume rate of flow through the pump. A model pump having a diameter of 8 in. is tested in the laboratory using water. When operated at an angular velocity of 40 rad/s the model pressure rise as a function of Q is shown in the figure helow. Use this curve to predict the pressure rise across a geometrically simuar pump (prototype) for a prototype flowrate of 4ft3/s. The prototype has a diameter of 10in. and operates at an angular velocity of 50nrad/s. The prototype fluid is also water. pp= psi