The pressure rise, , across a centrifugal pump of a given shape (see Fig. P7.45a) can be...

The pressure rise, , across a centrifugal pump of a given shape (see Fig. P7.45a) can be expressed as

where D is the impeller diameter, ω the angular velocity of the impeller, ρ 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 rises as a function of Q as shown in Fig. P7.45b. Use this curve to predict the pressure rise across a geometrically similar pump (prototype) for a prototype flowrate of 6 ft³/s. The prototype has a diameter of 12 in. and operates at an angular velocity of 60 π rad/s. The prototype fluid is also water.