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3. The pressure rise, p, of a liquid flowing steadily through a centrifugal pump depends on pump diameter, D, angular speed of the rotor, ω, volume flow rate, Q, and density, Ï.
a) Develop dimensionless variables for this process. (10 points)
b) The following table gives data for the prototype and for a geometrically similar model pump. For conditions corresponding to dynamic similarity between the model and prototype pumps, calculate the missing values in the table. (10 points)
Variable Ap Q P ω D
Prototype ? 1.25 m^3/min 800 kg/m^3 183 rad/s 150 mm
Model 29.3 kPa 1000 kg/m^3 367 rad/s 50 mm