The pressure rise, AP, of a liquid flowing steadily through a centrifugal pump depends on pump diameter, D, angular speed of the rotor, @, volume flow rate, Q, and density, p. The table below 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. Variable Prototype Model AP 52.5 КРa 800 kg/m3 183 rad/s 0.0928 m³/min 999 kg/m3 367 rad/s D 150 mm 50 mm

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Using Buckingham Pi Theorem 

The pressure rise, AP, of a liquid flowing steadily through a centrifugal pump depends on pump
diameter, D, angular speed of the rotor, @, volume flow rate, Q, and density, p. The table below 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.
Variable
Prototype
Model
AP
52.5 kPa
800 kg/m3
183 rad/s
0.0928 m³/min
999 kg/m3
367 rad/s
150 mm
50 mm
Transcribed Image Text:The pressure rise, AP, of a liquid flowing steadily through a centrifugal pump depends on pump diameter, D, angular speed of the rotor, @, volume flow rate, Q, and density, p. The table below 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. Variable Prototype Model AP 52.5 kPa 800 kg/m3 183 rad/s 0.0928 m³/min 999 kg/m3 367 rad/s 150 mm 50 mm
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