4. Agitators are widely used for mixing purposes in chemical industries. Researchers want to estimate the actual power (P) required for agitation using a geometrically similar one-eighth model. For an un- baffled vessel, P is expected to depend on the rotation speed, the impeller diameter, acceleration due to gravity g and the density of the fluid being agitated. The following data apply Model Prototype Impeller diameter, D, = 20 cm Density, p = 1200 kg/m³ Rotation speed, N = 10 s1 D, = ? p = 1200 kg/m³ N = ? a) Use dimensional analysis to develop a suitable set of dimensionless groups for this problem. b) For the model, determine the values indicated in the table with a question mark. c) What will be the power ratio Pm/Pp?

Structural Analysis
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Author:KASSIMALI, Aslam.
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4. Agitators are widely used for mixing purposes in chemical industries. Researchers want to estimate
the actual power (P) required for agitation using a geometrically similar one-eighth model. For an un-
baffled vessel, P is expected to depend on the rotation speed, the impeller diameter, acceleration due
to gravity g and the density of the fluid being agitated. The following data apply
Model
Prototype
Impeller diameter, D, = 20 cm
Density, p = 1200 kg/m3
Rotation speed, N = 10 s1
Da = ?
p = 1200 kg/m3
N = ?
a) Use dimensional analysis to develop a suitable set of dimensionless groups for this problem.
b) For the model, determine the values indicated in the table with a question mark.
c) What will be the power ratio Pm/P,?
Transcribed Image Text:4. Agitators are widely used for mixing purposes in chemical industries. Researchers want to estimate the actual power (P) required for agitation using a geometrically similar one-eighth model. For an un- baffled vessel, P is expected to depend on the rotation speed, the impeller diameter, acceleration due to gravity g and the density of the fluid being agitated. The following data apply Model Prototype Impeller diameter, D, = 20 cm Density, p = 1200 kg/m3 Rotation speed, N = 10 s1 Da = ? p = 1200 kg/m3 N = ? a) Use dimensional analysis to develop a suitable set of dimensionless groups for this problem. b) For the model, determine the values indicated in the table with a question mark. c) What will be the power ratio Pm/P,?
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