2. Consider a large industrial fan where the input power, W, depends on the fan impeller diameter, D, fluid viscosity, u, fluid density, p, volumetric flow rate, Q, and blade rotational rate, w. a) What are the appropriate dimensionless groups (Pi terms) if we consider D, p, and Q as repeating (reference) variables. b) If a model fan has a diameter, Dm, that is half of the prototype fan diameter, D, , what should be the ratio of the model blade rotation rate, Wm , to prototype, wp, to have dynamic similitude. Assume the same fluid (air) properties; that is viscosity and density are the same in both cases.

Elements Of Electromagnetics
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Author:Sadiku, Matthew N. O.
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2. Consider a large industrial fan where the input power, W, depends on the fan impeller diameter, D, fluid
viscosity, u, fluid density, p, volumetric flow rate, Q, and blade rotational rate, w.
a) What are the appropriate dimensionless groups (Pi terms) if we consider D, p, and Q as repeating (reference)
variables.
b) If a model fan has a diameter, Dm, that is half of the prototype fan diameter, D, , what should be the ratio of
the model blade rotation rate, Wm , to prototype, wp, to have dynamic similitude. Assume the same fluid (air)
properties; that is viscosity and density are the same in both cases.
Transcribed Image Text:2. Consider a large industrial fan where the input power, W, depends on the fan impeller diameter, D, fluid viscosity, u, fluid density, p, volumetric flow rate, Q, and blade rotational rate, w. a) What are the appropriate dimensionless groups (Pi terms) if we consider D, p, and Q as repeating (reference) variables. b) If a model fan has a diameter, Dm, that is half of the prototype fan diameter, D, , what should be the ratio of the model blade rotation rate, Wm , to prototype, wp, to have dynamic similitude. Assume the same fluid (air) properties; that is viscosity and density are the same in both cases.
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