It is known that the power required to drive a fan depends upon the impeller dia

Question

It is known that the power required to drive a fan depends upon the impeller diameter (D), the impeller rotational speed (omega), the fluid density (rho), and the volume flow rate (Q). (Note that the fluid viscosity is not important for gases under normal conditions.) What is the minimum number of fundamental dimensions required to define all of these variables? How many dimensionless groups are required to determine the relationship between the power and all the other variables? Find these groups by dimensional analysis, and arrange the results so that the power and the flow rate each appear in only one group.

Explanation / Answer

a) diameter is L
rotational speed is 1/T

fuid density us ML-3

volume floe rate is L3T-1

B) power = DxWyPzQw

= L^x *T^-y*M^z*L^-3z*L^3w*T^-w = ML^2T^-3

SO x- 3z + 3w = 2

-y + -w = -3

z = 1

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