Use dimensional analysis to determine the dependence of P on the other variables.

The stream function of a flow field is ?=Ax 3 -Bxy 2 where A =1m -1 s -1 and B =3m -1 s -1 , and the coordinates are measured in meters. Find expressions for the velocity field, the velocity potential, and the pressure gradient. The power, P, required to drive a fan is believed to depend on fluid density, ?, volume flow rate, Q, impeller diameter, D, and angular velocity, ?. Use dimensional analysis to determine the dependence of P on the other variables.

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