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As stated, you cannot. First, a fan speed value in m/s is meaningless. Presumably you are talking either about the speed of the fan blades, probably at their tips, or you are talking about the air velocity produced by the operation of the fan. In the first case, you have left out the diameter of the blades and their aerodynamic efficiency. In the second ...


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in Pfan = K FanSpeed^3 , K is not only an units conversion factor. In this specific case, the units factor will be one in W s3/m3 = (kg·m2/s3)(s3/m3) = kg/m , since m/s and W are from the IS of units Edit : it is an answer to the first question that had been changed for a new one ...


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It is converting units: \begin{align} 196.9\,\bar{V}\,[m/s]&\longrightarrow \bar{V}\,[ft/min]\\ 0.0040\, P \,[pa] &\longrightarrow P \,[in\,w]\\ 0.0624\,\rho \, [kg/m^3] &\longrightarrow \rho\,[lb/ft^3] \end{align} So your factor is just $$ 196.9\sqrt{2\times\frac{0.0624}{0.0040 }} $$



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