A centrifugal fan operating in a duct has the dimensionless parameters

\[ C_{Q}=\frac{Q}{\omega D^{3}} \quad \text { and } \quad C_{H}=\frac{\Delta p}{ho \omega^{2} D^{2}} \]

where \(C_{Q}\) is a flow coefficient, \(C_{H}\) is a head coefficient, \(Q\) is the volume flow rate, \(\omega\) is the fan speed, \(D\) is the fan diameter, \(ho\) is the fluid density, and \(\Delta p\) is the fan pressure rise. Figure P12.28 shows this fan's performance curve in dimensional form for a fan speed of \(\omega_{15}=1500 \mathrm{rpm}\). Find the fan operating points \((Q\) and \(\Delta p\) ) for \(\omega_{30}=3000 \mathrm{rpm}\) and corresponding to points 1,3 , and 5 at \(\omega_{15}=\) \(1500 \mathrm{rpm}\). Assume similarity between \(1500 \mathrm{rpm}\) and \(3000 \mathrm{rpm}\).

Figure P12.28

Transcribed Image Text:

Fan pressure rise, Ap (kPa) 3 2 0 'N 2 3 Ap=1-0.25 02 N15 = 1500 rpm 4 5 0 1 2 3 4 Volume flow rate, Q (m/s)