Abstract
A mathematical model is compiled which, without recourse to the existing physical laws governing fans, proposes a novel empirical formula relating fan static pressure, fan pitch angle and inlet volume. The formula introduces five parameters which are determined using discrete linear and nonlinear least squares optimization techniques. These parameters are seen to be important to the consultant modelling a ventilation system in that the optimal fan pitch angle for a given fan may be computed explicitly from the parameters for known volume requirement and pressure drop in the system. The mathematical model also proposes a novel formula which defines the boundary of the fan stall region. The parameters of this formula are also evaluated using a discrete nonlinear least squares algorithm. Numerical results for 10 fans computed from tests on the fans are reported and analysed; a formula is deduced from the numerical results connecting one of the parameters of the first novel formula with fan diameter.
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