Functions of Two Variables:

The performance variable of a component is frequently a function of more than one variables. For instance, the pressure developed by a centrifugal pump is a function of its speed (S) and flow rate (Q). Up to 3 variables may be accommodated in a X - Y plot. Each of the curve in the X - Y plot may be written as a 2^nd degree polynomial in Q (at constant S).

In general the pressure drop can be written as following

Δ p = A₀ + A₁ S + A₂ S ₂ + (B₀ + B₁ S + B₂ S²) Q + (C₀ + C₁ S + C₂ S² ) Q ²

The A, B, C constants of the above equation can be written by using the 9 data points.