Functions of Two Variables:
The performance variable of component is frequently a function of more than one variable. For instance, the pressure build by a centrifugal pump is a function of its speed (S) and flow rate (Q). Up to 3 variables might be accommodated in X - Y plot. Each of the curve in the X - Y plot might be written as a 2nd degree polynomial in Q (at constant S).
In general the pressure drop might be written as following
Δ p = A0 + A1 S + A2 S 2 + (B0 + B1 S + B2 S 2) Q + (C0 + C1 S + C2 S2) Q 2
The A, B, C constants of the above equation might be written by using the 9 data points.