The head developed across the pump at speed, N, is given by equation (17.28), and the corresponding pressure difference is:
where No is the design speed (rps) and the volume flow, Q is related to the mass flow, W, by:
Combining equations(17.50), (17.53) and (17.54) gives the following equation in volume flow rate, Q:
Solving equation (17.55) for a general, nonlinear function, fl,=, of head versus flow will require iteration.
However, the function may be represented by a loworder polynomial
where ai are constant coefficients. Sufficient accuracy is often obtained using a either a second-order or a third-order representation, allowing equation (17.55) to be re-expressed as:
Equation (17.57) may be solved either iteratively or, because it is a cubic, analytically. If a second-order expression for the pump characteristic, f e l , is sufficient then a3 = 0, and equation (17.57) becomes a quadratic, the solution of which is particularly easy.