The waterhammer theory when using four quadrant data in Suter Suter, P., Representation of Pump Characteristics for Calculation of Waterhammer, Sultzer Technical Review Research Issue, pp. 45-48, 1966. Suter form follows a similar approach to the Standard Pump Curve Waterhammer Theory.

First, we know from the compatibility equations that the pressure change across the pump is related to the mass flow:

We also know that the dimensionless four quadrant parameters are related to the values used for the Dimensional Reference Point:

From the definition of h we have a relationship between the curve FH (Θ), speed and flow.

Multiplying through by ρg we can attain a similar expression in pressure terms:

Similarly, there is a relationship for volumetric flow that can be converted to mass flow by multiplying by density:

The previous equations can be combined with the compatibility equation for the pump:

This equation contains three potential unknowns - speed (α), flow (ν), and FH (Θ). FH and Θ are related via tabulated data. The value of Θ is related to the speed and flow, bringing the unknown variables down to just speed and flow:

As with the Standard Pump Curve, for a fixed speed there is only one unknown - flow. The equations and tabulated data can be iterated on to find a solution for flow and therefore pressure rise across the pump.

During a pump trip or startup, when neither speed nor flow are known, additional equations are required. The necessary torque balance terms are described in Transient - Inertial Models resulting in the below equation for speed change:

It is helpful to modify this equation so that it is directly applicable in four quadrant terms. The following relations are required:

resulting in the following:

This equation represents the full torque balance with unknown driver torque, pump torque, and pump speed in four quadrant form. For a pump trip, the driver torque is zero leaving only two unknowns. For a startup, the driver torque vs speed must be specified. Like the head term above, the dimensionless torque β can be solved for in terms of speed (α), flow (ν), and FB (Θ).

These equations can then be solved for speed, flow, torque and head.