Apparatus comprising: a signal processor or processing module configured at least to: receive signaling containing information about a pump differential pressure (P i), flow rate (Q i) and corresponding power data (W i) at pump motor maximum speed (n max) published by pump manufacturers, as well as instant pump motor power (w) and speed (n); determine corresponding signaling containing information about instant pump differential pressure and flow rate using a combined affinity equation and numerical interpolation algorithm, based upon the signaling received by implementing the combined affinity equation and numerical interpolation algorithm as follows: obtaining a corresponding maximum power (w) at the pump's maximum speed (n max) with respect to the instant motor power (w) and speed (n) parameters by using a power affinity equation; obtaining corresponding pump differential pressure (P̂) and flow rate with respect to: - the previously obtained corresponding maximum power (ŵ) at the pump's maximum speed (n max), and - the pump differential pressure (P i), flow rate (Q i) respectively and corresponding power data (W i), at pump motor maximum speed (n max) published by pump manufacturers, by using direct numerical interpolation; determining the instant pump differential pressure and flow rate at an instant motor speed (n) and power (w) with respect to the pump's maximum speed (n max) and the previously obtained pump differential pressure (^P) and flow rate (^Q) respectively, by using pressure and flow affinity equations; and provide the corresponding signaling to control a pump in a pumping system. receive signaling containing information about a pump differential pressure (P i), flow rate (Q i) and corresponding power data (W i) at pump motor maximum speed (n max) published by pump manufacturers, as well as instant pump motor power (w) and speed (n); determine corresponding signaling containing information about instant pump differential pressure and flow rate using a combined affinity equation and numerical interpolation algorithm, based upon the signaling received by implementing the combined affinity equation and numerical interpolation algorithm as follows: obtaining a corresponding maximum power (w) at the pump's maximum speed (n max) with respect to the instant motor power (w) and speed (n) parameters by using a power affinity equation; obtaining corresponding pump differential pressure (P̂) and flow rate with respect to: - the previously obtained corresponding maximum power (ŵ) at the pump's maximum speed (n max), and - the pump differential pressure (P i), flow rate (Q i) respectively and corresponding power data (W i), at pump motor maximum speed (n max) published by pump manufacturers, by using direct numerical interpolation; determining the instant pump differential pressure and flow rate at an instant motor speed (n) and power (w) with respect to the pump's maximum speed (n max) and the previously obtained pump differential pressure (^P) and flow rate (^Q) respectively, by using pressure and flow affinity equations; and obtaining a corresponding maximum power (w) at the pump's maximum speed (n max) with respect to the instant motor power (w) and speed (n) parameters by using a power affinity equation; obtaining corresponding pump differential pressure (P̂) and flow rate with respect to: - the previously obtained corresponding maximum power (ŵ) at the pump's maximum speed (n max), and - the pump differential pressure (P i), flow rate (Q i) respectively and corresponding power data (W i), at pump motor maximum speed (n max) published by pump manufacturers, by using direct numerical interpolation; - the previously obtained corresponding maximum power (ŵ) at the pump's maximum speed (n max), and - the pump differential pressure (P i), flow rate (Q i) respectively and corresponding power data (W i), at pump motor maximum speed (n max) published by pump manufacturers, by using direct numerical interpolation; determining the instant pump differential pressure and flow rate at an instant motor speed (n) and power (w) with respect to the pump's maximum speed (n max) and the previously obtained pump differential pressure (^P) and flow rate (^Q) respectively, by using pressure and flow affinity equations; and provide the corresponding signaling to control a pump in a pumping system.