Head and flow rate are the important parameters for proper selection of centrifugal pump. However, the reversed operation of centrifugal pump leads to the off-design characteristic of head and flow rate. This paper presents an analytical model developed by using the system curves and velocity relations derived from pump application. Also, the differential technique is applied to the analytical model to develop the off-design characteristics of head ratio and flow rate ratio relations. The off-design characteristic relations were compared with literature and available conversion methods. Then, the analytical model coefficient (AMC) with the range between −4 and +4 was developed from the off-design characteristics of head ratio and flow rate ratio relations. The AMC value was equal to 1 when the pump operates in turbine mode and pump mode at the pump best efficiency point (BEP) and extended to either side up to ±4 when tested with literature data. Therefore, the analytical model consists of the off-design head and flow rate characteristics, when simplified leading to the AMC that could be applied to select the possible boundary limits of head and flow rate for different pumps.

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