ANS:B - η_m = η_v . η_ma

The various efficiencies of a centrifugal pump are related as follows: ηo=ηma×ηm×ηv\eta_o = \eta_{ma} \times \eta_m \times \eta_vηo​=ηma​×ηm​×ηv​ Here's the breakdown of each efficiency:

• ηm (Mechanical Efficiency): This efficiency accounts for losses due to mechanical factors within the pump, such as bearing friction and seal losses.
• ηv (Volumetric Efficiency): Volumetric efficiency represents the ratio of the actual volume of fluid delivered by the pump to the theoretical volume that would be delivered under ideal conditions.
• ηma (Manometric Efficiency): Manometric efficiency, also known as hydraulic efficiency, measures the effectiveness of the pump in converting shaft power into fluid power.
• ηo (Overall Efficiency): Overall efficiency is the ratio of the useful power output of the pump to the power input, considering all losses.

The relationships among these efficiencies are:

• The overall efficiency (ηo) is the product of the manometric efficiency (ηma), mechanical efficiency (ηm), and volumetric efficiency (ηv). This relationship accounts for losses in the pump due to mechanical inefficiencies (ηm), volumetric inefficiencies (ηv), and hydraulic losses (ηma).

Therefore, the correct relationship among the efficiencies is: ηo=ηma×ηm×ηv\eta_o = \eta_{ma} \times \eta_m \times \eta_vηo​=ηma​×ηm​×ηv​ This equation expresses how the overall efficiency of a centrifugal pump is influenced by its manometric, mechanical, and volumetric efficiencies.