A centrifugal pump is capable of delivering 50 L/s of fluid at a head of 18 m while operating at 3550 rpm with a 7-inch impeller. At this condition, the pump power draw is 12 kW and the pump efficiency is 68%. Use the affinity laws to predict the pump capacity, head, power draw, and efficiency if the impeller is changed to a diameter of 9-inches and the operational speed is adjusted to 1150 rpm.

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4.7.8 Affinity Laws Pump curves from manufacturers are presented for a specified rotational operating speed of the pump. Many pumps use a single-speed motor because they are reasonably priced. However, as technology has improved over the years, the variable speed motor is becoming very attractive for use with pumps. Varying the rotational speed of the pump changes its performance. Given the pump curves at a single operating speed, the design engineer can use the affinity laws to predict its performance at a different operating speed. The affinity laws are also helpful if the impeller diameter is modified along with the rotational speed. The affinity laws are derived using dimensional analysis and similitude. If all pumps of one type (e.g., centrifugal) behave similarly, then dimensional analysis should reveal how the pump parameters scale. In dimensional analysis, the Buckingham-Pi theorem is used to determine pertinent dimensionless groups. When analyzing centrifugal pumps using the Buckingham-Pi theorem, the performance parameters of the pump (head, power, and effi- ciency) are assumed to be a function of the fluid's density (p) and viscosity (u), the rotational speed of the pump (@), the impeller diameter (D) and the capacity delivered by the pump (+). Application of the Buckingham-Pi theorem to this functional dependence reveals five dimen- sionless groups shown in Table 4.20. The resulting functional dependence of these dimensionless groups are shown in the following equations, wD = f # pwD @D (4.77)