A centrifugal pump is being tested with water at 60°F. The pump is operating at 1150 rpm and has a 7-inch impeller. Performance test results indicate that the pump delivers 80 gpm at a head of 32 ft with a power draw of 2.75 hp. Using the affinity laws, predict what the pump capacity, head, and power draw would be if the operational speed was increased to 1770 rpm and the fluid is,

a. Water at 140°F

b. Toluene at 140°F

c. Ethanol at 140°F

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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)