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Pumps & Systems, February 2008

Q.  

When a centrifugal pump impeller is reduced in diameter to reduce total head and rate of flow, the affinity rules predict that the new rate of flow is equal to the original rate of flow times the ratio of the new diameter to the old-as in the equation Q₂= Q₁ x D₂/D₁. On the other hand, if the model of a larger pump is made to a smaller size to facilitate testing, the rate of flow is predicted as the cube of the diameter ratio or Q₂= Q₁ x (D₂/D₁)³. Why are these two equations different?

A.  

In the first case, only one dimension of the impeller is affected. In addition, no change is made to the surrounding casing. This relationship is also confirmed by innumerable tests of centrifugal pumps to establish the manufacturer's performance rating curves for a given pump. This is a one dimensional effect.

In the second case, with an existing pump model, all dimensions of the pump impeller are changed as well as the diameter. The pump casing design is also changed with the same ratio. In other words, this is a three dimensional change, and the pump rate of flow responds accordingly.

The figure below illustrates the comparison between a cut down impeller and a modeled impeller of the same diameter.

Q.

How do pump manufacturers decide what rate of flow and total head to use when designing pumps for their standard product lines? Is there some logic and reasoning for this or is it based on demand?

A.

The figure below shows a typical coverage chart for a series of standard centrifugal pumps suitable for operation at 3550-rpm. Note that there are five families of pumps which are grouped in approximately straight vertical lines. For example, pumps in the center group all produce about 300-gpm. The other groups form a similar, though less perfect, vertical line.

Note that the figure to the right is drawn using a log-log scale so that what appears as equal horizontal spacing is actually a geometric progression. The approximate center of each vertical family progresses with a factor of two from 75-gpm to 150-gpm, 300-gpm, 600-gpm, and 1200-gpm. The pump discharge size also progresses geometrically. The popular sizes used are 1-in, then 1.5-in, 2-in, 3-in, and 4-in. The two top pumps have smaller discharge openings because they were originally designed for lower speed and rate of flow.

The vertical spacing for total head progresses with a factor of 1.6. This has been found from experience to allow for cut down impellers to cover each pumps range without serious loss in efficiency. This also results in a happy coincidence that all of the pumps on a diagonal line upward and right have the same specific speed, n_s, and are geometrically similar. In other words, they are each models of the others. This simplifies the manufacturer's design task. For example, the 3x2x8 pump is similar to the 4x3x10.

Finally, experience and resulting industry standards make a contribution. The American Standard ASME B73.1 includes suggested rate of flow and total head which closely follows this chart. In a similar fashion, the ISO Standard dictates comparable rates of flow when converted to 50-HZ speeds.