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.

[[{"type":"media","view_mode":"media_large","fid":"233","attributes":{"alt":"Comparison of cut down and modeled impellers","class":"media-image","id":"1","style":"float: left;","typeof":"foaf:Image"}}]]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.

[[{"type":"media","view_mode":"media_large","fid":"234","attributes":{"alt":"Hydraulic Institute pump faqs","class":"media-image","id":"1","style":"float: left;","typeof":"foaf:Image"}}]]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, ns, 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.

Q. We are installing a multistage pump and plan on using a reduced voltage starter. Is this practical and what precautions should be taken?

A. A plot of speed versus torque requirements during the starting (accelerating) phase of a rotodynamic pump (any pump type) is sometimes needed to check against the speed-torque curve of the driving motor. Rotodynamic pumps typically have a speed-torque curve characteristic where the torque varies as the square of the speed. The driver must be capable of supplying more torque than required by the pump along the entire curve in order to bring the pump up to rated speed under the conditions present during the starting phase. This is generally attainable for rotodynamic pumps with normal induction or synchronous motor performance characteristics. However, under certain conditions, such as with high specific speed pumps or when motor terminal voltage is reduced below nominal tolerances, a motor with higher pull-in torque may be required to maintain adequate torque margins and ensure expected pump acceleration to operating speed.

Reduced motor terminal voltage will result in reduced motor torque. For induction motors, torque is reduced in proportion to the square of the applied terminal voltage. Thus, a motor whose terminal voltage dips to 80 percent of nominal voltage during start-up will only produce accelerating torque equal to 64 percent of the torque under nominal full voltage conditions. Obviously, available torque is reduced significantly further when starting voltage defined by the end user is lower than 80 percent, and care should be taken to consider these situations. See the figure below.

[[{"type":"media","view_mode":"media_large","fid":"235","attributes":{"alt":"Hydraulic Institute pump faqs","class":"media-image","id":"1","style":"float: left;","typeof":"foaf:Image"}}]]In this example, a 1500-hp motor rated (full voltage) torque of 2200-lb-ft provides 11 percent greater torque than the pump open valve rated condition of 1980-lb-ft and thus could be considered satisfactory.  However, at 80 percent voltage, motor rated torque would only be 1408-lb-ft and the motor could not start the pump. However, at the pump closed valve condition of 1393-lb-ft the motor does have enough torque at 80 percent voltage, but the margin would be considered too small and an adjustment would be needed either in the motor and/or the pump's defined closed valve condition.

If the standard motor design is not adequate to ensure necessary torque margin throughout the acceleration period, alternate designs may be proposed, or the closed valve condition may be specified as the start-up condition instead of the open valve condition if it is only the open valve condition that is compromised. See ANSI/HI 1.3 Rotodynamic (Centrifugal) Pumps for Application and Design for more detailed information on this subject.

Pumps & Systems, February 2008