The first article described the semi-open impeller with a tapered face, which was the subject of the test, and reported that the measured radial thrust on the impeller was three times the value calculated with the procedure established by Reference 3, and almost six times the procedure established by References 2, 5, 6 and 7. The article also suggested that the effective pressure area was not only the projected area of the impeller discharge but could be the total projected area of the impeller vane, from the impeller eye to the discharge.

With the 20-degree angle on the impeller face, the discharge width (B2) of 3/16-inch at the 11-inch maximum diameter almost doubled to 0.37 inch at the 10-inch diameter and nearly tripled to 0.55 inch at the 9-inch diameter. At the impeller eye diameter of 3 inches, the impeller width was 1.64 inches. The projected area of the impeller, due to the angled face - measured from the 3-inch diameter to the 11-inch outside diameter (OD) - was 7.34 square inches. Multiplying by the 208 psi differential pressure and the 0.18 K value from Reference 3 produced a force of 275 pounds, which was only 15 percent above the 240 pounds that we measured.

## Changes to the Impeller

If it was the extra impeller width at smaller diameters that was contributing to the excess thrust, we reasoned, then reducing the width at the smaller diameters should reduce the thrust. We left the discharge width (B2) at 3/16 of an inch, the face (bottom) angle at 20 degrees and machined the back (top) side of the impeller at an angle of 8.5 degrees, down to a diameter of 5 inches (see Figure 1). A tapered plate was bolted to the cover to match the 8.5-degree angle on the impeller. Hydraulic performance was not affected.

The projected area was reduced 1.35 square inches - an 18 percent reduction - to 5.99 square inches. Using the total vane projected area resulted in a calculated thrust of 224 pounds at shutoff. The measured thrust was 180 pounds, 80 percent of the above calculated value, and a 25 percent reduction. The thrust dropped more than the reduction in the projected area, indicating a greater effect from the larger impeller diameters. Our theory, though, that the excess thrust was caused by the larger impeller width at the smaller diameters, was confirmed. When calculating radial thrust, we cannot look at only the impeller discharge area (D2 x B2).

We then machined the top of the impeller at an angle of 12 degrees, down to a diameter of 5 inches. A new, tapered plate was bolted to the cover to match the 12-degree angle on the impeller. Hydraulic performance was again unaffected. The projected area was reduced 1.91 square inches - a 26 percent reduction - to 5.43 square inches. Using the total projected vane area, the thrust was calculated at 203 pounds. The measured thrust was 146 pounds - 72 percent of the calculated value - and a 39 percent reduction. Again, the reduction in radial thrust exceeded the reduction in projected area but also further confirmed our theory on the source of the extra thrust.

Figure 2 is a sketch of a single-volute casing. Figure 3 plots the relative radial thrusts created in single- and double-volute casings. Figure 4 illustrates a concentric circular casing, and Figure 5 shows the thrust created by such a casing.

To minimize radial thrust, a new impeller was machined with a face angle of 3.5 degrees. We knew that the hydraulic performance would be compromised, but the design allowed further confirmation of the effect of impeller profile on radial thrust.

A circular, concentric casing was machined from plate steel with a 3.5-degree face to match the impeller and an inside diameter of 15.5 inches, providing a radial clearance to the 11-inch impeller of 2.25 inches. As predicted in Figure 5, the radial thrust was near zero at shutoff. Somewhat reminiscent of the results reported in References 2 and 5, with modified concentric casings that have large radial clearance, the shutoff radial thrust was measured at only 8 pounds - 3 percent of the value measured - at shutoff, with this pump when equipped with the standard single-volute casing an an impeller with a 20-degree face angle. At the runout flow rate, the thrust increased to about 30 pounds, still well within acceptable limits.

### References

1. Stepanoff, A. J., Ingersoll-Rand, Centrifugal and Axial Flow Pumps, John Wiley & Sons, New York, 1948.

2. Agostinelli, A., Nobles, D., and Mockridge, C.R., Worthington, “An Experimental Investigation of Radial Thrust in Centrifugal Pumps,” Paper 59-HYD-2, Transactions of the ASME – Journal of Basic Engineering, American Society of Mechanical Engineers, 1959.

3. Hydraulic Institute Standards For Centrifugal, Rotary & Reciprocating Pumps, twelfth edition, 1969, Hydraulic Institute, New York, N. Y.

4. Specifications for Vertical In-Line Centrifugal Pumps for Chemical Process, ANSI B73.2 – 1975, The American Society of Mechanical Engineers, New York, N.Y.

5. Karassik, Igor J., Worthington, “Centrifugal Pump Construction,” Section 2.2 of the first edition of the Pump Handbook, edited by Karassik, Krutzsch, and Fraser, McGraw-Hill Book Co., New York, 1976.

6. Lobanoff, Val S & Ross, Robert R, United, CENTRIFUGAL PUMPS: Design & Application, Gulf Publishing Co., Houston, 1985.

7. Hydraulic Institute Standards for Centrifugal, Rotary & Reciprocating Pumps, 2009, Hydraulic Institute, Parsippany, N.J.