Using the Modeling Technique to Design a New Power Pump

Written by Terry Henshaw, Consulting Engineer

Pumps & Systems, March 2008

It is common practice for the designer of a new centrifugal pump to model the new pump from an existing pump. Each dimension of the existing pump (except the shaft diameter) is multiplied by a modeling factor "F" to obtain each dimension of the new pump.

I have successfully used the same approach to design a number of new reciprocating power pump liquid ends, and find that it also works for power ends. Such a procedure may be useful to other designers of power pumps.

The following example illustrates the use of the modeling technique, coupled with valve and spring parameters developed recently. It also reveals the significant increase in NPSHR when larger pumps are run at higher speeds.

Example

Let's say that a 3-in stroke triplex pump, with 2.5-in diameter plungers, has proven reliable in continuous-duty applications at a discharge pressure of 1000-psi, running at 400-rpm. The continuous-duty rod load rating is 5000-lbs. It is desired to model this pump to a larger pump with a 4-in stroke.

What is the modeling factor? What performance can we expect?

The modeling factor is F = 4/3 = 1.333, so F²= 1.778, F³ =2.37, F⁴ = 3.16, F^0.5 = 1.155, F^1.5 = 1.54, F^2.5 = 2.053.

Table 1 features the modeling data.

Table 1

	3"-Strk	Multiplier	4"-Strk
Plunger Diameter (inches)	2.5	F	3.33
Continuous Rod Load Rating (pounds)	5000	F²	8900
Displacement/Revolution (gal/rev)	0.191	F³	0.453
Crankshaft Speed (for same accel) (rev/min)	400	1/F^0.5	346
Displacement (for same accel) (gal/min)	76.5	F^2.5	157
Displacement Hydraulic Power (hp) (both pumps with 1000 psi discharge press.)	44.6	F^2.5	91.6
Maximum Recommended Valve Lift (inches) (based on same closing impact velocity)	0.18	F^0.5	0.21
Peak Flowrate/Valve (gal/min)	81.9	F^2.5	168
Valve Wing Diameter (inches)	2.125	F	2.833
Valve Seat Flow Area (in.²)	3.55	F²	6.31
Valve Lift (Escape) Area (in.²)	0.85	F^1.5	1.31
Peak Velocity at Lift Area (ft/sec)	31.0	F	41.3
Approx. Pressure Drop Across Lift Area (psi) (based on pumping cool water)	9.0	F²	15.9
Force Req'd. from Spring at Max. Valve Lift (lb)	31.8	F⁴	101

Comments

The plunger diameter would probably be rounded down to 3.25-in so that standard packing could be purchased.
After the initial approximate dimensions are determined and adjustments are made to accommodate standard hardware (packing, bearings and fasteners), stresses are calculated to confirm the selected dimensions.
The valve spring does not lend itself to direct modeling because-to obtain the same velocity (to avoid slamming and shock loading)-maximum valve lift on both pumps must be established by pump speed (RPM), not by valve size. Allowable valve lift does not vary with valve size.
In the absence of a significant pressure drop preceding the inlet (suction) valve, the approximate pressure drop across the valve lift area approximates the NPSH required by the pump.
Running a power pump at a lower speed allows the valve to lift higher and the use of weaker valve springs. This results in a significant reduction in the NPSHR. (With proper selection of valve springs for the different speeds, the NPSH required by a power pump varies to the fourth power of rpm.)

Terry Henshaw is a mechanical engineer, licensed in Texas and Michigan. He worked for Union Pump Co. for 25 years and served as chairman of the reciprocating pump section and the metrication subcommittee for the Hydraulic Institute.

He wrote the book Reciprocating Pumps, published in 1987, and the two sections on pumps in the 11^th edition of Mark's Handbook, published in 2007.

He has designed a number of high pressure pumps, control valves, and related jetting equipment.

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