CENTRIFUGAL PUMP SPECIFIC SPEE PRIMER AN THE AFFINITY LAWS Jacques Chaurette p. eg., Fluide esig Ic. November 004 www.fluidedesig.com There is a umber called the specific speed of a pump whose value tells us somethig about the type of pump. Is it a radial type pump which provides high head ad low flow or a axial or propeller type pump which provides low flow but high head or somethig i betwee. If you are worried whether you have the right type of pump or ot this umber will help you decide. The article gives you a example of how to calculate this umber. Also if you are worried that your pump may be cavitatig there is aother umber related to specific speed called suctio specific speed that will help you diagose ad avoid cavitatio. There is a multitude of pump desigs that are available for ay give task. Pump desigers have eeded a way to compare the efficiecy of their desigs across a large rage of pump model ad types. Pump users also would like to kow what efficiecy ca be expected from a particular pump desig. For that purpose pump have bee tested ad compared usig a umber or criteria called the specific speed (N S ) which helps to do these comparisos. The efficiecy of pumps with the same specific speed ca be compared providig the user or the desiger a startig poit for compariso or as a bechmark for improvig the desig ad icrease the efficiecy. Equatio [] gives the value for the pump specific speed, H is the pump total head, N the speed of the impeller ad Q the flow rate. ( rpm) Q( USgpm) N S = 0.75 H( ft fluid) [] 5764 Moklad aveue, Suite, Motreal, Quebec, Caada H4A E9 Tel: 54.484.PUMP (7867) Fax: 54.484.94 E-mail: jchaurette@fluidedesig.com Web site: www.fluidedesig.com
Specific speed primer Figure Specific speed values for the differet pump desigs. (source: the Hydraulic Istitute Stadards book, see www.pumps.org) Pumps are traditioally divided ito types, radial flow (see Figure ), mixed flow (see Figure ) ad axial flow (see Figure 4). There is a cotiuous chage from the radial flow impeller, which develops pressure pricipally from the actio of cetrifugal force, to the axial flow impeller, which develops most of its head by the propellig or liftig actio of the vaes o the liquid. Figure Radial flow pump cross-sectio, (source: Hydraulic Istitute www.pumps.org). Figure Mixed flow pump cross-sectio, (source: Hydraulic Istitute www.pumps.org). Figure 4 Axial flow pump cross-sectio, (source: Hydraulic Istitute www.pumps.org).
Specific speed primer Specific speed has also bee used as a criteria for evaluatig the efficiecy of stadard volute pumps (see Figure 5). Notice that larger pumps are iheretly more efficiet ad that efficiecy drops rapidly at specific speeds of 000 or less. Figure 5 Efficiecy values for pump with differet specific speeds (source: The Pump Hadbook published by McGraw Hill).
Specific speed primer 4 The followig chart provides the efficiecy data for pumps of various types vs the flow rate ad maybe easier to read tha Figure 5. However some correctios are required (use the chart i the upper left corer of Figure 6) to the values predicted. Figure 6 Efficiecy values for pumps of differet types (source: The Hydraulic Istitute www.pumps.org).
Specific speed primer 5 Let s take a example, we have selected a Goulds pump Model 75 which will provide us with a head of 97 feet at a flow rate of 500 USgpm, what is the specific speed? The efficiecy of this pump accordig to the Goulds performace curve (see Figure 6) is 7.5%. The chart i Figure 5 predicts that the efficiecy should be 78% for a specific speed of 66, this is a fair differece, perhaps Goulds would suggest aother pump as a alterative. NS = (rpm) Q(USgpm) 750x 500 = = 66 H( ft fluid)0.75 970.75 [] Figure 7 Goulds characteristic curves for a model 75 X6- pump at 770 rpm (from the Goulds pump catalogue). SUCTION SPECIFIC SPEE Suctio specific speed is a umber that is dimesioally similar to the pump specific speed ad is used as a guide to prevet cavitatio. S= (rpm) Q(USgpm) N.P.S.H.A ( ft fluid)0.75 []
Specific speed primer 6 Istead of usig the total head of the pump H, the N.P.S.H. A (Net Positive Suctio Head available) is used. Also if the pump is a double suctio pump the the flow value to be used is oe half the total pump output. From the previous article o cavitatio, the N.P.S.H. A at the pump suctio is : v. P. S. H. avail. ( ft fluid absol. ) = ( H F S + HEQ S ) + + ( z z + H) N + HA H S g va [4] where H A ad H va are i feet of fluid. Equatio [4] requires that the pipig ( H F-S ) frictio loss ad equipmet frictio loss ( H EQ-S ) be calculated. The meaig of some of the variables i equatio [4] are show i Figure 8. Figure 8 Meaig of the variables used for calculatig the N.P.S.H. A. We ca avoid doig the calculatios for equatio [4] by measurig the N.P.S.H.. The value for the N.P.S.H. A ca be deduced by takig a pressure measuremet at the pump ilet ad usig equatio [5] N. P. S. H. avail( ft fluid absol.) =. p GS ( psig ) SG + z GS z S v [5] S + + H A + H va g
The meaig of some of the variables i equatio [5] are show i Figure 9. Specific speed primer 7 Figure 9 Locatio of variables for measurig N.P.S.H. A. We may be cosiderig a icrease i the pump s speed to icrease the flow rate. If so, be aware that a icrease i speed will also require a icrease i N.P.S.H. required. The suctio specific speed value give us a idicatio of what the impeller speed limitatio will be for a give N.P.S.H. A. The Hydraulic Istitute recommeds that the suctio specific speed be limited to 8500 to avoid cavitatio. Other experimets have show that the suctio specific speed could be as high as 000. I the previous example the N.P.S.H. A of the pump was determied to be 5 feet absolute. Therefore the suctio specific speed will be 50. ( rpm) Q( USgpm) S = N. PS.. H. ( ft fluid) A 750 x = 5 500 = 0.75 0.75 50 [6] This is well below 8500. We ca easily calculate the ew suctio specific speed if we were to chage the impeller speed. Whe a pump has a high suctio specific speed value, it ca mea that the impeller ilet area is large reducig the ilet velocity which is eeded to eable a low NPSHR. However, if you cotiue to icrease the impeller ilet area (to reduce NPSHR), you will reach a poit where the ilet area is too large resultig i suctio recirculatio (hydraulically ustable causig vibratio, cavitatio, erosio etc..). The recommeded cap o the S value is to avoid reachig that poit. (paragraph cotributed by Mike Ta of the pump forum group).
Specific speed primer 8 Keepig the suctio specific speed below 8500 is also a way of determiig the maximum speed of a pump ad avoidig cavitatio. For a double suctio pump, half the value of Q is used for calculatig the suctio specific speed. Accordig to the Hydraulic Istitute the efficiecy of the pump is maximum whe the suctio specific speed is betwee 000 ad 4000. Whe S lies outside this rage the efficiecy must be de-rated accordig to the followig figure. Figure 0 Pump efficiecy correctio due to suctio specific speed. AFFINITY LAWS The affiity laws are derived from a dimesioless aalysis of three importat parameters that describe pump performace: flow, total head ad power (ref: The Pump Hadbook by McGraw-Hill, chapter ). The aalysis is based o the reduced impeller beig geometrically similar ad operated at dyamically similar coditios or equal specific speed. If that is the case the the affiity laws ca be used to predict the performace of the pump at differet diameters for the same speed or differet speed for the same diameter. Sice i practice impellers of differet diameters are ot geometrically idetical, the author's of the sectio called Performace Parameters i the Pump Hadbook recommed to limit the use of this techique to a chage of impeller diameter o greater tha 0 to 0%. I order to avoid over cuttig the impeller, it is recommeded that the trimmig be doe i steps with careful measuremet of the results. At each step compare your predicted performace with the measured oe ad adjust as ecessary. The affiity laws were developed usig the law of similitudes which provide basic relatioships. Flow vs. diameter ad speed
Specific speed primer 9 Q K = or Q = Q Total Head vs. diameter ad speed g H = K or H = H Power vs. diameter ad speed P = K γ 5 g or P = P 5 5 where subscripts ad deote the value before ad after the chage. P is the power, the speed, the impeller diameter, H the total head. If the speed is fixed the affiity laws become: Q = Q H H P = = 5 P 5 If the diameter is fixed the affiity laws become: Q = Q H H P = = P The process of arrivig at the affiity laws assumes that the two operatig poits that are beig compared are at the same efficiecy. The relatioship betwee two operatig poits, say ad, depeds o the shape of the system curve (see Figure ). The poits that lie o system curve A will all be approximately at the same efficiecy. Whereas the poits that lie o system curve B are ot. The affiity laws do ot apply to poits that belog to system curve B. System curve B describes a system with a relatively high static head vs. system curve A which has a low static head.
Figure Limitatio o the use of the affiity laws. Specific speed primer 0
Specific speed primer Symbols Variable omeclature Imperial system (FPS uits) Metric system (SI uits) g acceleratio due to gravity:.7 ft/s ft/s (feet/secod squared) m/s (meter/secod squared) N S specific speed S suctio specific speed H head ft (feet) m (meter) N.P.S.H. Net Positive Suctio Head H EQ equipmet head differece ft (feet) m (meter) H F frictio head differece ft (feet) m (meter) p pressure psi (poud per square kpa (kilopascal) ich) SG specific gravity; ratio of the fluid desity o-dimesioal to the desity of water at stadard coditios Q flow rate USgpm (US gallo per miute) Cubic meters per hour N impeller speed rpm v velocity ft/s (feet/secod) m/s (meter/secod) z vertical positio ft (feet) m (meter)