{"text_format":"3","workbook":"xlsx","n_sheets":4,"sheets":["SCE Exponents vs Set Point","Affinity Law","Y vs. X Comparison","Data and Support"],"not_rendered":{"charts":3,"images":4,"macros":1,"defined_names":3},"unopened":[{"sheet":"Y vs. X Comparison","index":2,"reason":"not_a_worksheet"}],"read":"whole","date_system":"1900"}

{"sheet":"SCE Exponents vs Set Point","index":0,"n_rows":28,"n_cols":4,"rows_kept":28,"merged":[[0,0,0,12],[2,0,2,12],[3,0,3,12],[5,0,5,3],[11,1,11,2],[12,0,12,3],[13,0,13,3],[14,0,14,3],[17,2,17,3],[19,0,21,0],[19,1,21,3],[22,0,24,0],[22,1,24,3],[25,1,25,12],[26,1,26,12],[27,1,27,13]]}
["This spreadsheet tool estimates an exponent to be applied to the affinity law relating pump and fan power to speed and flow (a.k.a. the \"cube rule\") to adjust it to reflect the factors impacting the true performance of a real-world variable flow system.  The exponents are based on information published by Southern California Edison to support one of their incentive programs.   The tool is intended to be used for work with variable flow systems.  But there exponents have also been developed that can be applied to fixed systems to adapt the \"cube rule\" to real world operating conditions like the lift of an open system serving a cooling tower.  These exponents are documented in the \"Affinity Law\" tab."]
[]
["Click here to go to an explanation of the affinity law and the basis for the exponents used to create this tool."]
[]
[]
["Chart Data Table"]
[null,"Set point as a percentage of the design pressure","Recommended Exponent"]
[null,{"$f":"AVERAGE(0,0.2)","v":{"v":0.1,"d":"10%"}},2.4]
[null,{"$f":"AVERAGE(0.2,0.5)","v":{"v":0.35,"d":"35%"}},{"v":2,"d":"2.0"}]
[null,{"$f":"AVERAGE(0.5,0.8)","v":{"v":0.65,"d":"65%"}},1.5]
[null,{"$f":"AVERAGE(0.8,1)","v":{"v":0.9,"d":"90%"}},{"v":1,"d":"1.0"}]
[null,"Note that the set point percentage is the midpoint of the recommended application range"]
["Exponent Calculator"]
["Enter your system data in the yellow cells."]
["Read the estimated/suggested exponent in the green cell"]
[null,"Design Operating Pressure - ",{"v":4.5,"d":"4.50"},"consistent units"]
[null,"Operating Pressure Control Set Point - ",0.75,"consistent units"]
[null,"Suggested exponent - ",{"$f":"IF(((-0.606061)*((C17/C16)^3))+((0.545455)*((C17/C16)^2))-(1.743939*(C17/C16))+ 2.569545<0.8,\"Set Point Not Valid\",((-0.606061)*((C17/C16)^3))+((0.545455)*((C17/C16)^2))-(1.743939*(C17/C16))+ 2.569545)","v":{"v":2.291234189814815,"d":"2.3"}}]
["Notes:"]
[{"v":1,"d":"1."},"The design operating pressure is the rated pressure for the fan or pump serving the system under the design flow condition.  Typically, this is the rated head for the pump or the rated fan static pressure for a fan."]
[]
[]
[{"v":2,"d":"2."},"The operating pressure control set point is the setting used by the controller to regulate fan or pump speed as conditions in the system vary.  "]
[]
[]
[{"v":3,"d":"3."},"If you have a set point that is reset (i.e. variable) then the recommended exponent from the SCE data is 2.4."]
[{"v":4,"d":"4."},"The tool uses the center point of the range of applicable setpoints that it applies to in the SCE data to come up with an exponent.  For example the SCE data recommends a using an exponent of 1.5 for all set points that are between 50% and 80% of the system design operating pressure.  The tool specifically assignes an exponent of 1.5 to a set point equal to 65% of the system design operating pressure, which is halfway between 50% and 80%.  \n\nBecause of this, the tool projects an exponent of 0.8 for a system that was operating at a set point that was 100% of the pump or fans rated operating pressure.  This means that if you used that exponent, it would indicate that as the system flow rate was reduced by valves throttling, the pump would use more energy that it would if the relationship between pump energy and speed was linear as can be seen by looking at the chart on the Y vs. X Comparison tab.  In other words, at 50% load, the exponent would calculate that the pump would use 7% - 8% more energy than it would if it simply unloaded linearly with flow.\n\nThis bothered me initially but when I thought about it, I decided that it could make sense.   For example, in the case of a pump, if it was literally being controlled for the differential pressure across the suction and discharge gauge taps, then using the pumps rated pressure as a set point would always be generating more pressure than the loads required because of the pressure drop in the pipe valve and fittings between the flange taps and the sensor points of connection.\n\nThus, I have concluded that given the intent and context of the recommended exponents (to provide a reasonable estimate of power requirements and energy savings associated with reducing them vs. an exact solution), an exponent of less than 1 under some conditions may be merited.\n\nHaving said that, you should use engineering judgement in applying such an exponent, which is true of all of the exponents that were recommended by SCE and are the driver behind the tool.  This judgement could be in the form of past experience, a supplemental mathematical analysis of some sort, or a field test that simulated various conditions and looked at the actaul power requirement."]
[{"v":5,"d":"5."},"The \"Set Point Not Valid\" message indicates you have entered a set point that is greater than the design operating pressure and you should check your information.   If the system you are working with really has a set point like that, then additional analysis and judgement would be meritted in order to determin a reasonable exponent to use."]

{"sheet":"Affinity Law","index":1,"n_rows":6,"n_cols":1,"rows_kept":6,"merged":[[0,0,0,12],[1,0,1,12],[5,0,5,12]]}
["Click here to return to the spreadsheet tool."]
["For a fixed system, the affinity laws state that the horsepower or kW required by a pump or a fan serving a fixed system will be directly proportional to the system flow rate and/or the pump or fan speed.  This relationship is often refered to as the \"cube rule\"."]
[]
[]
[]
["In real world applications, true fixed systems are not particularly common for a number of reasons related to the fact that the affinity law assumes the pump or fan in question is operating on a single, specific system curve with its orgin at 0 ft.w.c./0 gpm and that is rarely if ever true.  However, it is often desireable to estimate pump and fan energy consumption and the savings achieved by making various improvements to a fan or pumping system that optimize the flow and pressure characteristics.  Thus, tempting to try to come up with a way that would allow the affinity law to be adapted so it could be applied for this purpose.\n\nOne option would be to come up with an exponent other than \"3\" and it is possible to analyaze a system and come up with such an exponent.   Over the years, a number of organizations have done this and documented exponents that, when used with engineering judgement, can be applied in place of the \"3\" in the affinity law to allow it to be used with reasonable accuracy.\n\nThe development that follows is based on factors published by Souther California Edison in a document that provided technical support for one of their incentive programs.  The exponents shown are the basis for the tool contained in this spreadsheet."]

{"sheet":"Data and Support","index":3,"n_rows":49,"n_cols":12,"rows_kept":49,"merged":[[34,3,34,9],[35,3,35,9],[36,3,36,9],[37,3,37,9],[38,3,38,9],[39,3,39,9],[40,3,40,9],[41,3,41,9],[42,3,42,9],[43,3,43,9],[44,3,44,9],[45,3,45,9],[46,3,46,9],[47,3,47,9],[48,3,48,9]]}
[]
["Facility Dynamics Headquarters  - 6760 Alexander Bell Drive,  Suite 200,  Columbia, MD 21046, Phone: (410) 290-0900;  www.facilitydynamics.com"]
["Facility Dynamics Satellite Location  - 8560 North Buchanan Avenue,  Portland, Oregon 97203, Phone: ;  www.facilitydynamics.com"]
["Engineering Calculation"]
["Date:","2017-04-24T08:25:58.670"]
["Project Name: ","None"]
["Project Number: ","None"]
["Engineer: ","David"]
["Assumptions"]
[]
[null,null,"X, % Design Flow","Y=X2, Note 1, % Design Head","Y=X1.85, Note 2, % Design Head","Y=X3, Note 3, % Design Head","Y=X2.4, Note 4, % Design Head","Y=X2.2, Note 5, % Design Head","Y=X1.5, Note 6, % Design Head","Y=X1, Note 7, % Design Head","Y=X0.8, Note 8, % Design Head"]
[null,null,{"v":1,"d":"100.0000%"},{"v":1,"d":"100.0000%"},{"v":1,"d":"100.0000%"},{"v":1,"d":"100.0000%"},{"v":1,"d":"100.0000%"},{"v":1,"d":"100.0000%"},{"v":1,"d":"100.0000%"},{"v":1,"d":"100.0000%"},{"v":1,"d":"100.0000%"},"Base Point"]
[null,null,{"v":0.9,"d":"90.0000%"},{"$f":"C13^2","v":{"v":0.81,"d":"81.0000%"}},{"$f":"C13^1.85","v":{"v":0.8229029940476796,"d":"82.2903%"}},{"$f":"C13^3","v":{"v":0.7290000000000001,"d":"72.9000%"}},{"$f":"C13^2.4","v":{"v":0.7765725275664881,"d":"77.6573%"}},{"$f":"C13^2.2","v":{"v":0.7931101735123912,"d":"79.3110%"}},{"$f":"C13^1.5","v":{"v":0.8538149682454624,"d":"85.3815%"}},{"$f":"C13^1","v":{"v":0.9,"d":"90.0000%"}},{"$f":"C13^(0.8)","v":{"v":0.9191661188401216,"d":"91.9166%"}}]
[null,null,{"v":0.8,"d":"80.0000%"},{"$f":"C14^2","v":{"v":0.6400000000000001,"d":"64.0000%"}},{"$f":"C14^1.85","v":{"v":0.6617843245018656,"d":"66.1784%"}},{"$f":"C14^3","v":{"v":0.5120000000000001,"d":"51.2000%"}},{"$f":"C14^2.4","v":{"v":0.5853504664669777,"d":"58.5350%"}},{"$f":"C14^2.2","v":{"v":0.6120655998656237,"d":"61.2066%"}},{"$f":"C14^1.5","v":{"v":0.7155417527999327,"d":"71.5542%"}},{"$f":"C14^1","v":{"v":0.8,"d":"80.0000%"}},{"$f":"C14^(0.8)","v":{"v":0.8365116420730186,"d":"83.6512%"}}]
[null,null,{"v":0.7,"d":"70.0000%"},{"v":0.48999999999999994,"d":"49.0000%"},{"v":0.5169295677807219,"d":"51.6930%"},{"v":0.3429999999999999,"d":"34.3000%"},{"v":0.42484968054675043,"d":"42.4850%"},{"v":0.45626345839647037,"d":"45.6263%"},{"v":0.5856620185738528,"d":"58.5662%"},{"v":0.7,"d":"70.0000%"},{"v":0.7517586466500454,"d":"75.1759%"}]
[null,null,{"v":0.6,"d":"60.0000%"},{"v":0.36,"d":"36.0000%"},{"v":0.3886689196855297,"d":"38.8669%"},{"v":0.216,"d":"21.6000%"},{"v":0.29346951945813216,"d":"29.3470%"},{"v":0.3250369625210763,"d":"32.5037%"},{"v":0.46475800154489,"d":"46.4758%"},{"v":0.6,"d":"60.0000%"},{"v":0.6645398059489739,"d":"66.4540%"}]
[null,null,{"v":0.5,"d":"50.0000%"},{"v":0.25,"d":"25.0000%"},{"v":0.27739236801696127,"d":"27.7392%"},{"v":0.125,"d":"12.5000%"},{"v":0.18946457081379975,"d":"18.9465%"},{"v":0.21763764082403103,"d":"21.7638%"},{"v":0.3535533905932738,"d":"35.3553%"},{"v":0.5,"d":"50.0000%"},{"v":0.5743491774985175,"d":"57.4349%"}]
[null,null,{"v":0.4,"d":"40.0000%"},{"v":0.16000000000000003,"d":"16.0000%"},{"v":0.18357392089007762,"d":"18.3574%"},{"v":0.06400000000000002,"d":"6.4000%"},{"v":0.11090317490482345,"d":"11.0903%"},{"v":0.13320851318429971,"d":"13.3209%"},{"v":0.2529822128134704,"d":"25.2982%"},{"v":0.4,"d":"40.0000%"},{"v":0.4804497735925725,"d":"48.0450%"}]
[null,null,{"v":0.35,"d":"35.0000%"},{"v":0.12249999999999998,"d":"12.2500%"},{"v":0.1433923169046787,"d":"14.3392%"},{"v":0.04287499999999999,"d":"4.2875%"},{"v":0.08049396238517001,"d":"8.0494%"},{"v":0.09930010267962122,"d":"9.9300%"},{"v":0.20706279240848652,"d":"20.7063%"},{"v":0.35,"d":"35.0000%"},{"v":0.43177196038085225,"d":"43.1772%"}]
[null,null,{"v":0.3,"d":"30.0000%"},{"v":0.09,"d":"9.0000%"},{"v":0.10781379200616319,"d":"10.7814%"},{"v":0.027,"d":"2.7000%"},{"v":0.05560207655106707,"d":"5.5602%"},{"v":0.07074027770369602,"d":"7.0740%"},{"v":0.16431676725154978,"d":"16.4317%"},{"v":0.3,"d":"30.0000%"},{"v":0.38167789096181753,"d":"38.1678%"}]
[null,null,{"v":0.25,"d":"25.0000%"},{"v":0.0625,"d":"6.2500%"},{"v":0.07694652583405728,"d":"7.6947%"},{"v":0.015625,"d":"1.5625%"},{"v":0.03589682359365735,"d":"3.5897%"},{"v":0.047366142703449944,"d":"4.7366%"},{"v":0.12500000000000003,"d":"12.5000%"},{"v":0.25,"d":"25.0000%"},{"v":0.3298769776932236,"d":"32.9877%"}]
[null,null,{"v":0.2,"d":"20.0000%"},{"v":0.04000000000000001,"d":"4.0000%"},{"v":0.05092200462185695,"d":"5.0922%"},{"v":0.008000000000000002,"d":"0.8000%"},{"v":0.021012222435230148,"d":"2.1012%"},{"v":0.02899118654710782,"d":"2.8991%"},{"v":0.08944271909999162,"d":"8.9443%"},{"v":0.2,"d":"20.0000%"},{"v":0.27594593229224296,"d":"27.5946%"}]
[null,null,{"v":0.18,"d":"18.0000%"},{"v":0.0324,"d":"3.2400%"},{"v":0.04190387006623585,"d":"4.1904%"},{"v":5.8319999999999995E-3,"d":"0.5832%"},{"v":0.016317514686315933,"d":"1.6318%"},{"v":0.02299320499270678,"d":"2.2993%"},{"v":0.07636753236814713,"d":"7.6368%"},{"v":0.18,"d":"18.0000%"},{"v":0.25364015159477993,"d":"25.3640%"}]
[null,null,{"v":0.16,"d":"16.0000%"},{"v":0.0256,"d":"2.5600%"},{"v":0.033699384430956464,"d":"3.3699%"},{"v":0.004096000000000001,"d":"0.4096%"},{"v":0.01229951420396985,"d":"1.2300%"},{"v":0.017744507984771736,"d":"1.7745%"},{"v":0.06399999999999999,"d":"6.4000%"},{"v":0.16,"d":"16.0000%"},{"v":0.2308319849451541,"d":"23.0832%"}]
[null,null,{"v":0.14,"d":"14.0000%"},{"v":0.019600000000000003,"d":"1.9600%"},{"v":0.026323089839704435,"d":"2.6323%"},{"v":2.7440000000000008E-3,"d":"0.2744%"},{"v":0.008927035989184793,"d":"0.8927%"},{"v":0.013227619037000645,"d":"1.3228%"},{"v":0.05238320341483519,"d":"5.2383%"},{"v":0.14,"d":"14.0000%"},{"v":0.20744474060860166,"d":"20.7445%"}]
[null,null,{"v":0.12,"d":"12.0000%"},{"v":0.0144,"d":"1.4400%"},{"v":0.01979180052459869,"d":"1.9792%"},{"v":0.001728,"d":"0.1728%"},{"v":0.006166446820814374,"d":"0.6166%"},{"v":0.00942320721515382,"d":"0.9423%"},{"v":0.04156921938165306,"d":"4.1569%"},{"v":0.12,"d":"12.0000%"},{"v":0.18337705629789586,"d":"18.3377%"}]
[null,null,{"v":0.1,"d":"10.0000%"},{"v":0.010000000000000002,"d":"1.0000%"},{"v":0.014125375446227542,"d":"1.4125%"},{"v":1.0000000000000002E-3,"d":"0.1000%"},{"v":0.003981071705534975,"d":"0.3981%"},{"v":0.00630957344480193,"d":"0.6310%"},{"v":0.0316227766016838,"d":"3.1623%"},{"v":0.1,"d":"10.0000%"},{"v":0.15848931924611137,"d":"15.8489%"}]
[null,null,{"v":0.08,"d":"8.0000%"},{"v":0.0064,"d":"0.6400%"},{"v":0.009347952048016932,"d":"0.9348%"},{"v":5.1200000000000009E-4,"d":"0.0512%"},{"v":2.3303221798733815E-3,"d":"0.2330%"},{"v":0.003861872855388901,"d":"0.3862%"},{"v":0.022627416997969513,"d":"2.2627%"},{"v":0.08,"d":"8.0000%"},{"v":0.13257816069359946,"d":"13.2578%"}]
[null,null,{"v":0.06,"d":"6.0000%"},{"v":0.0036,"d":"0.3600%"},{"v":0.005490094414837762,"d":"0.5490%"},{"v":0.000216,"d":"0.0216%"},{"v":1.168323200351715E-3,"d":"0.1168%"},{"v":2.0508445873020625E-3,"d":"0.2051%"},{"v":0.014696938456699062,"d":"1.4697%"},{"v":0.06,"d":"6.0000%"},{"v":0.10532246145679582,"d":"10.5322%"}]
[null,null,{"v":0.04,"d":"4.0000%"},{"v":0.0016,"d":"0.1600%"},{"v":0.00259305055470842,"d":"0.2593%"},{"v":6.4000000000000011E-5,"d":"0.0064%"},{"v":4.4151349166758917E-4,"d":"0.0442%"},{"v":8.4048889740920534E-4,"d":"0.0840%"},{"v":0.008000000000000004,"d":"0.8000%"},{"v":0.04,"d":"4.0000%"},{"v":0.07614615754863513,"d":"7.6146%"}]
[null,null,{"v":0.02,"d":"2.0000%"},{"v":0.0004,"d":"0.0400%"},{"v":7.192924337582632E-4,"d":"0.0719%"},{"v":8.0000000000000013E-6,"d":"0.0008%"},{"v":8.3651164207301852E-5,"d":"0.0084%"},{"v":1.8292202077093046E-4,"d":"0.0183%"},{"v":2.8284271247461914E-3,"d":"0.2828%"},{"v":0.02,"d":"2.0000%"},{"v":0.043734482957731115,"d":"4.3734%"}]
[null,null,{"v":0.01,"d":"1.0000%"},{"v":1E-4,"d":"0.0100%"},{"v":1.9952623149688793E-4,"d":"0.0200%"},{"v":1.0000000000000002E-6,"d":"0.0001%"},{"v":1.5848931924611158E-5,"d":"0.0016%"},{"v":3.98107170553497e-05,"d":"0.0040%"},{"v":1.0000000000000002E-3,"d":"0.1000%"},{"v":0.01,"d":"1.0000%"},{"v":0.025118864315095805,"d":"2.5119%"}]
[null,null,{"v":0,"d":"0.0000%"},{"v":0,"d":"0.0000%"},{"v":0,"d":"0.0000%"},{"v":0,"d":"0.0000%"},{"v":0,"d":"0.0000%"},{"v":0,"d":"0.0000%"},{"v":0,"d":"0.0000%"},{"v":0,"d":"0.0000%"},{"v":0,"d":"0.0000%"}]
[null,null,"Notes:"]
[null,null,{"v":1,"d":"1."},"The \"Square Law\" defining the system flow versus pressure drop relationship for a piping or duct system with fully developed turbulent flow.  It is also the exponent recommended by Southern California Edison to adjust the \"Cube Rule\" for:"]
[{"$nulls":3},"a.   A constant volume air system serving open plenums."]
[{"$nulls":3},"b.  A variable flow air or water system with a fixed set point that is 20% - 50% of the total pressure required at design flow."]
[null,null,{"v":2,"d":"2."},"The ASHRAE research based system curve relationship for typical HVAC systems due to the fact that in some parts of the system, there is not fully developed turbulent flow."]
[null,null,{"v":3,"d":"3."},"The \"Cube Rule\" or Affinity Law defining the relationship between pump or fan power and flow or speed."]
[null,null,{"v":4,"d":"4."},"Southern California Edison's suggested affinity law exponent for: "]
[{"$nulls":3},"a.  A closed constant volume water system."]
[{"$nulls":3},"b.  A variable flow air or water system with a fixed set point that is 20% or less of the total pressure required at design flow."]
[{"$nulls":3},"c.  A variable flow air or water system with a reset set point."]
[null,null,{"v":5,"d":"5."},"Southern California Edison's suggested affinity law exponent for: "]
[{"$nulls":3},"a.  An open constant volume water system."]
[{"$nulls":3},"b.  A constant volume air system like a CRAC (Computer Room Air Conditioning) unit serving enclosed hot or cold aisles."]
[null,null,{"v":6,"d":"6."},"Southern California Edison's suggested affinity law exponent for a variable flow air or water system with a fixed set point that is 50% - 80% of the total pressure required at design flow."]
[null,null,{"v":7,"d":"7."},"The equation of a straight line and also Southern California Edison's suggested affinity law exponent for a variable flow air or water system with a fixed set point that is greater than 80% of the total pressure required at design flow."]
[null,null,{"v":8,"d":"8."},"This is the exponent you get if you extrapolate the SCE data to make the controlling set point equal to the pumps rated pressure."]