Fysikalkonstanter0.5019380.162888-0.1303560.907919-0.5511190.1465430.2356220.7893930.6736651.2075520.0670665-0.084337-0.274637-0.743539-0.959456-0.687343-0.4970890.1952860.1458310.2631290.3472470.2134860.100754-0.032932-0.0270448-0.0253093-0.0267758-0.08229040.0602253-0.0202595

Saturconstants1.8541220.00048362970.0000066961-0.00000005890.0000000029-00-003.77195799920.0315711253-0.00122647560.0001237497-0.00000523290.0000001241-0.00000000160-017.150.7969958204.21694-0.0033008610.0001081804-0.00000182890.0000000187-0.00000000010-004.86700649490.00880318460.0005128801-0.00003601620.000001598-0.00000003820.0000000005-0010.110.446997699708.8328440.03901931-0.00042952450.0000115986-0.00000013390.0000000008-00017.56910530230.0326470507-0.00256635060.0002071305-0.00000689880.000000123-0.00000000120-029.720.11250.511250.00055803780.00001961160.0000001202-0.00000000030-00-00106.4964491544-0.4054330411-0.00158916940.0000735635-0.00000151440.0000000141-0-0052.16-0.3525-0.4487516.7069236450.0380459030.0042318545-0.00018621280.0000039925-0.00000004520.0000000003-0051.0196562407-0.15622717660.1095809399-0.00818414780.0003025108-0.00000610020.0000000687-0.0000000004029330.21428571431.4732142857564.84322.100223-0.015008910.0001442461-0.00000199260.0000000176-0.00000000010-0614.9913206081-0.80678525-0.05835855590.0039270009-0.00012187680.000001775-0.0000000122004184.89285714291.38839285710.97883840.00139324-0.00010789930.0000027045-0.00000003060.0000000002-00-00.074644790.0030768920.00001310370.0000003476-0.000000004900-005.3873.206877325607.8024.33798081340

Datas16.8359927428.56067796-54.389233290.4330662834-0.65477116970.08565182060.06670375921.3889838010.08390104330.0261467089-0.03373439450.45209189040.1069036614-0.5975336707-0.0884753580.5958051609-0.51593033730.20750211220.1190610271-0.09867174130.1683998803-0.058094380.00655239010.0005710219193.6587558-1388.5224254126.607219-6508.2116775745.984054-2693.088365523.57186230.76333333330.40060739480.0863608163-0.85323229210.3460208861-7.691234564-26.08023696-168.170654664.23285504-118.96462254.1671173220.9750676100000000066824.687741-542.2063673-20966.6620539412.86787-67332.7773999023.81028-109391.177485908.41667-45111.6874214181.38926-2017.2711137.982692717-0.02616571840.00152241180.0228427905242.16470031.27E-102.07E-072.17E-081.11E-0912.934419340.00001308126.05E-140.84383754050.00053621621.720.07342278490.04975858870.653715430.000001150.0000151080.141887.0027531650.00029952850.204-6.8399-0.017226042-7.771750394.20460752-2.768070382.10419707-1.146495880.2231380850.116250363-0.08209005440.0194129239-0.0016947058-4.31157703300.70863608512.3679455-12.03890045.40437422-0.9938650430.0627523182-7.747430160-4.2988509243.1430538-14.16193134.041724591.55546326-1.665689350.32488115829.365532500.000007948480.8859747-83.61533835.86365177.51895954-12.6160641.097174622.12145492-0.5465295668.328754130.0000027597-0.000509074210.6363320.0552893534-0.23363659550.369707142-0.2596415470.0682808701-257.1600533-151.878371522.20723208-180.2039572357.09622-14623.3569845429.1663-70535.5643243815.71428-1.7176167473.526389875-2.6908993730.9070982605-0.11387911561.301023613-2.6427777431.996765362-0.66615570130.08270860590.0003426664-0.00123652130.001155018300

Air Data-73.150.01811.0070.7371.74580.00001325-23.150.02231.0060.721.39470.0000159626.850.02631.0070.7071.16140.0000184676.850.031.0090.70.9950.00002082126.850.03381.0140.690.87110.00002301176.850.03731.0210.6860.7740.00002507226.850.04071.030.6840.69640.00002701276.850.04391.040.6830.63290.00002884326.850.04691.0510.6850.58040.00003058376.850.04971.0630.690.53560.00003225426.850.05241.0750.6950.49750.00003388476.850.05491.0870.7020.46430.00003546526.850.05731.0990.7090.43540.00003698576.850.05961.110.7160.40970.00003843626.850.0621.1210.720.38680.00003981676.850.06431.1310.7230.36660.00004113726.850.06671.1410.7260.34820.00004244tkCpPrraguamCW/(m*K)kJ/(kg*K)-kg/m3Pa sAtmospheric air properties as a function of the temperatureAtmospheric air properties as a functionof the temperature(Table A.4)[1]

Water Data00.5694.21712.991000.001.75E-031.75E-061.35E-070.00611.850.5744.21112.221000.001.65E-031.65E-061.36E-070.00706.850.5824.19810.261000.001.42E-031.42E-061.39E-070.009911.850.5904.1898.811000.001.23E-031.23E-061.41E-070.013916.850.5984.1847.56999.001.08E-031.08E-061.43E-070.019221.850.6064.1816.62998.009.59E-049.61E-071.45E-070.026226.850.6134.1795.83997.018.55E-048.58E-071.47E-070.035331.850.6204.1785.2995.027.69E-047.73E-071.49E-070.047136.850.6284.1784.62993.056.95E-047.00E-071.51E-070.062241.850.6344.1794.16991.086.31E-046.37E-071.53E-070.081346.850.6404.183.77989.125.77E-045.78E-071.53E-070.105351.850.6454.1823.42987.175.28E-045.35E-071.56E-070.135156.850.6514.1843.15984.254.89E-044.97E-071.58E-070.171961.850.6564.1862.88982.324.53E-044.61E-071.60E-070.216966.850.6604.1882.66979.434.20E-044.29E-071.61E-070.271571.850.6644.1912.45976.563.89E-043.98E-071.63E-070.337476.850.6684.1952.29973.713.65E-043.75E-071.64E-070.416381.850.6714.1992.14970.873.43E-043.53E-071.65E-070.510286.850.6744.2032.02967.123.24E-043.35E-071.66E-070.621391.850.6774.2091.91963.393.06E-043.18E-071.67E-070.751896.850.6794.2141.8960.612.89E-043.01E-071.68E-070.90451000.6804.2171.76957.852.79E-042.91E-071.68E-071.0133tkCpPrraguamnaPsatCW/(m*K)kJ/(kg*K)-kg/m3Pa sm2/sm2/sbarSaturation properties of water as a function of the temperatureSaturated Water Properties as a Functionof Temperature (Table A.6)[1]

6.CS_Imp123456789101112131415161723Pipe Thickness [mm], according ASME B36.10M45ASME B36.10M SCHEDULE / IDENTIFICATIONApplicationDn =24mm6Sizedext5102030406080100120140160STDXSXXS(with input validation)SCH =XS71/221.31.652.11-2.412.77-3.73-0-4.782.773.737.47di =Pipe_Imp_CS_Dint_dn_schmm83/426.71.652.11-2.412.87-3.91-0-5.562.873.917.82de =Pipe_Imp_CS_Dext_dnmm9133.41.652.77-2.93.38-4.55-0-6.353.384.559.09s =Pipe_Imp_CS_Thickness_dn_schmm101 1/248.31.652.77-3.183.68-5.08-0-7.143.685.0810.1511260.31.652.77-3.183.91-5.54-0-8.743.915.5411.07ApplicationDn =16mm12388.92.113.05-4.785.49-7.62-0-11.135.497.6215.24(without input validation)SCH =81134114.32.113.05-4.786.02-8.56-11.13-13.496.028.5617.12di =Pipe_Imp_CS_Dint_dn_schmm145141.32.773.4--6.55-9.53-12.7-15.886.559.5319.05de =Pipe_Imp_CS_Dext_dnmm156168.32.773.4--7.11-10.97-14.27-18.267.1110.9721.95s =Pipe_Imp_CS_Thickness_dn_schmm168219.12.773.766.357.048.1810.3112.715.0918.2620.6223.018.1812.722.23The shedule entered is wrong17102733.44.196.357.89.2712.715.0918.2621.4425.428.589.2712.725.41812323.83.964.576.358.3810.3114.2717.4821.4425.428.5833.329.5312.725.41914355.63.966.357.929.5311.1315.0919.0523.8327.7931.7535.719.5312.7-2016406.44.196.357.929.5312.716.6621.4426.1930.9636.5340.499.5312.7-21184574.196.357.9211.1314.2719.0523.8329.3634.9339.6745.249.5312.7-22205084.786.359.5312.715.0920.6226.1932.5438.144.4550.019.5312.7-23225594.786.359.5312.7-22.2328.5834.9341.2847.6353.989.5312.7-24246105.546.359.5314.2717.4824.6130.9638.8946.0252.3759.549.5312.7-2526660-7.9212.715.88-------9.5312.7-2628711-7.9212.7--------9.5312.7-27307626.357.9212.715.88-------9.5312.7-2832813-7.9212.715.8817.48------9.5312.7-2934864-7.9212.715.8817.48------9.5312.7-3036914-7.9212.715.8819.05------9.5312.7-3138965-----------9.5312.7-32401016-----------9.5312.7-33421067-----------9.5312.7-34441118-----------9.5312.7-35461168-----------9.5312.7-36481219-----------9.5312.7-'PipeImp_CS_Dext_dn'The function PipeImp_CS_Dext_dn gives the exterior diameter of a pipe with'nominal diameter dn [in]'If the diameter is a fraction, the input cell has to be formated as a fractionFunction PipeImp_CS_Dext_dn(Dn)Dim msg As StringDim C(36, 3) As VariantMensaje = "NO"' Exterior diameters according ASME B36.10M, from Sheet 6.CS_Imp, 3th columnFor m = 1 To 36C(m, 3) = ThisWorkbook.Worksheets("6.CS_Imp").Cells(m, 3).ValueNext m' The corresponding line of the matrix C is asigned to its Dn-valueIf Dn = 0.5 Thenx = 7ElseIf Dn = 0.75 Then x = 8ElseIf Dn = 1 Then x = 9ElseIf Dn = 1.5 Then x = 10ElseIf Dn = 2 Then x = 11ElseIf Dn = 3 Then x = 12ElseIf Dn = 4 Then x = 13ElseIf Dn = 5 Then x = 14ElseIf Dn = 6 Then x = 15ElseIf Dn = 8 Then x = 16ElseIf Dn = 10 Then x = 17ElseIf Dn = 12 Then x = 18ElseIf Dn = 14 Then x = 19ElseIf Dn = 16 Then x = 20ElseIf Dn = 18 Then x = 21ElseIf Dn = 20 Then x = 22ElseIf Dn = 22 Then x = 23ElseIf Dn = 24 Then x = 24ElseIf Dn = 26 Then x = 26ElseIf Dn = 28 Then x = 26ElseIf Dn = 30 Then x = 27ElseIf Dn = 32 Then x = 28ElseIf Dn = 34 Then x = 29ElseIf Dn = 36 Then x = 30ElseIf Dn = 38 Then x = 31ElseIf Dn = 40 Then x = 32ElseIf Dn = 42 Then x = 33ElseIf Dn = 44 Then x = 34ElseIf Dn = 46 Then x = 35ElseIf Dn = 48 Then x = 36' If the Dn-value is not within the given values,' The function returns Dext = "N/A"ElsePipeImp_CS_Dext_dn = "N/A"Exit FunctionEnd If' In case the input value for Dn was identified and therefore an x-value "x" has been defined,' the value of the matrix element (x,3) is assigned to de exterior diameter DextPipeImp_CS_Dext_dn = C(x, 3)End Function'PipeImp_CS_Thickness_dn_sch'The function PipeImp_CS_Thickness_dn_sch gives the thickness of a pipe with'nominal diameter dn [in] and schedule sch'If the diameter is a fraction, the input cell ha to be formated as a fractionFunction PipeImp_CS_Thickness_dn_sch(Dn, SCH)Dim C(36, 17) As Variant' Thickness according ASME B36.10M, from Sheet 6.CS_ImpFor m = 1 To 36For j = 1 To 17C(m, j) = ThisWorkbook.Worksheets("6.CS_Imp").Cells(m, j).ValueNext jNext mIf PipeImp_CS_Dext_dn(Dn) = "N/A" ThenPipeImp_CS_Thickness_dn_sch = "N/A"Exit FunctionEnd IfIf Dn = 0.5 Thenx = 7ElseIf Dn = 0.75 Then x = 8ElseIf Dn = 1 Then x = 9ElseIf Dn = 1.5 Then x = 10ElseIf Dn = 2 Then x = 11ElseIf Dn = 3 Then x = 12ElseIf Dn = 4 Then x = 13ElseIf Dn = 5 Then x = 14ElseIf Dn = 6 Then x = 15ElseIf Dn = 8 Then x = 16ElseIf Dn = 10 Then x = 17ElseIf Dn = 12 Then x = 18ElseIf Dn = 14 Then x = 19ElseIf Dn = 16 Then x = 20ElseIf Dn = 18 Then x = 21ElseIf Dn = 20 Then x = 22ElseIf Dn = 22 Then x = 23ElseIf Dn = 24 Then x = 24ElseIf Dn = 26 Then x = 26ElseIf Dn = 28 Then x = 26ElseIf Dn = 30 Then x = 27ElseIf Dn = 32 Then x = 28ElseIf Dn = 34 Then x = 29ElseIf Dn = 36 Then x = 30ElseIf Dn = 38 Then x = 31ElseIf Dn = 40 Then x = 32ElseIf Dn = 42 Then x = 33ElseIf Dn = 44 Then x = 34ElseIf Dn = 46 Then x = 35ElseIf Dn = 48 Then x = 36ElsePipeImp_CS_Thickness_dn_sch(Dn, SCH) = "N/A"Exit FunctionEnd IfIf SCH = 5 ThenY = 4ElseIf SCH = 10 Then Y = 5ElseIf SCH = 20 Then Y = 6ElseIf SCH = 30 Then Y = 7ElseIf SCH = 40 Then Y = 8ElseIf SCH = 60 Then Y = 9ElseIf SCH = 80 Then Y = 10ElseIf SCH = 100 Then Y = 11ElseIf SCH = 120 Then Y = 12ElseIf SCH = 140 Then Y = 13ElseIf SCH = 160 Then Y = 14ElseIf SCH = "STD" Then Y = 15ElseIf SCH = "XS" Then Y = 16ElseIf SCH = "XXS" Then Y = 17ElsePipeImp_CS_Thickness_dn_sch = "N/A"Exit FunctionEnd IfPipeImp_CS_Thickness_dn_sch = C(x, Y)If PipeImp_CS_Thickness_dn_sch = " - " ThenPipeImp_CS_Thickness_dn_sch = "N/A"End IfEnd Function'PipeImp_CS_Dint_dn_sch'The function PipeImp_CS_Dint_dn_sch gives the interior diameter of a pipe with'nominal diameter dn [in] and schedule sch'If the diameter is a fraction, the input cell ha to be formated as a fractionFunction PipeImp_CS_Dint_dn_sch(Dn, SCH)If PipeImp_CS_Thickness_dn_sch(Dn, SCH) = "N/A" ThenPipeImp_CS_Dint_dn_sch = "N/A"Exit FunctionEnd IfIf PipeImp_CS_Dext_dn(Dn) = "N/A" ThenPipeImp_CS_Dint_dn_sch = "N/A"Exit FunctionEnd IfPipeImp_CS_Dint_dn_sch = PipeImp_CS_Dext_dn(Dn) - PipeImp_CS_Thickness_dn_sch(Dn, SCH) * 2End Function

Water hammerRev. cjc 30.01.2014Water hammer1.- Input dataSpeed of sound in water4.- Velocity change7. Critical time8.- Pressure increment due to waterhammer produced by a Not SuddenOperating pressure and flowrateInitial velocityMaximum over- pressure or under-Shutoff "NSS"pop =13.8barvi =5.47m/spressure are obtained when theMichadQ =635.9m3/hc: speed of sound (m/s)Final velocityshutoff time "Dt", is less or equal toFor a shutoff time greater than thevf =0.00m/sthe critical time "tc",critical time, the Michaud relation canPipe dataK: water bulk modulus (Pa)Velocity changebe used.Material:Carbon Steelr: water density (kg/m)Dv =vf - vim/sdn =8inc(K / r )^0.5Dv =-5.47m/ssch =40-K =2.1E+09Patc =2 * L / ahNSS: presure increment in a NonJoujovskyL =1524.0mr =1000kg/m5.- Pressure increment due to waterL =1,524mSudden ShutoffSteel pipe elasticity modulec =1438.2m/shammer produced by a sudden shutoff.a =1286.9m/shSS : Pressure increment in a SuddenEt =2,059,397bartc =2.4sShutoff (Joukovsky)s3.- CelerityThe pressure increment can betc : Critical timeBulk modulus and density of watercalculated with Joukovsky elasticityMichaudDt : Valver closing timeK =20,684bartheory, by a Sudden Shutoff "SS"r =1,000kg/mValve closing timehSS =(- a * Dv ) / gDt =5.0sEt =2,059,397bar2.- Auxiliary variablesa =1286.9m/ssDv =-5.47m/sPressure ncrement (NSS)Bulk modulus and density of waterPipe dimensionsa : celerity (wave velocity) (m/s)h =718mhNSS =hSS *( tc / Dt )K =20,684bardi =Pipe_Imp_CS_Dint_dn_schc: speed of sound (m/s)hSS =70.4barhSS =70.4bardi =202.74mmd: inside pipe diameter (mm)tc =2.4ss =Pipe_Imp_CS_Thickness_dn_schs: minimum wall thickness (mm)6.- Total pressure developed by aDt =5.0ss =8.18mmK: water bulk modulus (bar)sudden shutoffhNSS =33.4bara =c / (1 + (K/Et) * (d/s) )^(0.5)Pipe section areac =1438.2m/sptot_SS =pop + hSSA =(pi()/4)*d^2K =2.1E+09Papop =13.8bar9. Pressure developed due to valved =0.2027mEt =2.1E+11PahSS =70.4barshutoff in the time interval Dt > tcA =0.0323m2d =202.74mmptot_SS =84.2bars =8.18mmptot_NSS =pop + hNSSFluid velocitya =1286.9m/spop =13.8barv =Q / AhNSS =33.4barQ=0.1766m3/sptot_NSS =47.2barA =0.0323m2v =5.47m/sBulk modulus of waterSteel elasticity modulusK =2.1E+09PaEt =2.10E+06kp/cmK =20,684barEt =2.06E+11PaEt =2.1E+06bar

A1. TylerRev. cjc 30.01.2014Water hammer [2] Tyler, page 228Maximum pressure developed in a water pipeline with a pressure "p", if a valve is closed nearly instantly or pumps discharging into the line areall stoped at the same instant. Pipe data is: "steel", "dn", "sch", "L". The water flow rate is "Q". What is the maximum pressure developed ifthe valve closes in a time "Dt"?1. Data, SIPipe section3.-Speed of sound in water4.- CelerityTyler data in Anex A (This page, below)A =(pi()/4)*d^2d =0.2027mOperating pressure and flowrateA =0.0323m2p =13.8barMaterial datac: speed of sound (m/s)Q =0.1767m3/sBulk modulus and density of waterK: water bulk modulus (Pa)Pipe dataK =20,684barr: water density (kg/m)a : celerity (wave velocity) (m/s)Material:Carbon steelr =1,000kg/mc(K / r )^0.5c: speed of sound (m/s)dn =8inSteel pipe elasticity moduleK =2.1E+09Pad: inside pipe diameter (mm)sch =40-Et =2,068,428barr =1000kg/ms: minimum wall thickness (mm)L =1524.0mc =1438.2m/sK: water bulk modulus (bar)Valve closing time2. Fluid velocitya =c / (1 + (K/Et) * (d/s) )^(0.5)Dt =5.0sv =Q / Ac =1438.2m/sPipe dimensionsQ=0.1767m3/sK =2.1E+09Padi =Pipe_Imp_CS_Dint_dn_schA =0.0323m2Et =2.1E+11Padi =202.74mmv =5.47m/sd =202.74mms =Pipe_Imp_CS_Thickness_dn_schs =8.18mms =8.18mma =1287.5m/s5.- Pressure increment due to water6.- Maximum pressure developed due to8.- Pressure increment due to waterDP =h *( tc / Dt )hammer produced by a sudden shutoff.a sudden shutoffhammer produced by a Not suddenh =70.5barshutoff.tc =2.4sDP =h * 2 * L / (a * Dt)The pressure increment can be calculatedpmax =pop + hFor a shutoff time greater than theDt =5.0sh =718.4mwith Joukovsky elasticity theorypop =13.8barcritical time, the Michaud relation canDP =33.36barL =1524.0mh =70.5barbe used.a =1287.5m/spmax =84.2bar9. Pressure developed due to valveDt =5.0sh : pressure increment [mwc]pmax =1221.8psishutoff in the time interval Dt > tcDP =340.2ma : wave velocity [m/s]Dt =5sDP =33.4barDv : speed variation [m/s]7. Critical timeDP: presure increment (mwc)Dv =vfinal - vinitialL : pipe length (m)pmax =pop + hg : acceleration of gravity m/sMaximum over- pressure or under-Dv :speed changepop =13.8barThe pressure change "h" ispressure are obtained when theg : acceleration of gravity m/sh =33.4barh =(- a * Dv ) / gshutoff time "Dt", is less or equal toDt: shutoff time interval (s)pmax =47.1bara =1287.5m/sthe critical time "tc",pmax =683.8psiDP =2 * L * Dv / (g * Dt)Dv =vf - vim/sDP =2 * h * L / (a * Dt)L =1524.0m/svf =0m/sh =70.5barDv =5.47svi =5.47m/sL =1524.0mDt =5.0sDv =-5.47m/stc =2 * L / aa =1287.5m/sDP =340.2mg =9.81m/sL =1,524mDt =5.0sDP =33.4barh =718mwca =1287.5m/sDP =33.4barh =70.5bartc =2.4sAnex AAnex A. Tyler dataData, SITyler resultsp =200psip =13.8bardn =8indn =8in5.- Celeritysch =40sch =40a =1287.9m/sL =5,000ftL =1,524mCalculated valueQ =2,800gpmQ =0.177m3/sa =1287.5m/st =5st =5s6.- Pressure increment due to waterBulk modulus of waterhammer produced by a sudden shutoff.Bulk modulus of waterk =300,000psik =20,684barh =70.5bark =22000barr =1000kg/mk =2,068MpaCalculated valuePipe elasticity moduleh =70.5barPipe elasticity moduleE =30,000,000psiE =2,068,428bar8. Pressure developed due to valveE =2068428barE =206,843Mpashutoff in the time interval Dt > tcpmax =44.7barNote 1.di =202.74mmCalculated valueTyler errors =8.18mmpmax =47.1bar484 + 200 = 684 (psi) = 47.16 (bar)g =9.80665m/sCarlos J. Cruz. Rev.15.01.2012Water hammer [2] Tyler, page 228Maximum pressure developed in a water pipeline with a pressure "p", if a valve is closed nearly instantly or pumps discharging into the line areall stoped at the same instant. Pipe data is: "steel", "dn", "sch", "L". The water flow rate is "Q". What is the maximum pressure developed ifthe valve closes in a time "Dt"?1. Data, SIPipe section3.-Water speed of sound4.- CelerityTyler data in Anex A (This page, below)A =(pi()/4)*d^2d =0.20274mOperating pressure and flowrateA =0.0322826194m2p =13.78952barMaterial datac: speed of sound (m/s)Q =0.17665256m3/sBulk modulus and density of waterK: water bulk modulus (Pa)Pipe dataK =20684.28barr: water density (kg/m)a : celerity (wave velocity) (m/s)Material:Carbon steelr =1000kg/mc(K / r )^0.5c: speed of sound (m/s)dn =8inSteel pipe elasticity moduleK =2068428000Pad: inside pipe diameter (mm)sch =40-Et =2068428barr =1000kg/ms: minimum wall thickness (mm)L =1524mc =1438.2030454703m/sK: water bulk modulus (bar)Valve closing time2. Fluid velocitya =c / (1 + (K/Et) * (d/s) )^(0.5)Dt =5sv =Q / Ac =1438.2030454703m/sPipe dimensionsQ=0.17665256m3/sK =2068428000Padi =Pipe_Imp_CS_Dint_dn_schA =0.0322826194m2Et =206842800000Padi =202.74mmv =5.4720640209m/sd =202.74mms =Pipe_Imp_CS_Thickness_dn_schs =8.18mms =8.18mma =1287.5m/s5.- Pressure increment due to water6.- Maximum pressure developed due to8.- Pressure increment due to waterDP =h *( tc / Dt )hammer produced by a sudden shutoff.a sudden shutoffhammer produced by a Not suddenh =70.4515348018barshutoff.tc =2.3674219707sThe pressure increment can be calculatedpmax =pop + hFor a shutoff time greater than theDt =5swith Joukovsky elasticity theorypop =13.8barcritical time, the Michaud relation canDP =33.3577022714barh =70.5barbe used.pmax =84.2bar9. Pressure developed due to valveh : pressure increment [mwc]pmax =1221.8psishutoff in the time interval Dt > tca : wave velocity [m/s]Dt =5sDv : speed variation [m/s]7. Critical timeDP: presure increment (mwc)Dv =vfinal - vinitialL : pipe length (m)pmax =pop + hg : acceleration of gravity m/sMaximum over- pressure or under-Dv :speed changepop =13.78952barThe pressure change "h" ispressure are obtained when theg : acceleration of gravity m/sh =33.3577022714barh =(- a * Dv ) / gshutoff time "Dt", is less or equal toDt: shutoff time interval (s)pmax =47.1472222714bara =1287.4764354504m/sthe critical time "tc",pmax =683.8123773909psiDv =vf - vim/sDP =2 * h * L / (a * Dt)vf =0m/sh =70.45barvi =5.47m/sL =1524.00mDv =-5.47m/stc =2 * L / aa =1287.48m/sg =9.80665m/sL =1524mDt =5.00sh =718.4mwca =1287.5m/sDP =33.4barh =70.45bartc =2.4sAnex AAnex A. Tyler dataData, SITyler resultsp =200psip =13.78952bardn =8indn =8in5.- Celeritysch =40sch =40a =1287.9m/sL =5000ftL =1524mCalculated valueQ =2800gpmQ =0.17665256m3/sa =1287.4764354504m/st =5st =5s6.- Pressure increment due to waterBulk modulus of waterhammer produced by a sudden shutoff.Bulk modulus of waterk =300000psik =20684.28barh =70.5bark =22000barr =1000kg/mk =2068.428MpaCalculated valuePipe elasticity moduleh =70.4515348018barPipe elasticity moduleE =30000000psiE =2068428bar8. Pressure developed due to valveE =2068428barE =206842.8Mpashutoff in the time interval Dt > tcpmax =44.67barNote 1.di =202.74mmCalculated valueTyler errors =8.18mmpmax =47.1472222714bar484 + 200 = 684 (psi) = 47.16 (bar)g =9.80665m/sCarlos J. Cruz. Rev.15.01.2012

Note 1

A2. PehmcoRev. cjc 30.01.2014Pehmco water-hammer [3], page 7.211. DataPipe section5.-Speed of sound in watera : celerity (wave velocity) (m/s)Operating pressure and flowrateA =(pi()/4)*d^2c: speed of sound (m/s)pop =15mwcd =0.0514md: inside pipe diameter (mm)pop =1.47barA =0.0021m2s: minimum wall thickness (mm)Q =2l/sc: speed of sound (m/s)K: water bulk modulus (bar)Q =0.002m3/s3. Material dataK: water bulk modulus (Pa)a =c / (1 + (K/Ep) * (d/s) )^(0.5)Pipe dataBulk modulus and density of waterr: water density (kg/m)c =1483.2m/sMaterial:HDPE PE80k =22,000barc(K / r )^0.5K =2.20E+09Padn =2inr =1000kg/mK =2.2E+09PaEp =7.8E+08PaPN10barPipe elasticity moduler =1000kg/md =51.4mmL =70mEp =7,845barc =1483.2m/ss =5.8mmValve closing time784.532MPa6.- Celeritya =291.7m/sDt =< Tc4. Fluid velocity2. Pipe dimensions and sectionv =Q / Ade =Pipe_Imp_HDPE_PE80_Dext_DnQ=0.0020m3/sde =63mmA =0.0021m2s = Pipe_Imp_HDPE_PE80_Thickness_Dn_PNv =0.96m/ss =5.8mmdi =di =51.4mm7.- Pressure increment due to water8.- Maximum pressure developed due tohammer produced by a sudden shutoff.a sudden shutoff (Joukovsky)For this case, the pressure increment can bePmax_Jouk =pop + hJoukcalculated with Joukovsky elasticity theorypop =1.5barhJouk =2.81barPmax_Jouk =4.3barhJouk : pressure increment, JoukovskyOK. Pmax < PNa : wave velocity [m/s]Dv : speed variation [m/s]9. Critical timeDv =vfinal - vinitialg : acceleration of gravity m/sMaximum over- pressure or under-The pressure change "h" ispressures are obtained when thehJouk =(- a * Dv ) / gmshutoff time "Dt", is less or equal toa =291.7m/sthe critical time "tc",Dv =vf - vim/svf =0m/svi =0.96m/sDv =-0.96m/stc =2 * L / ag =9.81m/sL =70mhJouk =28.7mwca =291.7m/shJouk =2.81bartc =0.5sApproximate bulk modulusSteel elasticity modulusHDPE elasticity modulusE =2.95E+07psiPEECWater 2.2109Pa (value increases at higher pressures)E =2.03E+11PaEp =8,000kp/cmK =2.20E+09PaE =2.03E+06barEp =7.8E+08PaK =22,000barEp =7,845barWater bulh modulusAir 1.42105Pa (adiabatic bulk modulus)WaterAir 1.01105Pa (constant temperature bulk modulus)K =2.06E+04kp/cmK =2.2E+09PaK =22,000barg =9.80665m/s

4.HDPE_PE100162.3202.3ApplicationDn =355mm252.32.8(with input validation)PN =10322.433.6di =Pipe_HDPE_PE100_Dint_Dn_PN(N2; N3)312.8mm402.433.74.5de =Pipe_CS_Dext_dn =355mm502.433.74.65.6s =Pipe_HDPE_PE100_Thickness_Dn_PN(N2; N3)21.1mm632.333.84.75.87.1752.83.64.55.66.88.4902.33.34.35.46.78.210.11102.745.36.68.11012.3ApplicationDn =355mm1253.14.667.49.211.414(without input validation)PN =PN111403.55.16.78.310.312.715.7di =Pipe_CS_Dint_dn_sch =N/Amm16045.87.79.511.814.617.9de =Pipe_CS_Dext_dn =355mm1804.46.68.610.713.316.420.1s =Pipe_CS_Thickness_dn_sch =N/Amm2004.97.39.611.914.718.222.4The nominal pressure entered is wrong2255.58.210.813.416.620.525.22506.29.111.914.818.422.727.92806.910.213.416.620.625.431.33157.711.41518.723.228.635.23558.712.916.921.126.132.239.74009.814.519.123.729.436.344.74501116.321.526.733.140.950.350012.318.123.929.736.845.455.856013.720.326.733.241.250.863015.422.83037.446.257.271017.425.733.942.152.280019.62938.147.458.89002232.642.653.3100024.536.247.759.3120029.443.457.2140034.350.6160039.257.9Dn [mm]4681012.51620Presiones nominales PN [bar]HDPE PE100http://www.vinilit.cl/pdf_2/tub_fittings_hdpe_min.pdfhttp://www.vinilit.cl/pdf_2/tub_fittings_hdpe_min.pdf'La funcin Pipe_HDPE_PE100_Thickness_Dn_PN entrega el espesor de una caera de HDPE PE 100'de dimetro nominal dn [mm] presin nominal PN [bar]Function Pipe_HDPE_PE100_Dext_Dn(Dn)Dim C(32, 8) As VariantFor m = 1 To 32'For j = 1 To 8C(m, 1) = ThisWorkbook.Worksheets("4.HDPE_PE100").Cells(m, 1).Value'Next jNext mCC = C(24, 1)If Dn = 16 Thenx = 1ElseIf Dn = 20 Then x = 2ElseIf Dn = 25 Then x = 3ElseIf Dn = 32 Then x = 4ElseIf Dn = 40 Then x = 5ElseIf Dn = 50 Then x = 6ElseIf Dn = 63 Then x = 7ElseIf Dn = 75 Then x = 8ElseIf Dn = 90 Then x = 9ElseIf Dn = 110 Then x = 10ElseIf Dn = 125 Then x = 11ElseIf Dn = 140 Then x = 12ElseIf Dn = 160 Then x = 13ElseIf Dn = 180 Then x = 14ElseIf Dn = 200 Then x = 15ElseIf Dn = 225 Then x = 16ElseIf Dn = 250 Then x = 17ElseIf Dn = 280 Then x = 18ElseIf Dn = 315 Then x = 19ElseIf Dn = 355 Then x = 20ElseIf Dn = 400 Then x = 21ElseIf Dn = 450 Then x = 22ElseIf Dn = 500 Then x = 23ElseIf Dn = 560 Then x = 24ElseIf Dn = 630 Then x = 25ElseIf Dn = 710 Then x = 26ElseIf Dn = 800 Then x = 27ElseIf Dn = 900 Then x = 28ElseIf Dn = 1000 Then x = 29ElseIf Dn = 1200 Then x = 30ElseIf Dn = 1400 Then x = 31ElseIf Dn = 1600 Then x = 32ElsePipe_HDPE_PE100_Dext_Dn = "N/A"Exit FunctionEnd IfPipe_HDPE_PE100_Dext_Dn = C(x, 1)End FunctionFunction Pipe_HDPE_PE100_Thickness_Dn_PN(Dn, PN)Dim C(33, 8) As VariantFor m = 1 To 32For j = 1 To 8C(m, j) = ThisWorkbook.Worksheets("4.HDPE_PE100").Cells(m, j).ValueNext jNext mIf Dn = 16 Thenx = 1ElseIf Dn = 20 Then x = 2ElseIf Dn = 25 Then x = 3ElseIf Dn = 32 Then x = 4ElseIf Dn = 40 Then x = 5ElseIf Dn = 50 Then x = 6ElseIf Dn = 63 Then x = 7ElseIf Dn = 75 Then x = 8ElseIf Dn = 90 Then x = 9ElseIf Dn = 110 Then x = 10ElseIf Dn = 125 Then x = 11ElseIf Dn = 140 Then x = 12ElseIf Dn = 160 Then x = 13ElseIf Dn = 180 Then x = 14ElseIf Dn = 200 Then x = 15ElseIf Dn = 225 Then x = 16ElseIf Dn = 250 Then x = 17ElseIf Dn = 280 Then x = 18ElseIf Dn = 315 Then x = 19ElseIf Dn = 355 Then x = 20ElseIf Dn = 400 Then x = 21ElseIf Dn = 450 Then x = 22ElseIf Dn = 500 Then x = 23ElseIf Dn = 560 Then x = 24ElseIf Dn = 630 Then x = 25ElseIf Dn = 710 Then x = 26ElseIf Dn = 800 Then x = 27ElseIf Dn = 900 Then x = 28ElseIf Dn = 1000 Then x = 29ElseIf Dn = 1200 Then x = 30ElseIf Dn = 1400 Then x = 31ElseIf Dn = 1600 Then x = 32ElsePipe_HDPE_PE100_Thickness_Dn_PN = "N/A"Exit FunctionEnd If'____________________________________________________________________________If PN = "PN4" ThenY = 2ElseIf PN = "6" Then Y = 3ElseIf PN = "8" Then Y = 4ElseIf PN = "10" Then Y = 5ElseIf PN = "12.5" Then Y = 6ElseIf PN = "16" Then Y = 7ElseIf PN = "20" Then Y = 8ElsePipe_HDPE_PE100_Thickness_Dn_PN = "N/A"Exit FunctionEnd IfPipe_HDPE_PE100_Thickness_Dn_PN = C(x, Y)If Pipe_HDPE_PE100_Thickness_Dn_PN = " " ThenPipe_HDPE_PE100_Thickness_Dn_PN = "N/A"End IfEnd Function'La funcin Pipe_HDPE_PE100_Dint_Dn_PN entrega el dimetro interior de una caera de HDPE PE 100'de dimetro nominal dn [mm] y presin nominal PN [bar]'Function Pipe_HDPE_PE100_Dint_Dn_PN(Dn, PN)If Pipe_HDPE_PE100_Thickness_Dn_PN(Dn, PN) = "N/A" ThenPipe_HDPE_PE100_Dint_Dn_PN = "N/A"Exit FunctionEnd IfPipe_HDPE_PE100_Dint_Dn_PN = Dn - 2 * Pipe_HDPE_PE100_Thickness_Dn_PN(Dn, PN)End Function

4.HDPE_PE80162.21201.92.82ApplicationDn =355mm252.33.53(with input validation)PN =10321.82.94.44di =Pipe_HDPE_PE80_Dint_Dn_PN(N2,N3)290.6mm401.82.33.75.55de =Pipe_HDPE_PE80_Dext_Dn(N2)355mm501.82.02.94.66.96s =Pipe_HDPE_PE80_Thickness_Dn_PN(N2,N3)32.2mm631.82.02.53.65.88.67751.92.32.94.36.810.38902.22.83.55.18.212.391102.73.44.26.310.015.110ApplicationDn =355mm1253.13.94.87.111.417.111(without input validation)PN =111403.54.35.48.012.719.212di =Pipe_HDPE_PE80_Dint_Dn_PNN/Amm1604.04.96.29.114.621.913de =Pipe_CS_Dext_dn355mm1804.45.56.910.216.424.614s =Pipe_HDPE_PE100_Thickness_Dn_PNN/Amm2004.96.27.711.418.227.415The nominal pressure entered is wrong2255.56.98.612.820.530.8162506.27.79.614.222.734.2172806.98.610.715.925.438.318Application with imput diameter in imperial units3157.79.712.117.928.643.1193558.710.913.620.132.248.520ApplicationDn =14in4009.812.315.322.736.354.721(without input validation)PN =1045011.013.817.225.540.961.522di =Pipe_Imp_HDPE_PE80_Dint_Dn_PN(N2,N3)290.6mm50012.315.319.128.445.468.323de =Pipe_Imp_HDPE_PE80_Dext_Dn(N2)355mm56013.717.221.431.750.824s =Pipe_Imp_HDPE_PE80_Thickness_Dn_PN(N2,N3)32.2mm63015.419.324.135.757.22571017.421.827.240.264.52680019.624.530.645.32790022.027.634.451.028100024.530.638.256.729110026.933.742.062.430120029.436.745.968.031140034.442.953.532160039.249.061.233Dn [mm]2 1/23.2461016Presiones nominales PN [bar]HDPE PE80 DIN 8074 / ISO 4427Espesor [mm]1234567'La funcin Pipe_HDPE_PE100_Thickness_Dn_PN entrega el espesor de una caera de HDPE PE 80'de dimetro nominal dn [mm] presin nominal PN [bar]Function Pipe_HDPE_PE80_Dext_Dn(Dn)Dim C(33, 7) As VariantFor m = 1 To 33'For j = 1 To 7C(m, 1) = ThisWorkbook.Worksheets("4.HDPE_PE80").Cells(m, 1).Value'Next jNext mIf Dn = 16 Thenx = 1ElseIf Dn = 20 Then x = 2ElseIf Dn = 25 Then x = 3ElseIf Dn = 32 Then x = 4ElseIf Dn = 40 Then x = 5ElseIf Dn = 50 Then x = 6ElseIf Dn = 63 Then x = 7ElseIf Dn = 75 Then x = 8ElseIf Dn = 90 Then x = 9ElseIf Dn = 110 Then x = 10ElseIf Dn = 125 Then x = 11ElseIf Dn = 140 Then x = 12ElseIf Dn = 160 Then x = 13ElseIf Dn = 180 Then x = 14ElseIf Dn = 200 Then x = 15ElseIf Dn = 225 Then x = 16ElseIf Dn = 250 Then x = 17ElseIf Dn = 280 Then x = 18ElseIf Dn = 315 Then x = 19ElseIf Dn = 355 Then x = 20ElseIf Dn = 400 Then x = 21ElseIf Dn = 450 Then x = 22ElseIf Dn = 500 Then x = 23ElseIf Dn = 560 Then x = 24ElseIf Dn = 630 Then x = 25ElseIf Dn = 710 Then x = 26ElseIf Dn = 800 Then x = 27ElseIf Dn = 900 Then x = 28ElseIf Dn = 1000 Then x = 29ElseIf Dn = 1100 Then x = 30ElseIf Dn = 1200 Then x = 31ElseIf Dn = 1400 Then x = 32ElseIf Dn = 1600 Then x = 33ElsePipe_HDPE_PE80_Dext_Dn = "N/A"Exit FunctionEnd IfPipe_HDPE_PE80_Dext_Dn = C(x, 1)End FunctionFunction Pipe_HDPE_PE80_Thickness_Dn_PN(Dn, PN)Dim C(33, 7) As VariantFor m = 1 To 33For j = 1 To 7C(m, j) = ThisWorkbook.Worksheets("4.HDPE_PE80").Cells(m, j).ValueNext jNext mIf Dn = 16 Thenx = 1ElseIf Dn = 20 Then x = 2ElseIf Dn = 25 Then x = 3ElseIf Dn = 32 Then x = 4ElseIf Dn = 40 Then x = 5ElseIf Dn = 50 Then x = 6ElseIf Dn = 63 Then x = 7ElseIf Dn = 75 Then x = 8ElseIf Dn = 90 Then x = 9ElseIf Dn = 110 Then x = 10ElseIf Dn = 125 Then x = 11ElseIf Dn = 140 Then x = 12ElseIf Dn = 160 Then x = 13ElseIf Dn = 180 Then x = 14ElseIf Dn = 200 Then x = 15ElseIf Dn = 225 Then x = 16ElseIf Dn = 250 Then x = 17ElseIf Dn = 280 Then x = 18ElseIf Dn = 315 Then x = 19ElseIf Dn = 355 Then x = 20ElseIf Dn = 400 Then x = 21ElseIf Dn = 450 Then x = 22ElseIf Dn = 500 Then x = 23ElseIf Dn = 560 Then x = 24ElseIf Dn = 630 Then x = 25ElseIf Dn = 710 Then x = 26ElseIf Dn = 800 Then x = 27ElseIf Dn = 900 Then x = 28ElseIf Dn = 1000 Then x = 29ElseIf Dn = 1100 Then x = 30ElseIf Dn = 1200 Then x = 31ElseIf Dn = 1400 Then x = 32ElseIf Dn = 1600 Then x = 33ElsePipe_HDPE_PE80_Thickness_Dn_PN = "N/A"Exit FunctionEnd If'____________________________________________________________________________If PN = "2.5" ThenY = 2ElseIf PN = "3.2" Then Y = 3ElseIf PN = "4" Then Y = 4ElseIf PN = "6" Then Y = 5ElseIf PN = "10" Then Y = 6ElseIf PN = "16" Then Y = 7ElsePipe_HDPE_PE80_Thickness_Dn_PN = "N/A"Exit FunctionEnd IfPipe_HDPE_PE80_Thickness_Dn_PN = C(x, Y)If Pipe_HDPE_PE80_Thickness_Dn_PN = "" ThenPipe_HDPE_PE80_Thickness_Dn_PN = "N/A"End IfEnd Function'La funcin Pipe_HDPE_PE100_Dint_Dn_PN entrega el dimetro interior de una caera de HDPE PE 100'de dimetro nominal dn [mm] y presin nominal PN [bar]'Function Pipe_HDPE_PE80_Dint_Dn_PN(Dn, PN)If Pipe_HDPE_PE80_Thickness_Dn_PN(Dn, PN) = "N/A" ThenPipe_HDPE_PE80_Dint_Dn_PN = "N/A"Exit FunctionEnd IfPipe_HDPE_PE80_Dint_Dn_PN = Dn - 2 * Pipe_HDPE_PE80_Thickness_Dn_PN(Dn, PN)End Function

7.SS_ImpNOMINAL SIZENOMINAL O.D5S10S40S80Smmdi [mm]di [mm]di [mm]di [mm]Stainless Steel Pipe Schedule ANSI B36.10dndeInternal diameter [mm]ApplicationDn =1.5in1/810.29-7.816.835.47(with input validation)SCH =5S1/413.72-10.429.247.68di =Pipe_Imp_SS_Dint_Dn_SCH44.96mm3/817.15-13.8512.5310.75de =Pipe_Imp_SS_Dext_Dn48.26mm1/221.3418.0417.1215.8013.88s =Pipe_Imp_SS_Thickness_Dn_SCH1.65mm3/426.6723.3722.4520.9318.85133.4030.1027.8626.6424.301 1/442.1638.8636.6235.0432.46ApplicationDn =1.5in1 1/248.2644.9642.7240.9038.10(without input validation)SCH =5S260.3357.0354.7952.5149.25di =Pipe_Imp_SS_Dint_Dn_SCH44.96mm2 1/273.0368.8166.9362.7159.01de =Pipe_Imp_SS_Dext_Dn48.26mm388.9084.6882.8077.9273.66s =Pipe_Imp_SS_Thickness_Dn_SCH1.65mm3 1/2101.6097.3895.5090.1285.44The nominal diameter entered is wrong4114.30110.08108.20102.2697.185141.30135.76134.50128.20122.246168.28162.74161.48154.06146.348219.08213.54211.56202.72193.6810273.05266.25264.67254.51247.6512323.85315.93314.71304.79298.4514355.60347.68346.04--16406.40398.02396.84--18457.20448.82447.64--20508.00498.44496.91--22558.80549.24547.72--24609.60598.52596.90--30762.00749.30746.16--dnSchin-1/85S1/410S3/840S1/280S3/411 1/41 1/222 1/233 1/24568101214161820222430

Note 1

A3. Slurry hammerRev. cjc 30.01.2014Slurry hammer [8]DataOperating pressure and flowrateWaterPipe dimensions and sectionpop =15mwcEL :2.2E+09Pade =Pipe_Imp_HDPE_PE80_Dext_Dnpop =1.47barrL =1000kg/mde =63mmQ =2l/ss = Pipe_Imp_HDPE_PE80_Thickness_Dn_PNQ =0.002m3/sValve closing times =5.8mmDt =0.0sdi =Pipe_Imp_HDPE_PE80_Dint_Dn_PNPipe datadi =51.4mmMaterial:HDPE PE80A =(pi()/4)*d^2dn =2ind =0.0514mPN10barA =0.0021m2L =70mEP :7.8E+08PaFluid velocityv =Q / ASlurryQ=0.0020m3/sCv =0.4-A =0.0021m2rs =1800kg/mv =0.96m/srL =1000kg/mES :1.17E+11Pa(Copper)Celerity of slurriesSlurry celerity calculationa =( ( ( (Cv/rs) + ((1-Cv) / (rL)) )*EL ) / (1 - Cv + EL/Es * Cv + EL * D / (EP * e)) )^0.5Eq. 20, [8], page 340Cv =0.4-rs =1800kg/mrL =1000kg/mEP :7.85E+08PaPipe : HDPEEL :2.2E+09PaLiquid: Wateram2 :Celerity of an heterog.ES :1.2E+11PaSolids: copperCv :Solids concentration vol.D :63mmrs :Solids densitye :5.8mmrL :Water densitya =241.2m/sEP :Elastic modulus pipe mat.EL :Elastic modulus of liquidES :Elastic modulus of solidsD :Pipe diametere :Pipe wall thicknessPressure increment for heterogeneous sluryy, due to suddenly valve shut-offIn engineering practice the initial hammer pressure can usually be used to substitutethe slurry hammer pressureEq. 33, page 344P :slurry hammer pressure[Pa]am :celerity of mixture (slurry)[m/s]um0 :velocity ofmixture (slurrry) before valve closure[m/s]rL :liquid density[kg/m]rS :solids density[kg/m]CV:Volume concentration[ - ]P =am * um0 * rL * rS / ( (1 - CV) * rS + CV * rL )am =241.245m/sum0 =0.96m/srL =1000rS =1800CV =0.4P =282,802PaP =2.83barMaximum pressure developed due to a sudden shutoffPmax_Jouk =pop + PPop =1.47barP =2.83barPmax_Jouk =4.30bar

A4. Thermoplastic[9]a =c / ( 1 + (k/E) * (DR-2) )^0.5a: wave velocityC: speed of soundk: water bulk modulusE:pipe elasticity modulusDR: dimension Ratioc =4,660fpsk =300,000psiEPVC 12454 =400,000psiEPE 3408 =115,000psia)Dv =2fpsMaterialPVC 12454DR =25Celeritya =c / ( 1 + (k/E) * (DR-2) )^0.5c =4,660fpsK =300,000psiE =400,000psiDR =25a =1,091fpsSurge pressurePs =a * DV / (2.31*g)a =1,091fpsDv =2fpsg =32.2ft/sPs =29.3psib)Dv =2fpsMaterialPE 3408DR =11Celeritya =c / ( 1 + (k/E) * (DR-2) )^0.5c =4,660fpsK =300,000psiE =115,000psiDR =11a =942fpsSurge pressurePs =a * DV / (2.31*g)a =942fpsDv =2fpsg =32.2ft/sPs =25.3psi

Ref. 3Tehmco

REf. 8am2 :Celerity of an heterogeneous fluidPressure increment for heterogeneous sluryy, due to suddenly valve shut-offCv :Solids concentration by volumers :Solids densityrL :Water densityEP :Elastic moduli of pipe materialEL :Elastic modulus of liquidES :Elastic modulus of solidslT :tension stress on the pipe wallD :Pipe diametere :Pipe wall thicknessEq. 20, [8], page 340[8]http://tech.scichina.com:8082/sciEe/fileup/PDF/98ye0337.pdf

http://tech.scichina.com:8082/sciEe/fileup/PDF/98ye0337.pdf

Ref. 10[10]http://www.plasticpipe.org/pdf/chapter06.pdfDesign of PE Piping SystemsChapter 6, page 161Temporary surge pressuresPE pipes can safely tolerate the commonly observed maximum peaktemporary surge pressure of twice the steady state condition.Repetead cyclel loadsLong-term strength of PE pipes is not adversely affected by repeatedcyclic load. Thus, PE pipes are very fatigue resistant.Occasional surge pressuresRecurring surge pressuresNegative pressuresDesign principlesOccasional surge pressuresRecurring surge pressures

http://www.plasticpipe.org/pdf/chapter06.pdf

Ref[2]TylerPower generation calculations referenceTyler G. Hicks., P.E., EditorThe McGraw-Hill Engineering reference guide series1985Water-hammer in liquid pipelines. Page 228[3]Productos PECChttp://issuu.com/rockoicm/docs/catalogo_final_tehmcoTehmco S.A.Example page 7.21[4]Heat ans mass transferAnthony F. MillsIrwin, 1995[5]Heat transferJ. P. HolmanMcGraw-Hill, 1989[6]Water Hammerby Robert PelikanApril 1, 2005[7][8]http://tech.scichina.com:8082/sciEe/fileup/PDF/98ye0337.pdf[9]http://www.plasticengineeredproducts.com/manufacturers/unibell/pubs/uni-tr-7.pdf[10]http://www.plasticpipe.org/pdf/chapter06.pdfDesign of PE Piping Systems

http://www.plasticpipe.org/pdf/chapter06.pdf

Hoja1

MBD0014FAE9.unknown

MBD0014FAF1.unknown

MBD0014FAF5.unknown

MBD0014FAF9.unknown

MBD0014FAFB.unknown

MBD0014FAFD.unknown

MBD0014FAFC.unknown

MBD0014FAFA.unknown

MBD0014FAF7.unknown

MBD0014FAF8.unknown

MBD0014FAF6.unknown

MBD0014FAF3.unknown

MBD0014FAF4.unknown

MBD0014FAF2.unknown

MBD0014FAED.unknown

MBD0014FAEF.unknown

MBD0014FAF0.unknown

MBD0014FAEE.unknown

MBD0014FAEB.unknown

MBD0014FAEC.unknown

MBD0014FAEA.unknown

MBD0014FAE1.unknown

MBD0014FAE5.unknown

MBD0014FAE7.unknown

MBD0014FAE8.unknown

MBD0014FAE6.unknown

MBD0014FAE3.unknown

MBD0014FAE4.unknown

MBD0014FAE2.unknown

MBD0014FADD.unknown

MBD0014FADF.unknown

MBD0014FAE0.unknown

MBD0014FADE.unknown

MBD0014FADB.unknown

MBD0014FADC.unknown