Buckingham Pi Theorem — pint 0.10.1 documentation

Buckingham π theorem states that an equation involving n number of physical variables which are expressible in terms of k independent fundamental physical ... Navigation index modules| next| previous| pint0.10.1documentation» BuckinghamPiTheorem¶ Buckinghamπtheoremstatesthatanequationinvolvingnnumberof physicalvariableswhichareexpressibleintermsofkindependentfundamental physicalquantitiescanbeexpressedintermsofp=n-kdimensionless parameters. Tostartwithaverysimplecase,considerthatyouwanttofindadimensionless quantityinvolvingthemagnitudesV,TandLwithdimensions[length]/[time], [time]and[length]respectively. >>>frompintimportpi_theorem >>>pi_theorem({'V':'[length]/[time]','T':'[time]','L':'[length]'}) [{'V':1.0,'T':1.0,'L':-1.0}] Theresultindicatesthatadimensionlessquantitycanbeobtainedby multiplyingVbyTandtheinverseofL. WhichcanbeprettyprintedusingthePintformatter: >>>frompintimportformatter >>>result=pi_theorem({'V':'[length]/[time]','T':'[time]','L':'[length]'}) >>>print(formatter(result[0].items())) T*V/L YoucanalsoapplytheBuckinghamπtheoremassociatedtoaRegistry.Inthiscase, youcanusederiveddimensionssuchasspeed: >>>frompintimportUnitRegistry >>>ureg=UnitRegistry() >>>ureg.pi_theorem({'V':'[speed]','T':'[time]','L':'[length]'}) [{'V':1.0,'T':1.0,'L':-1.0}] orunitnames: >>>ureg.pi_theorem({'V':'meter/second','T':'second','L':'meter'}) [{'V':1.0,'T':1.0,'L':-1.0}] orquantities: >>>Q_=ureg.Quantity >>>ureg.pi_theorem({'V':Q_(1,'meter/second'), ...'T':Q_(1,'second'), ...'L':Q_(1,'meter')}) [{'V':1.0,'T':1.0,'L':-1.0}] Applicationtothependulum¶ Thereare3fundamentalphysicalunitsinthisequation:time,mass,andlength,and4dimensionalvariables,T(oscillationperiod),M(mass),L(thelengthofthestring),andg(earthgravity).Thusweneedonly4−3=1dimensionlessparameter. >>>ureg.pi_theorem({'T':'[time]', ...'M':'[mass]', ...'L':'[length]', ...'g':'[acceleration]'}) [{'T':2.0,'g':1.0,'L':-1.0}] whichmeansthatthedimensionlessquantityis: \[\Pi=\frac{gT^2}{L}\] andtherefore: \[T=constant\sqrt{\frac{L}{g}}\] (Incaseyouwonder,theconstantisequalto2π,butthisisoutsidethescopeofthishelp) Pressurelossinapipe¶ WhatisthepressurelosspinapipewithlengthLanddiameterDforafluidwithdensityd,andviscositymtravellingwithspeedv?Aspressure,mass,volume,viscosityandspeedaredefinedasderiveddimensionsintheregistry,weonlyneedtoexplicitlywritethedensitydimensions. >>>ureg.pi_theorem({'p':'[pressure]', ...'L':'[length]', ...'D':'[length]', ...'d':'[mass]/[volume]', ...'m':'[viscosity]', ...'v':'[speed]' ...}) [{'p':1.0,'m':-2.0,'d':1.0,'L':2.0},{'v':1.0,'m':-1.0,'d':1.0,'L':1.0},{'L':-1.0,'D':1.0}] TheseconddimensionlessquantityistheReynoldsNumber AboutPint UnitsinPython. Youarecurrentlylookingatthedocumentationofversion0.10.1. OtherFormats Youcandownloadthedocumentationinotherformatsaswell: asPDF aszippedHTML asePub UsefulLinks Pint@PyPI CodeinGitHub IssueTracker TableofContents BuckinghamPiTheorem Applicationtothependulum Pressurelossinapipe RelatedTopics Documentationoverview Previous Serialization Next Contexts ThisPage ShowSource Quicksearch