WithoutsimplifyingtheN-SequationsofGermano’s,westudytheflowinahelicalcircularpipeemployingperturbationmethod.Athirdperturbationsolutionisfullypresented.Thefirst-second-andthird-ordereffectsofcurvatureкandtorsionтonthesecondaryflowandaxialvelocityarediscussedindetail.Thefirst-ordereffectofcurvatureistoformtwocounter-rotatingcellsofthesecondaryflowandtopushthemaximurnaxialvelocitytotheouterbend.Thetwocellsarepushedtotheouterbendbythepuresecond-ordereffectofcurvature.Thecombinedhigher-order(second-,third-)effectsofcurvatureandtorsion,arefoundtobeanenlargementofthelowervortexofthesecondaryflowatexpenseoftheupperoneandaclockwiseshiftofthecentersofthesecondaryvorticesandthelocationofmaximumaxialvelocity.Whentheaxialpressuregradientissmallenoughorthetorsionissufficientlylargerthanthecurvature,thelocationofthemaximalaxialvelocityisneartheinnerbend.Theequationofthevolumefluxisobtainedfromintegratingtheperturbationsolutionsofaxialvelocity.Fromtheequationthevalidityrangeoftheperturbationsolutionsinthispapercanbeobtainedandtheconclusionthatthethreetermsoftorsionhavenoeffectonthevolumefluxcaneasilybedrawn.Whentheaxialpressuregradientislessthan22.67,thevolumefluxinahelicalpipeislargerthanthatinastraightpipe.
