Themassflowrateofagranularflowthroughanapertureundergravityisalong-standingchallengeissueinphysicalscience.Weshowthatforsteadyflowfieldclosetolaminarflow,thedynamicalequationstogetherwiththecontinueequationandMohr-circledescriptionofthestressareclosed,andhencesolvable.Inacaseofstreamlineguidedbythetwo-dimensionalhopper,weobtainaconsistentconditionanduseittodeterminethestressandthevelocitydistribution.Ourresultindicatesthat3/2powerscalingbehaviorisrecoveredwithacoefficientC(μ,α)beingafunctionoffrictionalcoefficientandthehopperangle.ItisfoundthatthepredictedcoefficientC(μ,α)iscompatiblewithpreviousstudies.
