Leaky Bucket Lab
LaboratoryExperiencesinMathema4calBiology
LabSetup:Studentscutanapertureof𝑎≈.25 ​cm↑2 andinscribehorizontalmarks
everycen4meterabove.Bucketisfilledtotwelvecmabovetheholewhiletheholeis
coveredwithducttape;studentsremovethetapeand4methebucket'sdrainage,
recordingthedynamicsofchangingheight.
Materials
Thefollowingmaterialsareneeded(foreachgroupof3-4students):
•  1-2quarttranslucentorclearplas4cjugssuchasthosecontainingmilk,sodaor
juiceforuseasleakybuckets
•  ScalpelsorX-Actoknivesforcuingaperturesandremovingburrs(adrillwithbits
isusefulforcircularholes,butnotnecessary)
•  Waterproofmarker
•  Stopwatch
•  Ducttape(justongeneralprinciples)
•  Rulerwithatleastmillimeterscale
•  Graduatedcylindersorkitchenmeasuringcupsformeasuringmetricvolumes
•  Accesstotapwater
•  Plas4cdishwashingtubtocapturedrainedwaterifalargesinkisnotavailable
Methods
When4meisnotavailableforgroupsofstudentstodevelopandrefinetheirown
procedures,orifinstructorswishtoofferastar4ngpointtogetthingsrolling,we
providethe
followingprocedure(basedonusinga1/2gallonmilkjug):
1.  Divideintogroupsof3-4.Eachgroupwillneedatleastonepersontomanagethe
stopwatch(Timer),spotfluidlevels(SpoJer)andrecorddata(Recorder).
2.  Setupthebucket.Wherethejugbeginstohaveregularhorizontalcrosssec4ons
(2-4cmabovebaseforastandardUSplas4chalfgallonmilkjug)cutahorizontal
slit1-2mmtalland1-2cmwide,beingcarefulthatthetopandboJomoftheslit
areparalleltothebaseofthejug.Everycmver4callyfromtheboJomoftheslit
makeahorizontalmark,uptobetween10and15cmabovetheboJomoftheslit
(dependingonhowfarthejugmaintainsarela4velyconsistentcrosssec4on).
3.  Measurethebucket.Ataminimum,studentsneedtoes4matethecross-sec4onal
areaofthebucketandtheareaoftheaperture.Studentsmaywishtomeasure
thecrosssec4onvolumetrically,addingaknownvolumetothebucketand
dividingbyameasuredver4calheight.
4.  Observedrainagetrajectories.
a)  Fillthebuckettothedesiredini4alheight(12or13cmareusedinthis
paper),asmeasuredbytheboJomofthefluidmeniscus.Theaperturewill
needtobecoveredeitherwithapieceofducttapeoraconvenientfinger.If
usingafingerbecarefulnottopresshardenoughtodeformthecontainer.
b)  Posi4onthebucketsothatitcandrainintoasinkorbasin.
c)  SpoJerremovestapeandsays“Start!”Timerstartsstopwatch.
d)  Asfluidpasseseachver4calmark,SpoJercalls“Mark!”andTimergivesthe
4meofthesplit,whichRecorderrecordsnexttotheappropriatever4cal
level.
e)  Con4nueun4ltheboJomofthefluidmeniscusislevelwiththetopofthe
slit.Timerrecordsfinalemptying4me.Fora1/2galloncontainerwith
apertureof.4cm2filledto12cmabovetheslitthiswillbebetween30and
60sec.
5.  Repeattheobserva4onsequenceatleastthree4mesforthesameini4alheightof
fluidtoassessvariability.
Oneofthebiggestissuesisdeterminingwhentostop;dependingonthesizeand
shapeofbothbucketandaperturetheflowmaytransi4onfromafreestreamtoan
aJacheddribbletoperiodicdrips.Ideallystudentsshoulddiscoverandaddressthis
ontheirown;if4meis4ghtinstructorscanexperimentwiththebucketinadvanceto
determineastoppingrulefortheobserva4onsequence.