AP 物理 B- 《伯努利方程》

國際部中美班-AP物理Fluid第2頁共3頁 DATE\@"yyyy-MM-dd"2013-09-11Bernoulli’sequation1ShowthatBernoulli’sequationreducestothehydrostaticvariationofpressurewithdepthwhenthereisnoflow(v1=v2=0)2Howfastdoeswaterflowfromaholeatthebottomofaverywide,4.6-m-deepstoragetankfilledwithwater?Ignoreviscosity.3Alargepipewithacross-sectionalareaof1.00m2descends5.00mandnarrowsto0.500m2,whereitterminatesinavalveatpoint1.Ifthepressureat4Anairplanehaswings,eachwitharea4.00m2,designedsothatairflowsoverthetopofthewingat245m/sandunderneaththewingat222m/s.Findthemassoftheairplanesuchthattheliftontheplanewillsupportitsweight,assumingtheforcefromthepressuredifferenceacrossthewingsisdirectedstraightupward.(Thedensityofair)5A6.0-cm-diameterhorizontalpipegradullynarrowsto4.0cm6Estimatetheairpressureinsideacategory5hurricane,wherethewindspeedin300km/h.7Wateratagaugepressureof3.8atmatstreetlevelflowsintoanofficebuildingataspeedof0.60m/sthroughapipe5.0cmindiameter.Thepipetapersdownto2.6cmindiameterbythetopfloor,18mabove,wherethefaucethasbeenleftopen.Calculatetheflowvelocityandthegaugepressureinsuchapipeonthetopfloor.Assumenobranchpipesandignoreviscosity.8(a)Showthattheflowvelocitymeasuredbyventurimeterisgivenbytherelation(b)Aventuritubeismeasuringtheflowofwater,ithasamaindiameterof3.0cmtaperingdowntoathroatdiameterof1.0cm,ifthepressuredifferenceismeasuredtobe18mm-Hg,whatisthevelocityofthewater?9InFig.9,takeintoaccoutthespeedofthetopsurfaceofthetankandshowthatthespeedoffluidleavingtheopeningatthebottomis,Where,andA1andA2aretheareasoftheopeningandofthetopsurface,respectively.Assumesothattheflowremainsnearlysteadyandlaminar.Fig.9Fig.910SupposetheopeninginthetankofFig.9isaheighth1abovethebaseandliquidsurfaceisaheighth2abovethebase.Thetankrestsonlevelground.(a)Atwhathorizontaldistancefromthebasestrikethegroun