22121244ddQvv21221()4vdvd222Revdv112222124/2Re22Revdvdvdvvv12Re2Re12Re/Re4.3水流经变断面管道,已知小管径为d1,大管径为d2,d2/d1=2。试问:哪个断面的雷诺数大?两个断面雷诺数的比值是多少?解:依题意有:即两断面平均流速之比:设此时水的运动粘性系数为ν,则:所以小管径对应的断面雷诺数大,20.222flvhmdg水柱2310/4dQvcms22400.4=dvd6464Revd4.8为了确定某圆管内径,在管中通水,温度为15℃,实测流量为Q=10cm3/s,长6m,水头损失hf=0.22m水柱,试求:圆管的直径d。解:(1)由(2)假设水流流态为层流,则:(1)(2)(3)20.01141/vcms22240()640.01141600224029.8100fdhcmddd0.6dcm24035.4/*0.6vcmsRe35.4*0.6/0.011411859.82300vdv(3)其中ν通过经验公式可算得:把(3)(2)两式及ν值代入(1)式有:检验流态:故为层流,所采用的计算公式正确。313600/kgm汞3860/kgm油4.11油的流量Q=7.7cm3/s,通过直径d=6mm的细管,在l=2m长的管段两端接水银差压计,差压计读数h=15cm,水银密度,油的密度,试求:油的运动粘性系数。(管中油的流动为层流)解:如图所示:1-1、2-2为渐变流过水断面,依题意:断面平均流速1222147.7427.23/0.6Qvvvdcms22111222120022fpvpvhgggg129.8136009.88430.152.2229.8843ggpphmggg汞油油212642.222Re2flvhdgRe36.32Re36.32vd227.32*0.60.4498/36.32cms故求得又因为4RevdQd51145000Re21221.29,2000Re103.1415200.01511/440.3160.3160.0262Re21221.2932.832.82001.91Re21221.290.0262Ldmm4.15有一水管,直径d为20cm,管壁绝对粗糙度Δ=0.2mm,已知液体的运动粘滞系数ν为0.015cm2/s。试求Q为5000cm3/s、4000cm3/s、2000cm3/s时,管道的沿程阻力系数λ各为若干?解:由于0.20.40.764Lmmmm242000Re8488.513.1415200.01521/440.3160.3160.0329Re8488.5132.832.82004.26Re8488.510.0329Ldmm0.20.41.70Lmmmm344000Re16977.033.1415200.01531/440.3160.3160.0277Re16977.0332.832.8*2002.32Re16977.03*0.0277Ldmm0.20.40.42.320.93Lmmmm0210,0.01310/tcms44150Re5831.820003.14152.50.0131Qd1/440.3160.3160.0362Re5831.8fh330.1510/Qms30.05/Qms4.18一压力钢管的当量粗糙度Δ=0.19mm,水温t=10℃,试求下列各种情况下的流态及沿程水头损失:(1)管长l=5m,管径d=25mm,流量时;(2)其他条件不变,如果管径改为d=75mm时;(3)管径保持不变,但流量增加至时。解:(1)所以流态为紊流,32.832.8250.739Re5831.80.0362Ldmm0.190.40.296Lmmmm224415030.56/3.14152.5Qvcmsd2250.30560.03620.034520.02529.8flvhmdg流态为紊流光滑区,22441503.395/3.14157.5Qvcmsd250.0340.03290.130.07529.8fhmm44150Re1943.9320003.14157.50.0131Qdv6464/1943.930.0329Re(2)流态为层流,64450000Re1.945103.14152.50.0131Qdv0.190.007625d0.03722440.0511.32/3.14150.075Qvcmsd22511.320.037016.1320.07529.8flvhmdg流态为紊流粗糙区,查图得(3)ARx00()Abmhh00Abmhh2021xbhm4.22某梯形断面土渠中为均匀流,已知:底宽b=2m,边坡系数m=cotθ=1.5,水深h=1.5m,水力坡度J=0.0004,土壤的粗糙系数n=0.0225,试求:(1)渠中流速v;(2)渠中流量Q。解:(1)水力半径:00220()(21.51.5)1.570.860521221.511.5bmhhARmxbhmvCRJ0.5Rm0.0225n0.0110.04n1.50.0225110.860542.9670.0225yCRn42.9670.86050.00040.8/vCRJms...