船舶阻力習題解

船舶阻力題解第一章總論第二章粘性阻力第五章船模阻力試驗第七章阻力的近似估算方法第八章船在限制航道中的阻力1/1習題1-7已知某遠洋貨輪的水線長152m，設計航速16.45kn，制作長為3.04m的船模，進行阻力試驗。分別求滿足粘性力、重力相似條件的船模速度（假定實船與船模的流體運動粘性系數(shù)相同）？解:已知Ls=152m,Lm=3.04m;Vs=16.45kn=8.455m/s?？s尺比：α=Ls/Lm=152/3.04=50Re相等：Vm=αVs=50×8.455=422.8(m/s)=822.5(kn)Fr相等：Vs=Vs/√α=8.455/√50=1.196(m/s)=2.326(kn)1/1習題1-8某艦設計水線長L=84.4m，濕面積S=728m2，航速Vs=34kn。今用α=40的船模在重力相似條件下進行阻力試驗，測得水池溫度t=12℃(淡水)。試求：1）相應的船模速度Vm(m/s)?2）此時實船及船模的雷諾數(shù)各是多少？3）若該相應速度時船模的興波阻力為Rwm=0.52kgf，試求該艦（在15℃海水）的興波阻力Rws？已知:實船Ls=84.4m,S=728m2,Vs=34kn=17.476m/s;ts=15℃(海水)船模α=40;t=12℃(淡水)2/3習題1-8解:1）相應的船模速度Vm(m/s)=17.476/√40=2.763m/s2）實船及船模的雷諾數(shù):Re=Lv/υ實船:(15℃海水)Re=84.4*17.476/1.19E-06=1.24E+09船模:(12℃淡水)Re=2.11*2.763/1.23E-06=4.74E+062/3習題1-8題1-8L(m)S(m2)Vs(m/s)υρReFrRw(kgf)實船84.472817.4761.19E-06104.5781.24E+090.60734162船模(a=40)2.110.4552.7631.23E-06101.8794.74E+060.6070.523）相應速度時船模的興波阻力為Rwm=0.52kgf，求該艦的興波阻力Rws按傅汝德比較定理形似船單位排水量的興波阻力相等，并考慮到水重度的影響:Rws=Rwm*γs/γm*α3=0.52*1025.91/999.43*403=34162(kgf)2/3習題2-11已知:Lw1=126m,B=18m,T=5.6mCb=0.62,Vs=12kn=6.168m/s,ts=15℃,ΔCf=0.0004,解:υs=1.18831*10-6,ρs=1025.91/9.81=104.58▽=0.62*0.97*126*18*5.6=7638.3m3Lw1/B=126/18=7,B/T=18/5.6=3.214計算S:1.瓦格寧根:S=(3.4▽1/3+0.5Lpp)▽1/3(m2)=(3.4*7638.31/3+0.97*126)7638.31/3=2522.22.單槳運輸船公式:S=(3.432+0.305Lw1/B+0.443B/T-0.643Cb)▽2/3=(3.432+0.305*7+0.443*3.214-0.643*0.62)*7638.32/3=2556.8(m2)3.格羅特公式:，取Cs=2.75S=2.75(7638.3*126)1/2=2697.8(m2)4.取1,2兩式的平均值S=(2552.2+2556.8)/2=2554.8(m2)習題2-112/3雷諾數(shù):Re=LV/ν=126*6.168/1.18831*10-6=6.540E8計算Cf:1.光滑平板(層流)Cf=1.328Re1/2=5.193E-052.光滑平板(紊流)=0.074/Re1/5=1.277E-033.桑海公式=0.4631/lg(Re)2.6=1.614E-034.柏蘭特-許立丁公式=0.455/lg(Re)2.58=1.657E-035.休斯公式=0.066/(lgRe-2.03)2=1.433E-036.1957ITTC公式=0.075/(lgRe-2)2=1.615E-03計算Rf=1.615E-3*0.5*104.58*6.1682*2554.8=1.024E+04kgf習題2-112/3習題2-12知:實船L=152m,ts=15℃,ΔCf=0.0004,α=50.船模L=3.04m;B=0.408m,T=0.164m,▽=0.132m3，Cm=0.984,tm=26℃實船:υ=1.188E-06,ρ=1025.91/9.81=104.58,船模:υ=8.731E-07,ρ=996.78/9.81=101.61,計算濕面積按桑地圖譜由B/T=2.488,Cm=0.984,得Cs=2.66Sm=Cs(▽Lw1)1/2=2.66(0.132*3.04)1/2=1.685m2Ss=Sm*α2=1.685*502=4212.55m2(1/2ρS)m=85.606(1/2ρS)s=2202702/3習題2-12船模:1.船模速度:vm(m/s)2.總阻力:Rm(kgf)3.雷諾數(shù):Rem=Lw1Vm/υ4.摩擦阻力系數(shù):(ITTC)5.總阻力系數(shù):Ctm=Rm/(1/2ρvm2Sm)6.剩余阻力系數(shù):Crm=Ctm-Cfm7.傅汝德數(shù):Fr=V/(gL)1/22/3習題2-12實船:1.船速:Vs=Vm*(α)1/2或者vs=Fr*(gL)1/2.2.計算雷諾數(shù):Res=Lw1Vs/υ3.計算摩擦阻力系數(shù):(ITTC)4.取Crs=Crm5.計算總阻力系數(shù):Cts=Cfs+0.0004+Crm6.計算總阻力Rs=Cts.1/2ρVs2S(kgf)2/3習題2-12船模速度vm=(m/s)11.2521.411.5451.618總阻力Rtm(kgf)0.3560.5690.8411.3962.012雷諾數(shù)Rem:3.482E+064.359E+064.909E+065.379E+065.633E+06摩擦阻力系數(shù)Cfm:3.636E-033.484E-033.408E-033.351E-033.323E-03總阻力系數(shù)Ctm：4.159E-034.240E-034.941E-036.832E-038.978E-03剩余阻力系數(shù)Crm:5.227E-047.558E-041.533E-033.480E-035.655E-03傅汝德數(shù)Frm:0.1830.2290.2580.2830.296實船航速Vs:(m/s)7.0718.8539.97010.92511.441實船航速Vs:(kn)13.7617.2219.4021.2522.26雷諾數(shù)Res:9.0448E+081.1324E+091.2753E+091.3974E+091.4634E+09摩擦阻力系數(shù)Cfs:1.5499E-031.5073E-031.4854E-031.4690E-031.4608E-03總阻力系數(shù)Cts：2.473E-032.663E-033.419E-035.349E-037.515E-03總阻力：(tf)2.723E+014.598E+017.485E+011.406E+022.167E+022/3習題2-12FrCtm2/3習題2-12Rts2/3習題5-9某艦長L=120m，用Lm=4m的船模進行阻力試驗，該艦的速度范圍為15-35kn，試求船模試驗的速度范圍，如果試驗水溫為20℃，則相應的試驗雷諾數(shù)范圍是多少？2/3解:按Fr數(shù)相等,Vm=Vs/√α

Vs(kn)15.00025.00035.000Vs(m/s)7.71012.85017.990

Vm(m/s)1.4082.3463.285

Rem=LmVm/ν5.610.E+069.349.E+061.309.E+07t(o)νρ淡水201.00E-06101.75習題5-10Vm(m/s)1.52.02.53.0Rtm(kgf)0.310.801.291.71某驅(qū)逐艦長L=110m，濕面積S=1300m2，船模比尺α=50，試驗水溫tm=20℃，結(jié)果如下:試用傅汝德?lián)Q算法給出實船的Rts-Vs曲線和Cr-Fr曲線。（△Cf=0.4×10-3）2/3解:基本條件Lw1(m)S(m2)ρυ1/2ρS實船：海水ts=15℃1101300104.581.1883E-0667975.69船模:α=50,淡水tm=20℃2.20.52101.751.0037E-0626.45習題5-10Vm:(m/s)1.522.53Rtm:(kgf)0.310.81.291.71Ctm:5.2080E-037.5601E-037.8020E-037.1821E-03Rem:3.2877E+064.3836E+065.4795E+066.5754E+06Cfm:(1975ITTC公式)3.6761E-033.4808E-033.3399E-033.2310E-03Crm:(傅汝德方法)1.5320E-034.0792E-034.4621E-033.9510E-032/3船模:Ctm=Rtm/(1/2ρVm2S)Rem=LmVm/υCfm=(1975ITTC公式)Crm=Ctm-Cfm習題5-10Frm:0.320.430.540.65Vs：(v/s)10.60714.14217.67821.213Vs：(kn)20.63527.51434.39241.271Res:9.8184E+081.3091E+091.6364E+091.9637E+09Cfs:(1975ITTC)1.5341E-031.4807E-031.4412E-031.4101E-03Cts:3.47E-035.96E-036.30E-035.76E-03Rts:(tf)26.50681.026133.897176.2272/3實船:Fr=Vm/(Lm.g)1/2Vs=Vm*(α)1/2(m/s)Res=LsVs/υCfs=(1975ITTC公式)Cts=Cfs+ΔCf+Crm;Rts=Cts(1/2ρVs2S)習題5-10Vs(m/s)Rts習題5-10習題5-1111.根據(jù)2-12題給出的模型試驗結(jié)果,分別用二因次和三因次換算方法計算實船全速航行時的有效功率。（△Cf=0.4×10-3,k用普魯哈斯卡法計算）。2/3解:二因次換算方法略。三因次換算方法解題如下:習題5-11已知船模總阻力系數(shù)Ctm,摩擦阻力系數(shù)Cfm,傅汝德數(shù)Fr。按普魯哈斯卡方法整理成下表:Ctm:Ctm:Ctm:Ctm:Ctm:Ctm:Ctm:Ctm:Ctm:Ctm:Ctm:Ctm:Ctm:Ctm:Ctm:Ctm:Ctm:Ctm:Ctm:Ctm:Ctm:Ctm:Ctm:Ctm:Ctm:Ctm:Ctm:Ctm:Ctm:Ctm:將Ctm/Cfm與Fr4/Cfm做成線性關(guān)系圖,則該直線的截距就是(1+k)習題5-11(1+k)=0.7習題5-11總阻力系數(shù)Ctm:總阻力系數(shù)Ctm:總阻力系數(shù)Ctm:總阻力系數(shù)Ctm:總阻力系數(shù)Ctm:總阻力系數(shù)Ctm:總阻力系數(shù)Ctm:總阻力系數(shù)Ctm:總阻力系數(shù)Ctm:總阻力系數(shù)Ctm:總阻力系數(shù)Ctm:總阻力系數(shù)Ctm:總阻力系數(shù)Ctm:總阻力系數(shù)Ctm:總阻力系數(shù)Ctm:總阻力系數(shù)Ctm:總阻力系數(shù)Ctm:總阻力系數(shù)Ctm:總阻力系數(shù)Ctm:總阻力系數(shù)Ctm:總阻力系數(shù)Ctm:總阻力系數(shù)Ctm:總阻力系數(shù)Ctm:總阻力系數(shù)Ctm:總阻力系數(shù)Ctm:總阻力系數(shù)Ctm:總阻力系數(shù)Ctm:總阻力系數(shù)Ctm:總阻力系數(shù)Ctm:總阻力系數(shù)Ctm:實船:總阻力系數(shù)Cts=Ctm-(1+k)(Cfm-Cfs)總阻力Rts=Cts*1/2ρVs2Ss/1000(tf)習題5-1212.將2-12題的計算結(jié)果分別按泰洛表達法整理成Rt/Δ—Fr和Rt/(ΔFr2)—Fr曲線；按傅汝德表達法整理成C--K曲線。2/3實船航速Vs:(m/s)7.0718.8539.97010.92511.441傅汝德數(shù)Frm:0.1830.2290.2580.2830.296總阻力：(tf)2.723E+014.598E+017.485E+011.406E+022.167E+02Rt/Δ1.61E-032.716E-034.422E-038.308E-031.280E-02Rt/Δ/Fr24.80E-025.17E-026.63E-021.04E-011.46E-01習題5-12習題5-12傅汝德數(shù)Frm:0.1830.2290.2580.2830.296(4π/g)1/2V/▽1/61.117E+011.751E+012.220E+012.666E+012.924E+01Ct*125/π(S)6.286E-016.771E-018.692E-011.360E+001.911E+00S/▽2/3

4213/

169272/3=

6.390C=(4π/g)1/2V/▽1/6K=Ct*125/πSS=S/▽2/3習題7-22.某艦長L=86m,寬B=8.95m,吃水T=2.71m,排水量△=1272m3,棱形系數(shù)Cp=0.6,按泰勒圖譜計算航速Vs=18～26kn時的有效功率EHP(△Cf=0.4×10-3,附體阻力Rap取裸體阻力的10%習題7-33.用陶德回歸公式計算2-12題船的有效功率。(xb=-0.45%L)2/3習題7-44.某雙螺旋槳船垂線間長Lpp=122m，設計水線長Lw1=125m，寬B=16.9m，吃水T=6.7m，排水量=8145t，Cp=0.62，浮心縱向位置xb=-1.5％Lpp，試用愛爾法計算船在14、15.16kn時的有效功率？2/3習題7-55.已知某遠洋客貨輪設計水線長Lw1＝152m，垂線間長Lpp＝147m，寬B＝20.4m，吃水T＝8.4m，排水量△＝17000m3，浸濕面積S＝4080m2，方形系數(shù)Cb＝0.675，中橫剖面系數(shù)Cm＝0.984，浮心縱向位置xb＝-0.45％L