船舶阻力习题解

船舶阻力题解第一章总论第二章粘性阻力第五章船模阻力试验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习题1-7已知某远洋货轮的水线长152m，设计航速16.45kn，制作长为3.04m的船模，进行阻力试验。分别求满足粘性力、重力相似条件的船模速度（假定实船与船模的流体运动粘性系数相同）？解:已知Ls=152m,Lm=3.04m;Vs=16.45kn=8.455m/s。缩尺比：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习题1-8某舰设计水线长L=84.4m，湿面积S=728m2，航速Vs=34kn。今用α=40的船模在重力相似条件下进行阻力试验，测得水池温度t=12℃(淡水)。试求：1）相应的船模速度Vm(m/s)?2）此时实船及船模的雷诺数各是多少？3）若该相应速度时船模的兴波阻力为Rwm=0.52kgf，试求该舰（在15℃海水）的兴波阻力Rws？已知:实船Ls=84.4m,S=728m2,Vs=34kn=17.476m/s;ts=15℃(海水)船模α=40;t=12℃(淡水)2/3习题1-8解:1）相应的船模速度Vm(m/s)=17.476/√40=2.763m/s2）实船及船模的雷诺数:Re=Lv/υ实船:(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习题1-8题1-8L(m)S(m2)Vs(m/s)υρReFrRw(kgf)实船84.472817.4761.19E-06104.5781.24E+090.60734162船模(a=40)2.110.4552.7631.23E-06101.8794.74E+060.6070.523）相应速度时船模的兴波阻力为Rwm=0.52kgf，求该舰的兴波阻力Rws按傅汝德比较定理形似船单位排水量的兴波阻力相等，并考虑到水重度的影响:Rws=Rwm*γs/γm*α3=0.52*1025.91/999.43*403=34162(kgf)2/3习题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计算S:1.瓦格宁根:S=(3.4▽1/3+0.5Lpp)▽1/3(m2)=(3.4*7638.31/3+0.97*126)7638.31/3=2522.22.单桨运输船公式: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.格罗特公式:，取Cs=2.75S=2.75(7638.3*126)1/2=2697.8(m2)4.取1,2两式的平均值S=(2552.2+2556.8)/2=2554.8(m2)习题2-112/3雷诺数:Re=LV/ν=126*6.168/1.18831*10-6=6.540E8计算Cf:1.光滑平板(层流)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.柏兰特-许立丁公式=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计算Rf=1.615E-3*0.5*104.58*6.1682*2554.8=1.024E+04kgf习题2-112/3习题2-12知:实船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℃实船:υ=1.188E-06,ρ=1025.91/9.81=104.58,船模:υ=8.731E-07,ρ=996.78/9.81=101.61,计算湿面积按桑地图谱由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习题2-12船模:1.船模速度:vm(m/s)2.总阻力:Rm(kgf)3.雷诺数:Rem=Lw1Vm/υ4.摩擦阻力系数:(ITTC)5.总阻力系数:Ctm=Rm/(1/2ρvm2Sm)6.剩余阻力系数:Crm=Ctm-Cfm7.傅汝德数:Fr=V/(gL)1/22/3习题2-12实船:1.船速:Vs=Vm*(α)1/2或者vs=Fr*(gL)1/2.2.计算雷诺数:Res=Lw1Vs/υ3.计算摩擦阻力系数:(ITTC)4.取Crs=Crm5.计算总阻力系数:Cts=Cfs+0.0004+Crm6.计算总阻力Rs=Cts.1/2ρVs2S(kgf)2/3习题2-12船模速度vm=(m/s)11.2521.411.5451.618总阻力Rtm(kgf)0.3560.5690.8411.3962.012雷诺数Rem:3.482E+064.359E+064.909E+065.379E+065.633E+06摩擦阻力系数Cfm:3.636E-033.484E-033.408E-033.351E-033.323E-03总阻力系数Ctm：4.159E-034.240E-034.941E-036.832E-038.978E-03剩余阻力系数Crm:5.227E-047.558E-041.533E-033.480E-035.655E-03傅汝德数Frm:0.1830.2290.2580.2830.296实船航速Vs:(m/s)7.0718.8539.97010.92511.441实船航速Vs:(kn)13.7617.2219.4021.2522.26雷诺数Res:9.0448E+081.1324E+091.2753E+091.3974E+091.4634E+09摩擦阻力系数Cfs:1.5499E-031.5073E-031.4854E-031.4690E-031.4608E-03总阻力系数Cts：2.473E-032.663E-033.419E-035.349E-037.515E-03总阻力：(tf)2.723E+014.598E+017.485E+011.406E+022.167E+022/3习题2-12FrCtm2/3习题2-12Rts2/3习题5-9某舰长L=120m，用Lm=4m的船模进行阻力试验，该舰的速度范围为15-35kn，试求船模试验的速度范围，如果试验水温为20℃，则相应的试验雷诺数范围是多少？2/3解:按Fr数相等,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习题5-10Vm(m/s)1.52.02.53.0Rtm(kgf)0.310.801.291.71某驱逐舰长L=110m，湿面积S=1300m2，船模比尺α=50，试验水温tm=20℃，结果如下:试用傅汝德换算法给出实船的Rts-Vs曲线和Cr-Fr曲线。（△Cf=0.4×10-3）2/3解:基本条件Lw1(m)S(m2)ρυ1/2ρS实船：海水ts=15℃1101300104.581.1883E-0667975.69船模:α=50,淡水tm=20℃2.20.52101.751.0037E-0626.45习题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习题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实船: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)习题5-10Vs(m/s)Rts习题5-10习题5-1111.根据2-12题给出的模型试验结果,分别用二因次和三因次换算方法计算实船全速航行时的有效功率。（△Cf=0.4×10-3,k用普鲁哈斯卡法计算）。2/3解:二因次换算方法略。三因次换算方法解题如下:习题5-11已知船模总阻力系数Ctm,摩擦阻力系数Cfm,傅汝德数Fr。按普鲁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:将Ctm/Cfm与Fr4/Cfm做成线性关系图,则该直线的截距就是(1+k)习题5-11(1+k)=0.7习题5-11总阻力系数Ctm:总阻力系数Ctm:总阻力系数Ctm:总阻力系数Ctm:总阻力系数Ctm:总阻力系数Ctm:总阻力系数Ctm:总阻力系数Ctm:总阻力系数Ctm:总阻力系数Ctm:总阻力系数Ctm:总阻力系数Ctm:总阻力系数Ctm:总阻力系数Ctm:总阻力系数Ctm:总阻力系数Ctm:总阻力系数Ctm:总阻力系数Ctm:总阻力系数Ctm:总阻力系数Ctm:总阻力系数Ctm:总阻力系数Ctm:总阻力系数Ctm:总阻力系数Ctm:总阻力系数Ctm:总阻力系数Ctm:总阻力系数Ctm:总阻力系数Ctm:总阻力系数Ctm:总阻力系数Ctm:实船:总阻力系数Cts=Ctm-(1+k)(Cfm-Cfs)总阻力Rts=Cts*1/2ρVs2Ss/1000(tf)习题5-1212.将2-12题的计算结果分别按泰洛表达法整理成Rt/Δ—Fr和Rt/(ΔFr2)—Fr曲线；按傅汝德表达法整理成C--K曲线。2/3实船航速Vs:(m/s)7.0718.8539.97010.92511.441傅汝德数Frm:0.1830.2290.2580.2830.296总阻力：(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习题5-12习题5-12傅汝德数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习题7-22.某舰长L=86m,宽B=8.95m,吃水T=2.71m,排水量△=1272m3,棱形系数Cp=0.6,按泰勒图谱计算航速Vs=18～26kn时的有效功率EHP(△Cf=0.4×10-3,附体阻力Rap取裸体阻力的10%习题7-33.用陶德回归公式计算2-12题船的有效功率。(xb=-0.45%L)2/3习题7-44.某双螺旋桨船垂线间长Lpp=122m，设计水线长Lw1=125m，宽B=16.9m，吃水T=6.7m，排水量=8145t，Cp=0.62，浮心纵向位置xb=-1.5％Lpp，试用爱尔法计算船在14、15.16kn时的有效功率？2/3习题7-55.已知某远洋客货轮设计水线长Lw1＝152m，垂线间长Lpp＝147m，宽B＝20.4m，吃水T＝8.4m，排水量△＝17000m3，浸湿面积S＝4080m2，方形系数Cb＝0.675，中横剖面系数Cm＝0.984，浮心纵向位置xb＝-0.45％L