船舶静力学习题详解

ShipHydrostaticsTheanwseroftheexercises第一章复习思考题1111．船舶静力学研究哪些内容？2222．在船舶静力学计算中，坐标系统是怎样选取的？3333．作图说明船体的主尺度是怎样定义的？其尺度比的主要物理意义如何？4444．作图说明船形系数是怎样定义的？其物理意义如何？试举一例说明其间的关系。5555．对船体近似计算方法有何要求？试说明船舶静力学计算中常用的近似计算法有哪几种？其基本原理、适用范围以及它们的优缺点。复习思考题6666．提高数值积分精确度的办法有哪些？并作图说明梯形法、辛浦生法对曲线端点曲率变化较大时如何处理？以求面积为例，写出其数值积分公式。7777．分别写出按梯形法，辛浦拉法计算水线面面积的积分公式，以及它们的数值积分公式和表格计算方法。(5,8,-1)(5,8,-1)(5,8,-1)(5,8,-1)法、(3,10,-1)(3,10,-1)(3,10,-1)(3,10,-1)法的适用范围。8888．写出计算水线面面积的漂心位置和水线面面积对xxxx轴yyyy轴的惯性矩的积分公式。并应用求面积的原理写出其数值积分公式和表格计算方法。复习思考题9999．如何应用乞贝雪夫法？试以九个乞贝雪夫坐标，写出求船舶排水体积的具体步骤。10101010．说明积分曲线、重积分曲线与原曲线的关系．并以水线面面积曲线为例说明积分曲线、重积分曲线的应用。Exercise1-1Exercise1-1Exercise1-1Exercise1-1已知:L=155m,B=18m,d=7.1m,V=10900m:L=155m,B=18m,d=7.1m,V=10900m:L=155m,B=18m,d=7.1m,V=10900m:L=155m,B=18m,d=7.1m,V=10900m3333,Am=115m,Am=115m,Am=115m,Am=115m2222,,,,Aw=1980mAw=1980mAw=1980mAw=1980m2222求：Cb=V/LBd=10900/(155Cb=V/LBd=10900/(155Cb=V/LBd=10900/(155Cb=V/LBd=10900/(155****18181818****7.1)=0.5507.1)=0.5507.1)=0.5507.1)=0.550Cp=V/Lam=10900/(155Cp=V/Lam=10900/(155Cp=V/Lam=10900/(155Cp=V/Lam=10900/(155****115)=0.62115)=0.62115)=0.62115)=0.62Cw=Aw/BL=19800/(18Cw=Aw/BL=19800/(18Cw=Aw/BL=19800/(18Cw=Aw/BL=19800/(18****155)=0.710155)=0.710155)=0.710155)=0.710Cm=Am/Bd=115/(18Cm=Am/Bd=115/(18Cm=Am/Bd=115/(18Cm=Am/Bd=115/(18****7.1)=0.9007.1)=0.9007.1)=0.9007.1)=0.900Cvp=V/Awd=10900/(1980Cvp=V/Awd=10900/(1980Cvp=V/Awd=10900/(1980Cvp=V/Awd=10900/(1980****7.1)=0.7757.1)=0.7757.1)=0.7757.1)=0.775某海洋客船L=155mL=155mL=155mL=155m，B=18mB=18mB=18mB=18m，d=7.1md=7.1md=7.1md=7.1m，V=10900m3V=10900m3V=10900m3V=10900m3，Am=115mAm=115mAm=115mAm=115m2222，Aw=1980mAw=1980mAw=1980mAw=1980m2222。试求Cb,Cp,Cw,Cm,CvpCb,Cp,Cw,Cm,CvpCb,Cp,Cw,Cm,CvpCb,Cp,Cw,Cm,Cvp。Exercise1-2Exercise1-2Exercise1-2Exercise1-2两相等的正圆锥体在底部处相连接，每个锥体的高等于其底部直径．这个组合体浮于水面，使其两个顶点在水表面上，试绘图并计算：（1111）中横剖面系数CmCmCmCm，（2222）纵向棱形系数CpCpCpCp，（3333）水线面系数CwCwCwCw，（4444）方形系数CbCbCbCb。V=(AV=(AV=(AV=(Adddd****h)/3h)/3h)/3h)/3Exercise1-2Exercise1-2Exercise1-2Exercise1-22/32/32/32/3已知：Lpp=315ft=96.012m;B=45ft6in=13.868m;Lpp=315ft=96.012m;B=45ft6in=13.868m;Lpp=315ft=96.012m;B=45ft6in=13.868m;Lpp=315ft=96.012m;B=45ft6in=13.868m;d=18ft8in=5.690m;d=18ft8in=5.690m;d=18ft8in=5.690m;d=18ft8in=5.690m;Δ=4618t(=4618t(=4618t(=4618t(海水););););Aw=10700sq.ft=994.03mAw=10700sq.ft=994.03mAw=10700sq.ft=994.03mAw=10700sq.ft=994.03m2222;;;;Am=828sq.ft=76.921mAm=828sq.ft=76.921mAm=828sq.ft=76.921mAm=828sq.ft=76.921m2222....解:Cp=:Cp=:Cp=:Cp=Δ////ω/(Am/(Am/(Am/(Am****Lpp)Lpp)Lpp)Lpp)=4618/(1.025=4618/(1.025=4618/(1.025=4618/(1.025****76.92176.92176.92176.921****96.012)=0.61096.012)=0.61096.012)=0.61096.012)=0.610Cm=Am/(BCm=Am/(BCm=Am/(BCm=Am/(B****d)d)d)d)=76.921/(13.868=76.921/(13.868=76.921/(13.868=76.921/(13.868****5.690)=0.9755.690)=0.9755.690)=0.9755.690)=0.975Cw=Aw/(LppCw=Aw/(LppCw=Aw/(LppCw=Aw/(Lpp****B)B)B)B)=994.03/(96.012=994.03/(96.012=994.03/(96.012=994.03/(96.012****13.868)=0.74713.868)=0.74713.868)=0.74713.868)=0.747TPI(s.w)=Aw/420=10700/420=25.476t/TPI(s.w)=Aw/420=10700/420=25.476t/TPI(s.w)=Aw/420=10700/420=25.476t/TPI(s.w)=Aw/420=10700/420=25.476t/””””TPI(f.w)=Aw/432=10700/432=24.768t/TPI(f.w)=Aw/432=10700/432=24.768t/TPI(f.w)=Aw/432=10700/432=24.768t/TPI(f.w)=Aw/432=10700/432=24.768t/””””Exercise1-2Exercise1-2Exercise1-2Exercise1-24/44/44/44/4∵Am=Am=Am=Am=πrrrr2222/2/2/2/2Aw=2Aw=2Aw=2Aw=2****0.20.20.20.2****4r4r4r4r****r=4rr=4rr=4rr=4r2222V=1/3(V=1/3(V=1/3(V=1/3(πrrrr2222))))****2r=2/32r=2/32r=2/32r=2/3πrrrr3333∴Cm=Am/(2rCm=Am/(2rCm=Am/(2rCm=Am/(2r****r)=r)=r)=r)=π/4=0.785/4=0.785/4=0.785/4=0.785Cp=V/(1/2Cp=V/(1/2Cp=V/(1/2Cp=V/(1/2πrrrr2222****4r)=1/3=0.3334r)=1/3=0.3334r)=1/3=0.3334r)=1/3=0.333Cwp=Aw/(4rCwp=Aw/(4rCwp=Aw/(4rCwp=Aw/(4r****2r)=1/2=0.5002r)=1/2=0.5002r)=1/2=0.5002r)=1/2=0.500Cb=V/(4rCb=V/(4rCb=V/(4rCb=V/(4r****2r2r2r2r****r)=r)=r)=r)=π/12=0.261/12=0.261/12=0.261/12=0.261Cvp=V/(4rCvp=V/(4rCvp=V/(4rCvp=V/(4r2222****r)=r)=r)=r)=π/6=0.522/6=0.522/6=0.522/6=0.522Exercise1-3Exercise1-3Exercise1-3Exercise1-3某海洋客货轮排水体积V=9750mV=9750mV=9750mV=9750m3333，长宽比L/B=8L/B=8L/B=8L/B=8，宽度吃水比B/d=2.63B/d=2.63B/d=2.63B/d=2.63，船型系数Cm=0.9,Cp=0.66,Cvp=Cm=0.9,Cp=0.66,Cvp=Cm=0.9,Cp=0.66,Cvp=Cm=0.9,Cp=0.66,Cvp=0.780.780.780.78，试求：（1111）船长LLLL；（2222）船宽B;B;B;B;（3333）吃水dddd；（4444）水线面系数CwCwCwCw；（5555）方形系数CbCbCbCb；（6666）水线面面积AwAwAwAw。解：Cp=V/CmBdL=V/CmB(B/2.63)(8B)=2.63V/8CmBCp=V/CmBdL=V/CmB(B/2.63)(8B)=2.63V/8CmBCp=V/CmBdL=V/CmB(B/2.63)(8B)=2.63V/8CmBCp=V/CmBdL=V/CmB(B/2.63)(8B)=2.63V/8CmB3333∴B=((9750B=((9750B=((9750B=((9750****2.63)/(82.63)/(82.63)/(82.63)/(8****0.660.660.660.66****0.9))0.9))0.9))0.9))1/31/31/31/3=17.54m=17.54m=17.54m=17.54mL=8L=8L=8L=8****17.54=140.32md=17.54/2.63=6.67m17.54=140.32md=17.54/2.63=6.67m17.54=140.32md=17.54/2.63=6.67m17.54=140.32md=17.54/2.63=6.67mCb=Cm.Cp=0.9Cb=Cm.Cp=0.9Cb=Cm.Cp=0.9Cb=Cm.Cp=0.9****0.66=0.5940.66=0.5940.66=0.5940.66=0.594Cw=Cb/Cvp=0.594/0.78=0.762Cw=Cb/Cvp=0.594/0.78=0.762Cw=Cb/Cvp=0.594/0.78=0.762Cw=Cb/Cvp=0.594/0.78=0.762Aw=0.762Aw=0.762Aw=0.762Aw=0.762****140.32140.32140.32140.32****175.54=1875.44m175.54=1875.44m175.54=1875