椭园封头卧式贮罐体积计算实例
设V 1为圆柱体部分体积，V 2为两个半椭球封头体积，总体积为V
圆柱的内半径为R=240/2，长度为L=1020，内部介质的高度为h=149， 椭球封头三个内半轴为R=120，R=120，C=55
V 1=L ⨯蓝色面积
=L (2⎰R
R -R 2-x 2dx )
x R 2x 22 =2L [R -x +)]|R
R -h 22R
πR 2(R -h ) R 2h 2=2L [-2Rh -h -arcsin(1-)]422R
πR 2h =L [-(R -h ) 2Rh -h 2-R 2arcsin(1-)]2R
=1020[3. 14*120^2149-(120-149)2*120*149-149^2-120^2arcsin(1-)] 2120=1020[22608-(-3376.9)-14400arcsin(1-1.24)]
=1020(25984.9-14400arcsin(-0.24)
=1020(25984.9+14400 *(π/12.9))
=30079816.6
V 2=4⎰
=
=R R -h 0⎰R 2-x 2πC 3R x 2y 2C 1-2-2dydx R R [3R 2h -R 3+(R -h ) 3]3. 14*55[3 *120^2 *149-120^3+（120-149）^3] 3*120
=0.48[6436800-1728000+(-24389)]
=0.48*4684411
=2248517.28
V =V 1+V 2
=L [
+πR 22-(R -h ) 2Rh -h 2-R 2arcsin(1-h )] R πC
3R [3R 2h -R 3+(R -h ) 3]
=30079816.6+2248517.28
=32328333.88
注：计算中arcsin()值的单位是弧度，不是角度！
例arcsin(0.5)=π/6，不能取成arcsin(0.5)=30。
设V 1为圆柱体部分体积，V 2为两个半椭球封头体积，总体积为V 圆柱的内半径为R=240/2，长度为L=480，内部介质的高度为h=127， 椭球封头三个内半轴为R=120，R=120，C=55
V 1=L ⨯蓝色面积
=L (2⎰R
R -R 2-x 2dx )
x R 2x 22 =2L [R -x +)]|R
R -h 22R
πR 2(R -h ) R 2h 2=2L [-2Rh -h -arcsin(1-)]422R
πR 2h =L [-(R -h ) 2Rh -h 2-R 2arcsin(1-)]2R
=480[3. 14*120^2127-(120-127)2*120*127-127^2-120^2arcsin(1-)] 2120=480[22608-(-838.6)-14400* arcsin(1-1.06)]
=480(23446.6-14400* arcsin(-0.06)
=480(23446.6+14400*(π/52.3))
=11669352.32
V 2=4⎰
=
=R R -h 0⎰R 2-x 2πC 3R x 2y 2C 1-2-2dydx R R [3R 2h -R 3+(R -h ) 3]3. 14*55[3*120^2*127-120^3+（120-127）^3] 3*120
=0.48[5486400-1728000+(-343)]
=0.48*3758057
=1803867.36
V =V 1+V 2
=L [
+πR 22-(R -h ) 2Rh -h 2-R 2arcsin(1-h )] R πC
3R [3R 2h -R 3+(R -h ) 3]
=11669352.32+1803867.36
=13473219.68
注：计算中arcsin()值的单位是弧度，不是角度！ 例arcsin(0.5)=π/6，不能取成arcsin(0.5)=30。