tailieunhanh - Ship Stability for Masters and Mates 5 Episode 9

Tham khảo tài liệu 'ship stability for masters and mates 5 episode 9', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Liquid pressure and thrust. Centres of pressure 269 The moment of the thrust w g b x2 sin 0 dx on the strip about AB The moment of the total thrust about AB a w g b x2 sin0 w g b sin Ỡ 3 Let X be the distance of the centre of pressure P from AB then X X Total thrust Total moment about AB X X w g b sin0 w g b sin0 2 3 or X 3 a unless sin 0 0 ii For any Plane Area immersed in a liquid. Fig. In Figure let OY be the line in which the plane cuts the surface of the liquid. Let the plane be inclined at an angle 0 to the horizontal. Let h the x co-ordinate of the centroid G and let w the mass density of the liquid. Depth of the element dA x sin 0 Thrust on dA w g x sin 0 dA Moment of thrust about OY w g x2 sin 0 dA Moment of total thrust about OY w g x2 sin 0 dA w g sin 0 x2 dA 270 Ship Stability for Masters and Mates Total thrust on A w g A Depth of centroid w g A h sin 0 Moment of total thrust about OY w g A h sin 0 X . wg A h sin 0 X w g sin 0 x2 dA or X ------ Unless sin 0 0 hA Let Ioy be the second moment of the area about OY then Ioy x2 dA and X Loy-hA or Second moment of area about the waterline X ---------------- -------- ------- --- First moment of area about the waterline Centres of pressure by Simpson s Rules Using Horizontal Ordinates Referring to Figure Thrust on the element wg x ydx Moment of the thrust about OY w g x2 y dx Moment of total thrust about OY wg x2 y dx w g x2 y dx Total Thrust w g A Depth of centroid w g r x y dx y dx f J y dx w g x y dx Moment of total thrust about OY Total Thrust X X Liquid pressure and thrust. Centres of pressure 271 where X Depth of centre of pressure below the surface . Moment of total thrust about OY w g x y dx X X or w g x y dx X X w g x2 ydx and x2 y dx X x y dx The value of the expression x2 y dx can be found by Simpson s Rules using values of the product x2y as ordinates and the value of the expression x y dx can be found in a similar manner using values of the product xy as ordinates. Example 1 A lower