Chapter 3 Fluid Statics.ppt

(a) Centroid: 3m above B Solution: (b) Lc L 3.6 Hydrostatic Forces on Plane surfaces Example There is a cistern filled with water in the following figure. A rectangle strobe is connected to the wall by the gemel at N while an iron chain is connected to the strobe at M. The width of the strobe b is 1m. And h1=2.9m，h2=0.5m，h3=0.3m. The angle between iron chain and the line of horizon is 45o. 3.6 Hydrostatic Forces on Plane surfaces Determine 1) the pressure center 2) the force T for lifting up the strobe in neglecting all weights and frictions. 3.6 Hydrostatic Forces on Plane surfaces Solution 1) The pressure center is at the point 3.157 meters deep under the free surface. Therefore T ＞11220 N. 2) 3.6 Hydrostatic Forces on Plane surfaces The distance e from gemel point N to force F * * Hoover Dam Channel 1) Select a dA and find the three forces on 2) Integration 3.7 Hydrostatic Forces on Curved surfaces 3.7 Hydrostatic Forces on Curved surfaces dF p dF px dF pz ? ? dA dA x dA z z x d c P a o h c h b a dA A dF p 3.7 Hydrostatic Forces on Curved surfaces h c A x dF p dF px dF pz ? ? dA dA x dA z z x d c P a o h b a dA A dF p 3.7 Hydrostatic Forces on Curved surfaces dF p dF px dF pz ? ? dA dA x dA z z x d c P a o h b a dA A dF p A z In which Conclusion: x 1. Horizontal forces: x O z A Ax 2. Vertical forces: O z V 3.7 Hydrostatic Forces on Curved surfaces Notes 1）Pressure Volume V: a column between the free surface and the curved surface. 3.7 Hydrostatic Forces on Curved surfaces Notes 1）Pressure Volume V: a column between the free surface and the curved surface. 3.7 Hydrostatic Forces on Curved surfaces F dAz ? Notes 1）Pressure Volume V: a column between the free surface and the curved surface. 3.7 Hydrostatic Forces on Curved surfaces Notes 1）Pressure Volume V: a column between the free surface and the curved surface. 3.7 Hy