Aula Teórica 5 Forças hidrostáticas sobre superfícies curvas. Flutuabilidade e estabilidade. Curve Surfaces • The vertical forces balances the weight of the fluid located above. • The horizontal forces balance the force applied to any surface with the same projection on a vertical plane. Pressure center • Must be computed knowing the action lines of the vertical and horizontal forces and using the rules from statics. When the shape of the surface is complex, the calculation of the gravity center of the fluid above is computing intensive…. Variable density Vertical integration must be done per steps of uniform density. Buoyancy (Impulsão) • Is the weight of the displaced volume: b fluid gV • This equation assumes that density is uniform along the whole surface…. • In fact buoyancy is the summation of the pressure distribution…. Buoyancy Downward force: weight of the fluid above the upper surface Upward force: weight of the fluid above the lower surface. Resulting force= Upward force minus Downward force Resulting force is applied in the gravity center of the displaced volume: buoyancy center . Stability of floating bodies If the body gravity center was located below the buoyancy center, the body would be stable. A boat would not be interesting to organize touristic cruises…. Stability of floating bodies (cont.) Problems • The Mediterranean Sea salinity is 39 (g/l) and the Atlantic’s Ocean at Gibraltar latitude is 36. If the straight’s depth is 400 m and temperature was the same on both sides (Atlantic and Mediterranean) at any depth what would be the level difference between both sides of the straight? A 1000kg / m 3 36kg / m 3 A 1036kg / m 3 M 1000kg / m 3 39kg / m 3 M 1039kg / m 3 A g 400 z M g 400 400 M A z 0.77 m A • Poderá este degrau manter-se? • Se não puder o que é que acontece? • Qual seria a situação de equilíbrio se não existisse evaporação?