Lecture 6
Hydrostatic forces on curved surfaces.
Buoyancy and stability.
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.
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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….
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Variable density
Vertical integration must be done per
steps of uniform density.
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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….
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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 .
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Stability of floating bodies
If the body gravity center was located below the buoyancy center, the body would be
stable. Such boat would not be interesting for touristic cruises….
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Stability of floating bodies
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Problems
• The Mediterranean Sea salinity is 39 (g/l) and the Atlantic’s
Ocean at Gibraltar salinity is 36. If the straight’s depth is 400
m and temperature was the same at any depth on both sides
(Atlantic and Mediterranean).
• What would be the level difference between both sides of
the straight?
 A  1000kg / m 3  36kg / m 3
 M  1000kg / m 3  39kg / m 3
 A  1036kg / m 3
 M  1039kg / m 3
 A g 400  z    M g 400 
400 M   A 
z 
 0.77m

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A
Atlantic
Mediterranean
• Can this step be kept? (Poderá este degrau manter-se?)
• If not what happens? (Se não puder o que é que acontece?)
• Why exist this difference in salinity between the two seas? (Porque existe
esta diferença de salinidade entre os dois mares?)
• What would be the equilibrium in the absence of evaporation? (Qual seria
a situação de equilíbrio se não existisse evaporação?)
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