# Aula Teórica 5 ```Aula Te&oacute;rica 5
For&ccedil;as hidrost&aacute;ticas sobre superf&iacute;cies
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 (Impuls&atilde;o)
• 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
• Poder&aacute; este degrau manter-se?
• Se n&atilde;o puder o que &eacute; que acontece?
• Qual seria a situa&ccedil;&atilde;o de equil&iacute;brio se n&atilde;o existisse evapora&ccedil;&atilde;o?
```