Lecture 6 Hydrostatic forces on curved surfaces. Buoyancy and stability.

Lecture 6

Hydrostatic forces on curved surfaces. Buoyancy and stability.

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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:

• This equation assumes that density is uniform along the whole surface….

• In fact buoyancy is the summation of the pressure distribution….

gVb fluid

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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?

3

33

/1036

/36/1000

mkg

mkgmkg

A

A

3

33

/1039

/39/1000

mkg

mkgmkg

M

M

mz

gzg

A

AM

MA

77.0400

400400

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• 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?)

Atlantic Mediterranean

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