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MCE 240 – Fluid Mechanics

Lecture 9
(Chapter 3) – IV

PRESSURE AND FLUID STATICS

Dr
...
The
buoyant force is caused by the increase of pressure with depth in a fluid
...

For a fluid with constant density,
the buoyant force is independent
of the distance of the body from
the free surface
...

A flat plate of uniform thickness h submerged in a
liquid parallel to the free surface
...

The buoyant forces acting on a solid
body submerged in a fluid and on a
fluid body of the same shape at the
same depth are identical
...
For a solid of uniform
density, its weight Ws also acts through
the centroid, but its magnitude is not
necessarily equal to that of the fluid it
displaces
...
)
4

Buoyancy – Buoyant Force (continued)
For floating bodies, the weight of the entire body must be equal to the
buoyant force, which is the weight of the fluid whose volume is equal to the
volume of the submerged portion of the floating body:

A solid body dropped
into a fluid will sink,
float, or remain at rest at
any point in the fluid,
depending on its
average density relative
to the density of the
fluid
...
When the balloon is
neither rising nor falling, the
upward buoyant force exactly
balances the downward
weight
...


For floating bodies such as ships, stability is
an important consideration for safety
...


An immersed neutrally buoyant body is
(a) stable if the center of gravity G is
directly below the center of buoyancy B
of the body, (b) neutrally stable if G and
B are coincident, and (c) unstable if G
is directly above B
...


A ball in a trough between
two hills is stable for small
disturbances, but unstable for
large disturbances
...

However, the body is unstable if point M is below point G
...

The length of the metacentric height GM above G is a measure of the
stability: the larger it is, the more stable is the floating body

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