
We may use the Steiner Theorem, according to which
- where
is the inertia radius.

For the distance
between the centre of gravity and centre of pressure
insertion of the Steiner Theorem leads to:
...so that, as a result:

The horizontal position of the hydrostatic centre
- in the
direction - is usually no problem: in
the most often encountered symmetric shapes,
is
located on the vertical axis of symmetry. In nonsymmetric cases the position is found
from the moment condition relative to axis
:
... so that 
|
Fig.B-18
|
|  |
| 
3) The case of a curved wall
- may be mathematically quite demanding. For the present purpose, it will be sufficient to
use a simple method of substitution plane
as shown in Fig.B-18. The curved wall (such as e.g. the convex cover in the case A)
is separated by an imaginary plane from the rest of fluid.
Then the hydrostatic force
acting upon this plane
is evaluated by the approach from Fig.B-17.
The hydrostatic effect of fluid in the space between this substitution plane and the wall
may be shown to be equal to weight, gravity force
.
Evaluating it is a question of calculating the volume of this space. The resultant force is finally
obtained as the vector addition of the two components. In the case B the substitution plane
is located ourside the space occupied by the liquid. As a result, the vertical component
evaluated as the hydrostatic effect of fluid between the wall and the substitution plane is negative
- acting upwards. It is lift
, the magnitude of which
is equal to the corresponding gravity force
. This
is nothing else but the
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This is page Nr. B07 from textbook
Vaclav TESAR : "BASIC FLUID MECHANICS"
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tesar@fsid.cvut.cz
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