Basics of Fluid Mechanics, 2014a

136 CHAPTER 4. FLUIDS STATICS
metacentric height is
GM new =
Td
W total θ
(4.174)
If the change in the GM can be neglected, equation (4.174) provides the solution. The
calculation of GM can be improved by taking into account the effect of the measuring
weight. The change in height of G is
✁gm total G new = gm ✁ ship G actual + gTh ✁ (4.175)
Combining equation (4.175) with equation (4.174) results in
m total T
GM a ctual = GM new − h
(4.176)
m ship m ship
The weight of the ship is obtained from looking at the ship depth.
4.6.1.3 Stability of Submerged Bodies
The analysis of submerged bodied is different from the stability when the body lays
between two fluid layers with different density. When the body is submerged in a single
fluid layer, then none of the changes of buoyant centroid occurs. Thus, the mass
centroid must be below than buoyant centroid in order to have stable condition.
However, all fluids have density varied in some degree. In cases where the density
changes significantly, it must be taken into account. For an example of such a case is
an object floating in a solar pond where the upper layer is made of water with lower
salinity than the bottom layer(change up to 20% of the density). When the floating
object is immersed into two layers, the stability analysis must take into account the
changes of the displaced liquids of the two liquid layers. The calculations for such cases
are a bit more complicated but based on the similar principles. Generally, this density
change helps to increase the stability of the floating bodies. This analysis is out of the
scope of this book (for now).
4.6.1.4 Stability of None Systematical or “Strange” Bodies
While most floating bodies are symmetrical
or semi–symmetrical, there are situations
where the body has a “strange”
and/or un-symmetrical body. Consider the
first strange body that has an abrupt step
change as shown in Figure 4.46. The body
weight doesn’t change during the rotation
that the green area on the left and the
green area on right are the same (see Figure
4.46). There are two situations that
can occur. After the tilting, the upper part
δβ
ΔF
M
a
ΔF
G
GM
B B’ b
Fig. -4.46.
shape body.
Calculations of GM for abrupt