FLUID-INDUCED STRUCTURAL FORCES
29
Figure 2.10 Cross section of a ship showing buoyant and gravîtational forces.
For example, consider the ship shown in Figure 2.10 which has an actual
weight (in air at sea level) of m^g. The volume of water that the ship displaces
is V and the weight density of the water is denoted by 7W. The resuit of applying
Archimedes principle to this System is
™b9 = 7W^ ~ mo9
(2-24)
This buoyant force 7WV acts at point B on the ship, in a vertical direction
opposite to that of the résultant gravitational force m^g. The latter force acts
at the ship’s center of gravity. Thus, a ship’s actual weight is generally referred
to as its displacement.
In general, point B is not coincident with point G of the solid body. In
précisé terms:
If the displaced fluid is of constant density, B is located at the centroid of the displaced fluid volume V.
This statement can be proved in general for solid body of arbitrary shape (Batchelor, 2000). Its validity can be simply illustrated for the following spécial case
of a solid, prismatic block partially submerged in water. Refer now to the séquence of illustrations (a) through (f) in Figure 2.11. Suppose that the solid
block (a) is removed from the water and then replaced by pressure forces around
the void of volume V so that the water remains undisturbed (b). The pressure
distribution, shown as “gage” pressure, is constant on any horizontal plane and
varies linearly with depth. The pressure distribution on the solid block (c) is
identical to that on the void. In fact this identical pressure distribution would
also occur on a water block (d) of volume P which would just fi 11 the same void.
29
Figure 2.10 Cross section of a ship showing buoyant and gravîtational forces.
For example, consider the ship shown in Figure 2.10 which has an actual
weight (in air at sea level) of m^g. The volume of water that the ship displaces
is V and the weight density of the water is denoted by 7W. The resuit of applying
Archimedes principle to this System is
™b9 = 7W^ ~ mo9
(2-24)
This buoyant force 7WV acts at point B on the ship, in a vertical direction
opposite to that of the résultant gravitational force m^g. The latter force acts
at the ship’s center of gravity. Thus, a ship’s actual weight is generally referred
to as its displacement.
In general, point B is not coincident with point G of the solid body. In
précisé terms:
If the displaced fluid is of constant density, B is located at the centroid of the displaced fluid volume V.
This statement can be proved in general for solid body of arbitrary shape (Batchelor, 2000). Its validity can be simply illustrated for the following spécial case
of a solid, prismatic block partially submerged in water. Refer now to the séquence of illustrations (a) through (f) in Figure 2.11. Suppose that the solid
block (a) is removed from the water and then replaced by pressure forces around
the void of volume V so that the water remains undisturbed (b). The pressure
distribution, shown as “gage” pressure, is constant on any horizontal plane and
varies linearly with depth. The pressure distribution on the solid block (c) is
identical to that on the void. In fact this identical pressure distribution would
also occur on a water block (d) of volume P which would just fi 11 the same void.