24
2. Water at Rest and in Motion
Let the barge be tilted an angle () (Fig. 2.4b). The centre of mass remains at
point G, but this new centre of buoyancy, B", is found at the centre of gravity
of the water displaced by the barge. A vertical line drawn upward from B"
intersects the line of symmetry at a point M, called the metacentre. If point
M is situated above G, that is, if the metacentric height M G is positive, a
restoring moment is present and the original position of the barge is stable. If
M is situated below G (negative MG), the body is unstable and will overturn,
if disturbed. The value of metacentric height gives an indication of the stability
which increases with increasing MG. For a body of varying cross-section and
draft, such as a yacht, the computation of the metacentre is more complicated.
2.3 Water in Motion: Hydrodynamics
2.3.1 Methods of the Study
In a microscopic sense, fluids are aggregations of molecules and the distance
between molecules is very large compared to the molecular diameter. However,
the treatment of fluid mechanics from the molecular point of view, a subject
dealt with in the kinetic theory of fluids, is beyond the scope of this book. For
the purpose of this book we assume that the fluid in question is continuous.
Fluid can be regarded as continuous when the measured fluid property is constant for sensitive volumes: volumes which are small on the macroscopic scale
but large on the microscopic. With regard to a continuous fluid, we can define
a fluid particle as consisting of the fluid contained within an infinitesimal
volume. That is to say, a volume, whose size may be considered so small, that
for the particular purpose in hand its linear dimensions are negligible. Thus, a
fluid particle may be treated as a geometric point. This elementary fluid particle is assumed to be homogeneous, isotropic and continuous in the macroscopic
sense.
Fluid mechanics is a highly visual subject. The patterns of the flow can be
visualized in many different ways. However, there are a few basic types of line
patterns used to visualize flows, such as:
• a streamline - a line everywhere tangent to the velocity vector at a
given time (Fig. 2.5a),
• a streak line - the locus of particles introduced into the fluid at the same
point at the regular intervals of time (Fig. 2.5b).
The streamline is an instantaneous representation of flow and it is convenient
for mathematical treatment. Streamlines do not cross, except at points of
theoretically infinite velocity, and at stagnation and separation points of a
body where the velocity is zero.
A streakline is a line joining all particles which have passed through a particular point, such as a dye trace or a chimney plume, ignoring the finite width
and diffusion (Fig. 2.5b). In addition to a streamline and a streakline, the
path of a specific particle of fluid is defined by its position as a function of
2. Water at Rest and in Motion
Let the barge be tilted an angle () (Fig. 2.4b). The centre of mass remains at
point G, but this new centre of buoyancy, B", is found at the centre of gravity
of the water displaced by the barge. A vertical line drawn upward from B"
intersects the line of symmetry at a point M, called the metacentre. If point
M is situated above G, that is, if the metacentric height M G is positive, a
restoring moment is present and the original position of the barge is stable. If
M is situated below G (negative MG), the body is unstable and will overturn,
if disturbed. The value of metacentric height gives an indication of the stability
which increases with increasing MG. For a body of varying cross-section and
draft, such as a yacht, the computation of the metacentre is more complicated.
2.3 Water in Motion: Hydrodynamics
2.3.1 Methods of the Study
In a microscopic sense, fluids are aggregations of molecules and the distance
between molecules is very large compared to the molecular diameter. However,
the treatment of fluid mechanics from the molecular point of view, a subject
dealt with in the kinetic theory of fluids, is beyond the scope of this book. For
the purpose of this book we assume that the fluid in question is continuous.
Fluid can be regarded as continuous when the measured fluid property is constant for sensitive volumes: volumes which are small on the macroscopic scale
but large on the microscopic. With regard to a continuous fluid, we can define
a fluid particle as consisting of the fluid contained within an infinitesimal
volume. That is to say, a volume, whose size may be considered so small, that
for the particular purpose in hand its linear dimensions are negligible. Thus, a
fluid particle may be treated as a geometric point. This elementary fluid particle is assumed to be homogeneous, isotropic and continuous in the macroscopic
sense.
Fluid mechanics is a highly visual subject. The patterns of the flow can be
visualized in many different ways. However, there are a few basic types of line
patterns used to visualize flows, such as:
• a streamline - a line everywhere tangent to the velocity vector at a
given time (Fig. 2.5a),
• a streak line - the locus of particles introduced into the fluid at the same
point at the regular intervals of time (Fig. 2.5b).
The streamline is an instantaneous representation of flow and it is convenient
for mathematical treatment. Streamlines do not cross, except at points of
theoretically infinite velocity, and at stagnation and separation points of a
body where the velocity is zero.
A streakline is a line joining all particles which have passed through a particular point, such as a dye trace or a chimney plume, ignoring the finite width
and diffusion (Fig. 2.5b). In addition to a streamline and a streakline, the
path of a specific particle of fluid is defined by its position as a function of