the distance to the point of contact between the free fluid and the flat surface
(Fig. A2.8).
Fluid flow comprises two distinct regions. One is the boundary layer adjacent to
the surface plate, where tangential shear stresses occur. As mentioned before, the
height of the boundary layer increases with distance to the point of contact. The
outer zone is located above the boundary layer. In this latter zone, the vertical
velocity gradient is zero, there are no tangential stresses, and viscosity is not used
in the study of laminar flows.
Another important problem concerns stationary, laminar, and incompressible
flow around circular sections of solid bodies, such as cylinders, in which both
viscous and pressure forces are relevant (Fig. A2.9).
In this case, the streamlines are symmetrical around the circular section while the
central line collides with the circular section at point A, divides and bypasses the
section. Point A is known as the stagnation point. As in a flat surface flow, a
boundary layer is formed in the circular section by the action of the viscosity. The
velocity distribution, around the section, can be evaluated by the spacing between
the streamlines. If the streamlines are more compacted, because there is no flow
between them, the fluid velocity is greater. On the contrary, the fluid velocity will
be lower if the current lines are farthest from each other. If the flow is inviscid (fluid
without viscosity), then the streamlines are symmetrical relative to the circular
section. The speed around the section increases to a point D (Fig. A2.9b) where the
streamlines are more compacted, then decreasing as the fluid bypasses and deviates
from the section.
According to Bernoulli’s principle the speed increase occurs simultaneously
with a pressure decrease whereas a decrease leads to an increase in pressure. Thus,
in the case of a steady and incompressible inviscid flow, the pressure along the
surface section decreases from point A to point D and again increases up to point E.
In this ideal flow, a boundary layer is not considered because of the absence of
viscosity, and the pressure and fluid velocity fields are symmetrical along section,
with no pressure gradient likely to exert a dragging effect on the section. Since the
pressure increases again, in the zone posterior section of the section beyond point B,
it is natural that the particles in that zone of the boundary layer, experience a
balance of pressure forces, in the opposite direction to their movement. From a
point C, called the separation point, the fluid inside the boundary layer is brought to
rest and separated from the surface. The separation of the boundary layer results in a
low-pressure zone at the back of the section, called a wake, with effects of local
fluid recirculation.
Under real flow with viscosity (Fig. A2.9a) data suggests that the boundary layer
between points A and B is very thin, and it can be assumed that the streamlines
above the boundary layer and the consequent distribution of pressures are like that
of inviscid flow. As the pressure increases again, in the posterior zone of the section
beyond the point B, the particles in that zone of the boundary layer are subject to
opposing pressure forces, in the opposite direction to their movement. From the
separation point C, called the separation point, the fluid inside the boundary layer is
brought to rest and separated from the surface. The separation of the boundary layer
Annex A2: Basic Topics on Laws of Motion and Evaporation
357
(Fig. A2.8).
Fluid flow comprises two distinct regions. One is the boundary layer adjacent to
the surface plate, where tangential shear stresses occur. As mentioned before, the
height of the boundary layer increases with distance to the point of contact. The
outer zone is located above the boundary layer. In this latter zone, the vertical
velocity gradient is zero, there are no tangential stresses, and viscosity is not used
in the study of laminar flows.
Another important problem concerns stationary, laminar, and incompressible
flow around circular sections of solid bodies, such as cylinders, in which both
viscous and pressure forces are relevant (Fig. A2.9).
In this case, the streamlines are symmetrical around the circular section while the
central line collides with the circular section at point A, divides and bypasses the
section. Point A is known as the stagnation point. As in a flat surface flow, a
boundary layer is formed in the circular section by the action of the viscosity. The
velocity distribution, around the section, can be evaluated by the spacing between
the streamlines. If the streamlines are more compacted, because there is no flow
between them, the fluid velocity is greater. On the contrary, the fluid velocity will
be lower if the current lines are farthest from each other. If the flow is inviscid (fluid
without viscosity), then the streamlines are symmetrical relative to the circular
section. The speed around the section increases to a point D (Fig. A2.9b) where the
streamlines are more compacted, then decreasing as the fluid bypasses and deviates
from the section.
According to Bernoulli’s principle the speed increase occurs simultaneously
with a pressure decrease whereas a decrease leads to an increase in pressure. Thus,
in the case of a steady and incompressible inviscid flow, the pressure along the
surface section decreases from point A to point D and again increases up to point E.
In this ideal flow, a boundary layer is not considered because of the absence of
viscosity, and the pressure and fluid velocity fields are symmetrical along section,
with no pressure gradient likely to exert a dragging effect on the section. Since the
pressure increases again, in the zone posterior section of the section beyond point B,
it is natural that the particles in that zone of the boundary layer, experience a
balance of pressure forces, in the opposite direction to their movement. From a
point C, called the separation point, the fluid inside the boundary layer is brought to
rest and separated from the surface. The separation of the boundary layer results in a
low-pressure zone at the back of the section, called a wake, with effects of local
fluid recirculation.
Under real flow with viscosity (Fig. A2.9a) data suggests that the boundary layer
between points A and B is very thin, and it can be assumed that the streamlines
above the boundary layer and the consequent distribution of pressures are like that
of inviscid flow. As the pressure increases again, in the posterior zone of the section
beyond the point B, the particles in that zone of the boundary layer are subject to
opposing pressure forces, in the opposite direction to their movement. From the
separation point C, called the separation point, the fluid inside the boundary layer is
brought to rest and separated from the surface. The separation of the boundary layer
Annex A2: Basic Topics on Laws of Motion and Evaporation
357