with l being the length of surface exposed to airflow. The corresponding
resistance to momentum transfer is expressed as:
s M ¼ 1:5V
À1 Re
0:5
ðA2:50Þ
A2.4.6 Streamlines and the Boundary Layer
The streamlines are the tangential lines, in each moment of time, to the flow
direction. Since the current lines are tangential to the velocity vector of each fluid
particle, flow perpendicular to the streamlines cannot occur. In steady flow, the
velocity at each point remains constant over time, so the streamlines also do not
vary between consecutive time instants. This means that particles passing at a given
fixed point in space belong to the same streamline, or that they are under stationary
flow conditions, e.g. the fluid particle remains in the same streamline (e.g. Fox and
McDonald 1985).
The boundary layer concept, in laminar flow, is readily derived from the analysis
of tangential tensions in fluids. The concept of the laminar layer limit is a
simplification of the real conditions existing in the physical conditions of the
environment, under which the turbulent flow, of a more complex nature
predominates (Fig. A2.7), which dynamizes the vertical flows of mass and energy.
The transition between laminar and turbulent flow can be analysed in terms of
the ratio of the inertial forces associated with the horizontal movement of the fluid
to the viscous forces generated by molecular interaction. This ratio (see Chap. 3),
the Reynolds number Re, defined as Vd/m, where V is the velocity of the fluid, d is
the characteristic dimension of the system, and m is the kinematic viscosity coefficient. This coefficient is defined as the ratio of the dynamic or absolute viscosity to
the density of the fluid. Under flow on a flat plate, the characteristic dimension is
the distance in abscissa, from the point of fluid considered, to the point of contact
between the fluid and the plate. The critical values of Re, for the transition between
the laminar and turbulent flow zones, are about 2 x 10
3 .
Suppose, then, a fluid, moving on a flat immobile plate, approaching it with a
uniform velocity U ∞ . In this case, the fluid layer adjacent to the plate, due to
adhesion to its surface, remains immobile, and Eq. (A2.47) remains valid.
Therefore, even though the speed of the fluid on the stationary surface of the
plate is zero, there is fluid flow, with velocity gradients and tangential shear
stresses. In this case, the slowing effect of sliding fluid layers induces a vertical
increase in fluid velocity. At a certain point, located vertically, this retarding effect
caused by the surface is no longer present, with the fluid speed being equal to that
existing in the previous region, to the fluid contact point with the V ∞ plate.
The fluid velocity, in contact with the immobile plate in the vertical direction 0
y
y B varies, therefore, in the range 0
v
V ∞ . The vertical height,
influenced by the retarding effect of the plate on the flow of the fluid, increases with
356
Annex A2: Basic Topics on Laws of Motion and Evaporation
resistance to momentum transfer is expressed as:
s M ¼ 1:5V
À1 Re
0:5
ðA2:50Þ
A2.4.6 Streamlines and the Boundary Layer
The streamlines are the tangential lines, in each moment of time, to the flow
direction. Since the current lines are tangential to the velocity vector of each fluid
particle, flow perpendicular to the streamlines cannot occur. In steady flow, the
velocity at each point remains constant over time, so the streamlines also do not
vary between consecutive time instants. This means that particles passing at a given
fixed point in space belong to the same streamline, or that they are under stationary
flow conditions, e.g. the fluid particle remains in the same streamline (e.g. Fox and
McDonald 1985).
The boundary layer concept, in laminar flow, is readily derived from the analysis
of tangential tensions in fluids. The concept of the laminar layer limit is a
simplification of the real conditions existing in the physical conditions of the
environment, under which the turbulent flow, of a more complex nature
predominates (Fig. A2.7), which dynamizes the vertical flows of mass and energy.
The transition between laminar and turbulent flow can be analysed in terms of
the ratio of the inertial forces associated with the horizontal movement of the fluid
to the viscous forces generated by molecular interaction. This ratio (see Chap. 3),
the Reynolds number Re, defined as Vd/m, where V is the velocity of the fluid, d is
the characteristic dimension of the system, and m is the kinematic viscosity coefficient. This coefficient is defined as the ratio of the dynamic or absolute viscosity to
the density of the fluid. Under flow on a flat plate, the characteristic dimension is
the distance in abscissa, from the point of fluid considered, to the point of contact
between the fluid and the plate. The critical values of Re, for the transition between
the laminar and turbulent flow zones, are about 2 x 10
3 .
Suppose, then, a fluid, moving on a flat immobile plate, approaching it with a
uniform velocity U ∞ . In this case, the fluid layer adjacent to the plate, due to
adhesion to its surface, remains immobile, and Eq. (A2.47) remains valid.
Therefore, even though the speed of the fluid on the stationary surface of the
plate is zero, there is fluid flow, with velocity gradients and tangential shear
stresses. In this case, the slowing effect of sliding fluid layers induces a vertical
increase in fluid velocity. At a certain point, located vertically, this retarding effect
caused by the surface is no longer present, with the fluid speed being equal to that
existing in the previous region, to the fluid contact point with the V ∞ plate.
The fluid velocity, in contact with the immobile plate in the vertical direction 0
y
y B varies, therefore, in the range 0
v
V ∞ . The vertical height,
influenced by the retarding effect of the plate on the flow of the fluid, increases with
356
Annex A2: Basic Topics on Laws of Motion and Evaporation