LAMINAR AND TURBULENT FLOW
Average (Bulk) Velocity
In many fluid flow problems, instead of determining exact velocities at different locations in the
same flow cross-section, it is sufficient to allow a single average velocity to represent the
velocity of all fluid at that point in the pipe. This is fairly simple for turbulent flow since the
velocity profile is flat over the majority of the pipe cross-section. It is reasonable to assume that
the average velocity is the same as the velocity at the center of the pipe.
If the flow regime is laminar (the velocity profile is parabolic), the problem still exists of trying
to represent the "average" velocity at any given cross-section since an average value is used in
the fluid flow equations. Technically, this is done by means of integral calculus. Practically, the
student should use an average value that is half of the center line value.
Viscosity is a fluid property that measures the resistance of the fluid to deforming due to a shear
force. Viscosity is the internal friction of a fluid which makes it resist flowing past a solid
surface or other layers of the fluid. Viscosity can also be considered to be a measure of the
resistance of a fluid to flowing. A thick oil has a high viscosity; water has a low viscosity. The
unit of measurement for absolute viscosity is:
µ = absolute viscosity of fluid (lbf-sec/ft2).
The viscosity of a fluid is usually significantly dependent on the temperature of the fluid and
relatively independent of the pressure. For most fluids, as the temperature of the fluid increases,
the viscosity of the fluid decreases. An example of this can be seen in the lubricating oil of
engines. When the engine and its lubricating oil are cold, the oil is very viscous, or thick. After
the engine is started and the lubricating oil increases in temperature, the viscosity of the oil
decreases significantly and the oil seems much thinner.
An ideal fluid is one that is incompressible and has no viscosity. Ideal fluids do not actually
exist, but sometimes it is useful to consider what would happen to an ideal fluid in a particular
fluid flow problem in order to simplify the problem.
The flow regime (either laminar or turbulent) is determined by evaluating the Reynolds number
of the flow (refer to figure 5). The Reynolds number, based on studies of Osborn Reynolds, is
a dimensionless number comprised of the physical characteristics of the flow. Equation 3-7 is
used to calculate the Reynolds number (NR) for fluid flow.
NR = r v D / µ gc