Page 19 - Instrumentation Reference Book 3E

4 Measurement of flow
point the motion of the particles of fluid is not of p1 kg and would require a force of 9.8.1 p1 N to
all parallel to the tube walls but has a transverse support it at a point where the gravitational con-
velocity also. This form of flow pattern is called stant g is 9. 81 ds. Therefore if it is at a height of
turbulent flow. Summarizing, therefore, for vel- z meters above a reference plane it would have
ocities below the critical velocity, flow is said to be 9.81 plz joules of energy by virtue of its height.
streamlined or laminar, and for velocities above
the critical value flow is said to be turbulent-this
situation is most common in practice. 1.2.1.4 Kinetic energy
Reynolds formulated his data in a dimension- A fluid has this energy by virtue of its motion.
less form 1 m3 of fluid of density p1 kg/m3 with a velocity
V1 ds would have a kinetic energy of (1)/(2)plV:
joules.

where Re is the Reynolds number, D is the diameter 1.2.1.5 Pressure energy
of the throat of the installation, v is velocity, p is
density of fluid, and p is absolute viscosity. Flow A fluid has this energy by virtue of its pressure.
of fluid in pipes is expected to be laminar if the For example, a fluid having a volume qm3 and a
Reynolds number is less than 2000 and turbulent pressure of p1 Nlm2 would have a pressure energy
if it is greater than 4000. Between these values is of p1 v1 joules.
the critical zone. If systems have the same Rey-
nolds number and are geometrically similar they 1.2.1.6 Internal energy
are said to have dynamic similarity.
The fluid will also have energy by virtue of its
temperature (i.e., heat energy). If there is resis-
1.2.1.1 Flow profile tance to flow in the form of friction, other forms
The velocity across the diameter of a pipe varies of internal energy will be converted into heat
due to many influence quantities. The distribu- energy.
tion is termed the velocity profile of the system.
For laminar flow the profile is parabolic in na- 1.2.1.7 Total energy
ture. The velocity at the center of the pipe is
approximately twice the mean velocity. For tur- The total energy E of a fluid is given by the
bulent flow, after a sufficient straight pipe run the equation
flow profile becomes fully developed. total energy (E) =potential energy
The concept of “fully developed flow” is critical
to good flow measurement system design. In a +kinetic energy
fully developed flow, the velocity at the center of +pressure energy
the pipe is only about 1.2 times the mean velocity. +internal energy
This is the preferred flow measurement situation.
It permits the most accurate, most repeatable, and E=P.E.+K.E.+PR.E.+I.E. (1.2)
most linear measurement of flow.
1.2.2 Viscosity
1.2.1.2 Energy of aJZuid in motion Viscosity is the frictional resistance that exists in a
Let’s look at the forms in which energy is repre- flowing fluid. It will be discussed in more detail in
sented in a fluid in motion. This will help to the next chapter. Briefly, the particles of fluid
understand the use of the Reynolds number in actually in contact with the walls of the channel
universal flow formulas. The basic types of are at rest, while those at the center of the channel
energy associated with a moving fluid are: move at maximum velocity. Thus, the layers of
fluid near the center, which are moving at max-
(a) Potential energy or potential head. imum velocity, will be slowed down by the slower
(b) Kinetic energy. moving layers, and the slower moving layers will
(c) Pressure energy. be speeded up by the faster moving layers.
(d) Heat energy. Dynamic viscosity of a fluid is expressed in
units of Ns/m2. Thus a fluid has a dynamic vis-
1.2.1.3 Potential energy cosity of 1 Nslm’ if a force a 1 N is required to
move a plane of 1 m2 in area at a speed of 1 m/s
The fluid has this energy by virtue of its position parallel to a fixed plane, the moving plane being
or height above some fixed level. For example, lm away from the fixed plane and the space
1 m3 of liquid of density p1 kg/m3 will have a mass between the planes being completely filled with