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Department of Chemical EngineeringProcess Instrumentation and Control III
Lecturer: TP Makhathini
Email: thobeka@mut.ac.za
031 907 7141
Section Objectives
This chapter will introduce you to the concepts of fluid velocity and flow and its relation to
pressure and viscosity. The chapter will help you understand the units used in flow measurement
and become familiar with the most commonly used flow standards.
• This chapter covers the following topics:
• Reynolds number and its application to flow patterns s Formulas used in flow
measurements
Bernoulli equation and its applications
Difference between flow rate and total flow
• Pressure losses and their effects on flow
• Flow measurements using differential pressure measuring devices and their
characteristics
• Open channel flow and its measurement
• Considerations in the use of flow instrumentation
7.1 Introduction
This chapter discusses the basic terms and formulas used in flow measurements an
instrumentation. The measurement of fluid flow is very important in industrial applications.
Optimum performance of some equipment and operations require specific flow rates. The cost of
many liquids and gases are based on the measured flow through a pipeline making it necessary to
accurately measure and control the rate of flow for accounting purposes.
7.2 Basic Terms
This section will be using terms and definitions from previous chapters as well as introducing a
number of new definitions related to flow and flow rate sensing.
Velocity is a measure of speed and direction of an object. When related to fluids it is the rate of
flow of fluid particles in a pipe. The speed of particles in a fluid flow varies across the flow, i.e.,
where the fluid is in contact with the constraining walls (the boundary layer) the velocity of the
liquid particles is virtually zero; in the center of the flow the liquid particles will have the maximum
velocity. Thus, the average rate of flow is used in flow calculations. The units of flow are normally
feet per second (fps), feet per minute (fpm), meters per second (mps), and so on. Previously, the
pressures associated with fluid flow were defined as static, impact, or dynamic.
Laminar flow of a liquid occurs when its average velocity is comparatively low and the fluid
particles tend to move smoothly in layers, as shown in Fig. 7.1a. The velocity of the particles
across the liquid takes a parabolic shape.
William, D., Fundamentals of Industrial Instrumentation and Process Control Rev date: 01 November 2020
, Department of Chemical Engineering
Process Instrumentation and Control III
Lecturer: TP Makhathini
Email: thobeka@mut.ac.za
Turbulent flow occurs when the flow velocity is high and the particles no longer flow smoothly
031 907 in7141
layers and turbulence or a rolling effect occurs. This is shown in Fig. 7.1b. Note also the flattening
of the velocity profile.
Viscosity is a property of a gas or liquid that is a measure of its resistance to motion or flow. A
viscous liquid such as syrup has a much higher viscosity than water and water has a higher
viscosity than air. Syrup, because of its high viscosity, flows very slowly and it is very hard to
move an object through it. Viscosity (dynamic) can be measured in poise or centipoise, whereas
kinematic viscosity (without force) is measured in stokes or centistokes. Dynamic or absolute
viscosity is used in the Reynolds and flow equations. Table 7.1 gives a list of con- versions.
Typically, the viscosity of a liquid decreases as temperature increases.
The Reynolds number R is a derived relationship combining the density and viscosity of a liquid
with its velocity of flow and the cross-sectional dimensions
William, D., Fundamentals of Industrial Instrumentation and Process Control Rev date: 01 November 2020
, Department of Chemical Engineering
Process Instrumentation and Control III
Lecturer: TP Makhathini
Email: thobeka@mut.ac.za
031 907 7141
Flow patterns can be considered to be laminar, turbulent, or a combination of both. Osborne
Reynolds observed in 1880 that the flow pattern could be predicted from physical properties of the
liquid. If the Reynolds number for the flow in a pipe is equal to or less than 2000 the flow will be
laminar. From 2000 to about 5000 is the intermediate region where the flow can be laminar,
turbulent, or a mixture of both, depending upon other factors. Beyond 5000 the flow is always
turbulent.
The Bernoulli equation is an equation for flow based on the law of conservation of energy, which
states that the total energy of a fluid or gas at any one point in a flow is equal to the total energy at
all other points in the flow.
Energy factors. Most flow equations are based on the law of energy conservation and relate the
average fluid or gas velocity, pressure, and the height of fluid above a given reference point. This
relationship is given by the Bernoulli equation. The equation can be modified to take into account
energy losses due to friction and increase in energy as supplied by pumps.
Energy losses in flowing fluids are caused by friction between the fluid and the containment walls
and by fluid impacting an object. In most cases these losses should be taken into account. Whilst
these equations apply to both liquids and gases, they are more complicated in gases because of the
fact that gases are compressible.
Flow rate is the volume of fluid passing a given point in a given amount of time and is typically
measured in gallons per minute (gpm), cubic feet per minute (cfm), liter per minute, and so on.
Table 7.2 gives the flow rate con- version factors.
Total flow is the volume of liquid flowing over a period of time and is measured in gallons, cubic
feet, liters and so forth.
William, D., Fundamentals of Industrial Instrumentation and Process Control Rev date: 01 November 2020
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