This document discusses different types of fluid flow measurement. It begins by describing early crude methods of flow measurement used by ancient Sumerians and later inventors. It then covers the main types of fluid flow - laminar, turbulent, and transitional - and defines the Reynolds number used to characterize these flows. Finally, it discusses common principles for measuring flow rate, including differential pressure, velocity, positive displacement, mass flow, and open channel flow meters.

1. Flow
Measurement(basics)
Ashvani Shukla
C&I
Reliance

2. INTRODUCTION
• In the physical world, mechanical engineers are frequently
required to monitor or control the flow of various fluids through
pipes, ducts and assorted vessels. This fluid can range from thick
oils to light gasses. While some techniques work better with some
groups of fluids, and less well with others, some are not at all
suitable for some applications. In this primer on fluid flow
instrumentation we will look at a wide variety of flow transducers
and their application in the physical world.

3. Fluid flow measurement
• Fluid flow measurement can encompass a wide variety of fluids and
applications. To meet this wide variety of applications the instrumentation
industry has, over many years, developed a wide variety of instruments. The
earliest known uses for flow come as early as the first recorded history. The
ancient Sumerian cities of UR and Kish, near the Tigris and Euphrates rivers
(around 5000 B.C.) used water flow measurement to manage the flow of water
through the aqueducts feeding their cities. In this age the a simple obstruction
was placed in the water flow, and by measuring the height of the water flowing
over the top of the obstruction, these early engineers could determine how
much water was flowing. In 1450 the Italian art architect Battista Alberti
invented the first mechanical anemometer. It consisted of a disk placed
perpendicular to the wind, and the force of the wind caused it to rotate. The
angle of inclination of the disk would then indicate the wind velocity. This was
the first recorded instrument to measure wind speed. An English inventor,
Robert Hooke reinvented this device in 1709, along with the Mayan Indians
around that same period of time. Today we would look down our noses at these
crude methods of flow measurement, but as you will see, these crude methods
are still in use today.

4. TYPE OF FLOW
• There are in general three types of fluid flow in pipes
• laminar
• turbulent
• transient
• Laminar flow
• Laminar flow generally happens when dealing with small pipes and low flow
velocities. Laminar flow can be regarded as a series of liquid cylinders in the pipe,
where the innermost parts flow the fastest, and the cylinder touching the pipe isn't
moving at all.
• Shear stress in a laminar flow depends almost only on viscosity - μ - and is
independent of density - ρ.
• Turbulent flow
• In turbulent flow vortices, eddies and wakes make the flow unpredictable.
Turbulent flow happens in general at high flow rates and with larger pipes.
• Shear stress in a turbulent flow is a function of density - ρ.
• Transitional flow

5. CONTINUE…..
• Transitional flow is a mixture of laminar and turbulent flow, with turbulence in
the center of the pipe, and laminar flow near the edges. Each of these flows
behave in different manners in terms of their frictional energy loss while
flowing and have different equations that predict their behavior.
• Turbulent or laminar flow is determined by the dimensionless Reynolds Number.
• Reynolds Number
• The Reynolds number is important in analyzing any type of flow when there is
substantial velocity gradient (i.e. shear.) It indicates the relative significance of
the viscous effect compared to the inertia effect. The Reynolds number is
proportional to inertial force divided by viscous force.
• The flow is
• laminar when Re < 2300
• transient when 2300 < Re < 4000
• turbulent when 4000 < Re

6. TYPE OF FLOW
• Uniform Flow, Steady Flow
• It is possible - and useful - to classify the type of flow which is being examined into
small number of groups. If we look at a fluid flowing under normal circumstances - a
river for example - the conditions at one point will vary from those at another point
(e.g. different velocity) we have non-uniform flow. If the conditions at one point
vary as time passes then we have unsteady flow. Under some circumstances the flow
will not be as changeable as this. He following terms describe the states which are
used to classify fluid flow: •
• uniform flow: If the flow velocity is the same magnitude and direction at every
point in the fluid it is said to be uniform. •
• non-uniform: If at a given instant, the velocity is not the same at every point the
flow is non-uniform. (In practice, by this definition, every fluid that flows near a
solid boundary will be non-uniform - as the fluid at the boundary must take the
speed of the boundary, usually zero. However if the size and shape of the of the
cross-section of the stream of fluid is constant the flow is considered uniform.) •
• steady: A steady flow is one in which the conditions (velocity, pressure and cross-
section) may differ from point to point but DO NOT change with time. • unsteady: If
at any point in the fluid, the conditions change with time, the flow is described as
unsteady. (In practice there is always slight variations in velocity and pressure, but
if the average values are constant, the flow is considered steady.

7. CONTINUOUS
• Combining the above we can classify any flow in to one of four type:
• 1. Steady uniform flow. Conditions do not change with position in the
stream or with time. An example is the flow of water in a pipe of
constant diameter at constant velocity. Fluid Mechanics Fluid Dynamics:
The Momentum and Bernoulli Equations.
• 2. Steady non-uniform flow. Conditions change from point to point in the
stream but do not change with time. An example is flow in a tapering
pipe with constant velocity at the inlet - velocity will change as you
move along the length of the pipe toward the exit.
• 3. Unsteady uniform flow. At a given instant in time the conditions at
every point are the same, but will change with time. An example is a
pipe of constant diameter connected to a pump pumping at a constant
rate which is then switched off.
• 4. Unsteady non-uniform flow. Every condition of the flow may change
from point to point and with time at every point. For example waves in a
channel.

8. CONTINUOUS
• Compressible or Incompressible All fluids are compressible - even
water - their density will change as pressure changes. Under
steady conditions, and provided that the changes in pressure are
small, it is usually possible to simplify analysis of the flow by
assuming it is incompressible and has constant density. As you will
appreciate, liquids are quite difficult to compress - so under most
steady conditions they are treated as incompressible. In some
unsteady conditions very high pressure differences can occur and
it is necessary to take these into account - even for liquids.
Gasses, on the contrary, are very easily compressed, it is essential
in most cases to treat these as compressible, taking changes in
pressure into account.

9. continuous
• Three-dimensional flow Although in general all fluids flow three-
dimensionally, with pressures and velocities and other flow properties
varying in all directions, in many cases the greatest changes only occur
in two directions or even only in one. In these cases changes in the other
direction can be effectively ignored making analysis much more simple.
Flow is one dimensional if the flow parameters (such as velocity,
pressure, depth etc.) at a given instant in time only vary in the direction
of flow and not across the cross-section. The flow may be unsteady, in
this case the parameter vary in time but still not across the cross-
section. An example of one-dimensional flow is the flow in a pipe. Note
that since flow must be zero at the pipe wall - yet non-zero in the
Centre - there is a difference of parameters across the cross-section.
Should this be treated as two-dimensional flow? Possibly - but it is only
necessary if very high accuracy is required. A correction factor is then
usually applied.

10. continuous
• Flow is two-dimensional if it can be assumed that the flow parameters vary in
the direction of flow and in one direction at right angles to this direction.
Streamlines in two-dimensional flow are curved lines on a plane and are the
same on all parallel planes. An example is flow over a weir foe which typical
streamlines can be seen in the figure below. Over the majority of the length of
the weir the flow is the same - only at the two ends does it change slightly.
Here correction factors may be applied.
One
dimensional
flow

11. Two dimensional flow

12. Flow rate.
• Mass flow rate If we want to measure the rate at which water is flowing along
a pipe. A very simple way of doing this is to catch all the water coming out of
the pipe in a bucket over a fixed time period. Measuring the weight of the
water in the bucket and dividing this by the time taken to collect this water
gives a rate of accumulation of mass. This is know as the mass flow rate.
• Volume flow rate - Discharge. More commonly we need to know the volume
flow rate - this is more commonly know as discharge. (It is also commonly, but
inaccurately, simply called flow rate). The symbol normally used for discharge
is Q. The discharge is the volume of fluid flowing per unit time. Multiplying
this by the density of the fluid gives us the mass flow rate.

13. Type of flow measurement
•The most common principals for fluid flow
metering are:
•Differential Pressure Flow meters
•Velocity Flow meters
•Positive Displacement Flow meters
•Mass Flow meters
•Open Channel Flow meters

14. 1.Differential Pressure Flow meters
• In a differential pressure
drop device the flow is
calculated by measuring
the pressure drop over an
obstructions inserted in the
flow. The differential
pressure flow meter is
based on the Bernoulli's
Equation, where the
pressure drop and the
further measured signal is a
function of the square flow
speed.

15. • Common types of differential pressure flow meters are:
• Orifice Plates
• Flow Nozzles
• Venturi Tubes
• Variable Area - Rota meters
• Orifice Plate
An orifice plate is a device used for measuring flow rate, for
reducing pressure or for restricting flow (in the latter two
cases it is often called a restriction plate). Either a volumetric
or mass flow rate may be determined, depending on the
calculation associated with the orifice plate.With an orifice
plate, the fluid flow is measured through the difference in
pressure from the upstream side to the downstream side of a
partially obstructed pipe. The plate obstructing the flow offers
a precisely measured obstruction that narrows the pipe and
forces the flowing fluid to constrict.

16. continuous
• Orifice Plate is the heart of the Orifice Meter. It restricts
the flow and develops the Differential Pressure which is
proportional to the square of the flow rate. The flow
measuring accuracy entirely depends upon the quality of
Orifice plate, its installation and maintains.
• When measuring wet gas or saturated steam a weep hole
is drilled in a concentrically bored orifice plate. This is a
small hole drilled on the orifice plate such that its
location is exactly on ID of the main pipe.

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