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UNIT-5
MEASURING INSTRUMENTS

Flow Measurement:
Measuring instruments used to measure the linear, nonlinear, mass, or volumetric flow rate
of a gas or a liquid. Flow meters are also known as Flow Gauges or flow measurement
instruments. Accurate flow measurements of gases and liquids are required for better
control and quality of industrial processes.

Flow meter is a device that measures the rate of flow or quantity of a moving fluid in
an open or closed conduit. Flow measuring devices are generally classified into four
groups
Flow, or volumetric flow rate, is simply the volume of fluid that passes per unit of time. In
water resources, flow is often measured in units of cubic feet per second (cfs), cubic meters
per second (cms), gallons per minute (gpm), millions of gallons per day (MGD), or other
various units.
The units used to describe the flow measured can be of several types depending on
how the specific process needs the information.
Solids: Normally expressed in weight rate like Tonnes/hour, Kg/minute etc.
Liquids: Expressed both in weight rate and in volume rate.
Examples : Tonnes/hour, Kg/minute, litres/hour, litres/minute, m3/hour etc.
Gases: Expressed in volume rate at NTP or STP like Std m3/hour, Nm3/hour etc.
Steam: Expressed in weight rate like Tonnes/hour, Kg/minutes etc. Steam density
at different temperatures and pressures vary. Hence the measurement is converted
into weight rate of water which is used to produce steam at the point of measurement.

Classification of Flow Meter Scientific Diagram

Basic of Flow Measurement Technique

Industrial Instrumentation
There are different types of flow measuring techniques that are used in industries. The
common types of flow meters that find industrial applications can be listed as below:
(a) Obstruction type (differential pressure or variable area)
(b) Inferential (turbine type)
(c) Electromagnetic
(d) Positive displacement (integrating)
(e) Fluid dynamic (vortex shedding)
(f) Anemometer
(g) Ultrasonic and
(h) Mass flow meter.
Flow measuring devices are generally classified into four groups.
They are :
1. Mechanical type flow meters. Fixed restriction variable head type flow meters using
different sensors like orifice plate, venturi tube, flow nozzle, pitot tube, dall tube, quan- tity
meters like positive displacement meters, mass flow meters etc. fall under mechanical type
flow meters.
2. Inferential type flow meters. Variable area flow meters (Rotameters), turbine flow
meter, target flow meters etc.
3. Electrical type flow meters. Electromagnetic flow meter, Ultrasonic flow meter,
Laser doppler Anemometers etc. fall under electrical type flow meters.
4. Other flow meters. Purge flow regulators, Flow meters for Solids flow measure- ment,
Cross-correlation flow meter, Vortex shedding flow meters, flow switches etc.

Mechanical Flowmeters:
Fixed restriction variable head type flow meters using different sensors like orifice plate, venturi
tube, flow nozzle, pitot tube, dall tube, quantity meters like positive displacement meters,
mass flow meters are the popular types of mechanical flow meters.

Obstruction type flow meter

Obstruction or head type flow meters are of two types: differential pressure type and variable area
type. Orifice meter, Venturimeter, Pitot tube fall under the first category, while rotameter is of
the second category. In all the cases, an obstruction is created in the flow passage and the
pressure drop across the obstruction is related with the flow rate.

Basic Principle:

We consider the fluid flow through a closed channel of variable cross section. The channel
is of varying cross section and we consider two cross sections of the channel, 1 and 2. Let the
pressure, velocity, cross sectional area and height above the datum be expressed as p1, v1, A1
and z1 for section 1 and the corresponding values for section 2 be p2, v2, A2 and z2
respectively. We also assume that the fluid flowing is incompressible.
 𝐶𝑑𝐴2 2𝑔(𝑝1 − 𝑝2)
𝑄= √
√1 − 𝛽2 𝛾

Where γ is the specific weight of the fluid. β

as the ratio of the two diameters

Cd is defined as the ratio of the actual flow and the ideal flow and is always less than one.

From the above expression, we can infer that if there is an obstruction in the flow path that
causes the variation of the cross sectional area inside the closed flow channel, there would be
difference in static pressures at two points and by measuring the pressure difference, one can obtain
the flow rate using the equation. However, this expression is valid for incompressible fluids (i.e.
liquids) only and the relationship between the volumetric flow rate and pressure difference is
nonlinear.

Orifice:

An Orifice Meter is basically a type of flow meter used to measure the rate of flow of Liquid
or Gas, especially Steam, using the Differential Pressure Measurement principle. It is mainly
used for robust applications as it is known for its durability and is very economical. As the
name implies, it consists of an Orifice Plate which is the basic element of the instrument.
When this Orifice Plate is placed in a line, a differential pressure is developed across the
Orifice Plate. This pressure drop is linear and is in direct proportion to the flow-rate of the
liquid or gas. Since there is a drop in pressure, just like Turbine Flow meter, hence it is used
where a drop in pressure or head loss is permissible.

Working

As the fluid approaches the orifice the pressure increases slightly and then drops suddenly as
the orifice is passed. It continues to drop until the “vena contracta” is reached and then
gradually increases until at approximately 5 to 8 diameters downstream a maximum
pressure point is reached that will be lower than the pressure upstream of the orifice. The
decrease in pressure as the fluid passes thru the orifice is a result of the increased velocity of
the gas passing thru the reduced area of the orifice. When the velocity decreases as the fluid
leaves the orifice the pressure increases and tends to return to its original level. All of the
pressure loss is not recovered because of friction and turbulence losses in the stream. The
pressure drop across the orifice increases when the rate of flow increases. When there is no
flow there
is no differential. The differential pressure is proportional to the square of the velocity, it
therefore follows that if all other factors remain constant, then the differential is proportional to
the square of the rate of flow.

Types

Orifice Plates are normally mounted between a set of Orifice Flanges and are installed
in a straight run of smooth pipe to avoid disturbance of flow patterns from fittings and
valves. Orifice plates cover a wide range of applications including fluid and other
operating conditions. They give an acceptable level of uncertainties at lowest cost and long
life without regular maintenance.

Concentric is by far the most common, it’s used on most processes, but not recommended
for use on slurries or highly corrosive processes.
Eccentric Bore – Eccentric bore orifice plates are plates with the orifice off-center, or
eccentric, as opposed to concentric. Location of the bore prevents accumulation of solid
materials or foreign particles and makes it useful for measuring fluids containing suspended
solid particles. Eccentric bore orifice plates are more uncertain as compared to the concentric
orifice.
Segmental Bore – The segmentally bored orifice plates contain a hole that is a segment of a
concentric circle. Like the eccentric orifice plate design, the segmental hole should be offset
downward in gas flow applications. Segmental bores are generally used for measuring liquids
or gases which carry non-abrasive impurities such as sewage treatment, steel, chemical, water
conditioning, paper and petrochemical industries.

Venturi Meter

The major disadvantage of using orifice plate is the permanent pressure drop that is normally
experienced in the orifice plate as shown in fig.3. The pressure drops significantly after the orifice
and can be recovered only partially. The magnitude of the permanent pressure drop is around 40%,
which is sometimes objectionable. It requires more pressure to pump the liquid. This problem
can be overcome by improving the design of the restrictions. Venturimeters and flow nozzles
are two such devices. The construction of a venturimeter is shown in figure. Here it is so
designed that the change in the flow path is gradual. As a result, there is no permanent pressure
drop in the flow path. The discharge coefficient Cd varies between 0.95 and 0.98. The construction
also provides high mechanical strength for the meter. However, the major disadvantage is the
high cost of the meter. Flow nozzle is a compromise between orifice plate and venturimeter.

Construction

The entry of the venture is cylindrical in shape to match the size of the pipe through which
fluid flows. This enables the venture to be fitted to the pipe. After the entry, there is a
converging conical section with an included angle of 19’ to 23’. Following the
converging section, there is a cylindrical section with minimum area called as the throat. After
the throat, there is a diverging conical section with an included angle of 5’ to 15’. Openings
are provided at the entry and throat (at sections 1 and 2 in the diagram) of the venture meter
for attaching a differential pressure sensor (u-tube manometer, differential pressure gauge,
etc) as shown in diagram.

Working

The fluid whose flow rate is to be measured enters the entry section of the venturi meter with a
pressure P1. As the fluid from the entry section of venturi meter flows into the converging
section, its pressure keeps on reducing and attains a minimum value P2 when it enters the
throat. That is, in the throat, the fluid pressure P2 will be minimum. The differential pressure
sensor attached between the entry and throat section of the venturi meter records the pressure
difference (P1-P2) which becomes an indication of the flow rate of the fluid through the pipe
when calibrated. The diverging section has been provided to enable the fluid to regain its
pressure and hence its kinetic energy. Lesser the angle of the diverging section, greater is the
recovery.

Applications of venturi meters

 It is used where high pressure recovery is required.

 Can be used for measuring flow rates of water, gases, suspended solids, slurries and
dirty liquids.
 Can be used to measure high flow rates in pipes having diameters in a few meters.
Advantages of venturi meters

 Less changes of getting clogged with sediments

  Coefficient of discharge is high.
 Its behaviour can be predicted perfectly.
 Can be installed vertically, horizontally or inclinded.
 Low pressure drop (around 10% of Δp)
 Lower sensitivity to installation effects than orifice plates
 Less susceptibility to damage
 More suitable for gas flows with entrained liquid
 Comprehensive standards (ISO 5167)
Limitations of venturi meters

 They are large in size and hence where space is limited, they cannot be used.
 Expensive initial cost, installation and maintenance.
 Require long laying length. That is, the veturimeter has ti be proceeded by a straight pipe
which is free from fittings and misalignments to avoid turbulence in flow, for satisfactory
operation. Therefore, straightening vanes are a must.
 Low turndown (can be improved with dual range Δp cells)
 Greater cost to manufacture
 Greater susceptibility to “tapping errors” in high Reynolds number gas flows owing to
the high velocity fluid passing the pressure tapping at the throat.
 Less experimental data than orifice plates

Flow Nozzle:

The flow nozzles are a flow tube consisting of a smooth convergent section leading to a cylindrical
throat area. The throat is the smallest section of the nozzle. Pressure taps are located on the
upstream side of the nozzle plate and on the downstream side of the nozzle outlet. They may
be in the form of an annular ring, i.e. equally spaced holes connected together which open into
the pipeline, or in the form of single holes drilled into the pipeline.

As mentioned above, flow nozzles are primary elements in differential pressure flow meters. These
flow meters use the primary elements as an obstruction to generate a pressure drop to calculate
the flow rate. This is based on Bernoulli’s principle, according to which any obstruction placed
in the path of a flowing fluid will cause the velocity of the fluid to increase and the pressure
to decrease in the area of the obstruction.
As the fluid passes through the nozzle, the obstruction causes the velocity of the fluid to
increase while its static pressure decreases simultaneously. At the point of maximum
convergence, i.e. at the vena contracta, the velocity is at its maximum and the pressure is at
its minimum. As the fluid exits the nozzles, its flow expands and the velocity reduces and the
pressure rises again. This difference in pressure before and after the primary element is
measured using differential pressure transmitters, also called secondary elements

Applications of Flow Nozzle

1. It is used to measure flow rates of the liquid discharged into the atmosphere.
2. It is usually used in situation where suspended solids have the property of settling.
3. Is widely used for high pressure and temperature steam flows.
Advantages of flow Nozzle
1. Installation is easy and is cheaper when compared to venturi meter
2. It is very compact
3. Has high coefficient of discharge.
Disadvantages of flow Nozzle
1. Pressure recovery is low
2. Maintenance is high
3. Installation is difficult when compared to orifice flow meter.
Rotameter:

A rotameter is a device that measures the flow rate of liquid or gas in a closed tube. It belongs to
a class of meters called variable area meters, which measure flow rate by allowing the cross-
sectional area the fluid travels through, to vary, causing a measurable effect. A rotameter
consists of a tapered tube, typically made of glass with a ‘float’, made either of anodized
aluminum or a ceramic, actually a shaped weight, inside that is pushed up by the drag force
of the flow and pulled down by gravity. The drag force for a given fluid and float cross
section is a function of flow speed squared only.

A higher volumetric flow rate through a given area increases flow speed and drag force, so
the float will be pushed upwards. However, as the inside of the rotameter is cone shaped
(widens), the area around the float through which the medium flows increases, the flow speed and
drag force decrease until there is mechanical equilibrium with the float’s weight. Floats are made
in many different shapes, with spheres and ellipsoids being the most common. The float may be
diagonally grooved and partially colored so that it rotates axially as the fluid passes. This shows
if the float is stuck since it will only rotate if it is free. Readings are usually taken at the top
of the widest part of the float; the center for an ellipsoid, or the top for a cylinder. Some
manufacturers use a different standard. The “float” must not float in the fluid: it has to have a
higher density than the fluid; otherwise it will float to the top even if there is no flow. The
mechanical
nature of the measuring principle provides a flow measurement device that does not require any
electrical power.

 A rotameter requires no external power or fuel, it uses only the inherent properties of the
fluid, along with gravity, to measure flow rate.
 A rotameter is also a relatively simple device that can be mass manufactured out of
cheap materials, allowing for its widespread use.
 Since the area of the flow passage increases as the float moves up the tube, the
scale is approximately linear.
 Clear glass is used this is highly resistant to thermal shock and chemical action.
Disadvantages:

 Due to its use of gravity, a rotameter must always be vertically oriented and right way
up, with the fluid flowing upward.
 Due to its reliance on the ability of the fluid or gas to displace the float, graduations on
a given rotameter will only be accurate for a given substance at a given temperature. The
main property of importance is the density of the fluid; however, viscosity may also be
significant. Floats are ideally designed to be insensitive to viscosity; however, this is
seldom verifiable from manufacturers’ specifications. Either separate rotameter for
different densities and viscosities may be used, or multiple scales on the same rotameter
can be used.
 Due to the direct flow indication the resolution is relatively poor compared to other
measurement principles. Readout uncertainty gets worse near the bottom of the scale.
Oscillations of the float and parallax may further increase the uncertainty of the
measurement.
 Since the float must be read through the flowing medium, some fluids may obscure the
reading. A transducer may be required for electronically measuring the position of the
float.
 Rotameter are not easily adapted for reading by machine; although magnetic floats that drive
a follower outside the tube are available.
 Rotameter are not generally manufactured in sizes greater than 6 inches/150 mm, but
bypass designs are sometimes used on very large pipes.

Pitot Tube:

The Pitot tube is named after Henri Pitot who used a bent glass tube to measure velocities
in a river in France in the 1700s. Pitot tubes can be very simple devices with no moving parts
used to measure flow velocities.
Pitot tubes are a common type of insertion flowmeter. The below figure shows the basics for
a Pitot tube, where a pressure is generated in a tube facing the flow, by the velocity of the
fluid.

This ‘velocity’ pressure is compared against the reference pressure (or static pressure) in the pipe,
and the velocity can be determined by applying a simple equation.

The tube inserted in the center of the pipe is used to measure Total Pressure and the next
second tube is used to measure the static pressure.

When the flow rate through the pipe changes, the pressures at the total pressure tube and
static pressure tube varies with respect to the flow velocities. The difference between the total
pressure and static pressure is used to measure the proportional flow rate passing through the pipe.

A DP type transmitter is used to measure the difference between total pressure and static
pressure and it is converted into proportional flow rate.

In practice, two tubes inserted into a pipe would be cumbersome, and a simple Pitot tube will
consist of one unit as shown in Below Figure. Here, the hole measuring the velocity pressure and
the holes measuring the reference or static pressure are incorporated in the same device.
Because the simple Pitot tube (Above Figure ) only samples a single point, and, because the
flow profile of the fluid (and hence velocity profile) varies across the pipe, accurate placement of
the nozzle is critical. To avoid this type of problems by using averaging Pitot tubes.
2∆𝑝
𝑈1 = √
𝜌

Where,

U1 is the fluid velocity in the pipe

∆p is Dynamic pressure – Static pressure ρ

is Density

Averaging Pitot tube

The averaging Pitot tube was developed with a number of upstream sensing tubes to overcome the
problems associated with correctly siting the simple type of Pitot tube.

These sensing tubes sense various velocity pressures across the pipe, which are then averaged
within the tube assembly to give a representative flowrate of the whole cross section.
Advantages of the Pitot tube

1. Presents little resistance to flow.

2. Inexpensive to buy.
3. Simple types can be used on different diameter pipes.

Disadvantages of the Pitot tube:

1. Turndown is limited to approximately 4:1 by the square root relationship

between pressure and velocity.
2. If steam is wet, the bottom holes can become effectively blocked. To counter this,
some models can be installed horizontally.
3. Sensitive to changes in turbulence and needs careful installation and
maintenance.
4. The low pressure drop measured by the unit, increases uncertainty, especially on
steam.
5. Placement inside the pipe work is critical.

Applications for the Pitot tube:

1. Occasional use to provide an indication of flow rate

2. Determining the range over which a more appropriate steam flow meter may be used.

Turbine flow meter:

Turbine Flow Meter is a volumetric measuring turbine type. The flowing fluid engages the rotor
causing it to rotate at an angular velocity proportional to the fluid flow rate.
The angular velocity of the rotor results in the generation of an electrical signal (AC sine wave
type) in the pickup. The summation of the pulsing electrical signal is related directly to total
flow.
The frequency of the signal relates directly to flow rate. The vaned rotor is the only moving
part of the flow meter.

The Turbine flow meter (axial turbine) was invented by Reinhard Woltman and is an accurate
and reliable flow meter for liquids and gases. It consists of a flow tube with end connections
and a magnetic multi bladed free spinning rotor (impeller) mounted inside; in line with the flow.
The rotor is supported by a shaft that rests on internally mounted supports.
The Supports in Process Automatics Turbine Flow Meters are designed to also act as flow
straighteners, stabilizing the flow and minimizing negative effects of turbulence. The Supports
also house the unique open bearings; allowing for the measured media to lubricate the bushes –
prolonging the flow meters life span. The Supports are fastened by locking rings (circlips) on
each end.
The rotor sits on a shaft, which in turn is suspended in the flow by the two supports. As the
media flows, a force is applied on the rotor wings. The angle and shape of the wings transform
the horizontal force to a perpendicular force, creating rotation. Therefore, the rotation of the
rotor is proportional to the applied force of the flow.

Because of this, the rotor will immediately rotate as soon as the media induces a forward force.
As the rotor cannot turn thru the media on its own, it will stop as soon as the media stops. This
ensures an extremely fast response time, making the Turbine Flow Meter ideal for batching
applications.

A pick-up sensor is mounted above the rotor. When the magnetic blades pass by the pickup
sensor, a signal is generated for each passing blade. This provides a pulsed signal proportional
to the speed of the rotor and represents pulses per volumetric unit.; and as such the flow rate too.

Advantages

1. Very good at clean

2. Cost is very low
3. low viscosity fluids of moderate velocity and a steady rate.
4. Turndown is very good as it can read very low compared to the maximum flow.
5. They are reliable if put in a clean fluid especially if it has some lubricity.
6. AGA and API approved for custody transfers.
Disadvantages

1. They do cause some pressure drop where that may be a factor such as gravity flows.
2. Not reliable for steam
3. Bearings wear out.
Applications

1. these are used in oil and gas,

2. water and waste water,
3. gas utility,
4. chemical,
5. power, food and beverage,
6. aerospace, pharmaceutical,
7. Metals and mining, and pulp and paper.
Positive Displacement Flow Meter:

Positive Displacement (PD) Flow meters are volumetric flow measurement

instruments that measure flow by passing a precise volume of fluid with each revolution. PD
flow meters are precision instruments whose internal moving components are hydraulically
locked in tandem with the volume of fluid moving through the flow meter.
The result is that the meter can measure intermittent flows, very low flow rates, and liquids of
almost any viscosity. The PD meter instantly moves when there is fluid motion, and instantly
stops when the fluid motion stops.

This type of measurement is not affected by the liquid’s viscosity, density or the turbulence in
the pipe. All incompressible fluids will occupy the same volume and there is no need to correct
the meter’s output to compensate for these factors.

Positive Displacement Meter is a type of flow meter that requires fluid to mechanically
displace components in the meter in order for flow measurement. Positive displacement (PD)
flow meters measure the volumetric flow rate of a moving fluid or gas by dividing the media
into fixed, metered volumes (finite increments or volumes of the fluid).
A basic analogy would be holding a bucket below a tap, filling it to a set level, then quickly
replacing it with another bucket and timing the rate at which the buckets are filled (or the total
number of buckets for the “totalized” flow). With appropriate pressure and temperature
compensation, the mass flow rate can be accurately determined.
These devices consist of a chamber(s) that obstructs the media flow and a rotating or reciprocating
mechanism that allows the passage of fixed-volume amounts. The number of parcels that pass
through the chamber determines the media volume.

The rate of revolution or reciprocation determines the flow rate. There are two basic types of
positive displacement flow meters. Sensor-only systems or transducers are switch-like devices
that provide electronic outputs for processors, controllers, or data acquisition systems.

Types of Positive Displacement Flow Meters

1. Reciprocating or oscillating piston

Each piston is mechanically or magnetically operated to fill a cylinder with the fluid and then
discharge the fluid. Each stroke represents a finite measurement of the fluid.

2. Gear
Gear flow meters rely on internal gears rotating as fluid passes through them. There are various
types of gear meters named mostly for the shape of the internal components
 Oval Gear
Two rotating oval gears with synchronized teeth “squeeze” a finite amount of fluid through
the meter for each revolution. With oval gear flow meters, two oval gears or rotors are
mounted inside a cylinder.

As the fluid flows through the cylinder, the pressure of the fluid causes the rotors to rotate.
As flow rate increases, so does the rotational speed of the rotors.

 Helical Gear

Helical gear flow meters get their name from the shape of their gears or rotors. These rotors
resemble the shape of a helix, which is a spiral-shaped structure.

As the fluid flows through the meter, it enters the compartments in the rotors, causing the
rotors to rotate. Flow rate is calculated from the speed of rotation.

3. Nutating disk
A disk mounted on a sphere is “wobbled” about an axis by the fluid flow and each rotation
represents a finite amount of fluid transferred. A nutating disc flow meter has a round disc
mounted on a spindle in a cylindrical chamber.
By tracking the movements of the spindle, the flow meter determines the number of times
the chamber traps and empties fluid. This information is used to determine flow rate.

4. Rotary vane
A rotating impeller containing two or more vanes divides the spaces between the vanes into
discrete volumes and each rotation (or vane passing) is counted.
5. Diaphragm
Fluid is drawn into the inlet side of an oscillating diaphragm and then dispelled to the outlet.
The diaphragm oscillating cycles are counted to determine the flow rate.

PD Meters types

PD flow meters are mainly named after the inbuilt mechanical device in the meter unit. Various
types of positive displacement flow meters are available for industrial use. All these types are
based on the common operating principle. Besides, they all are volumetric flow measuring
devices.
Major types of positive displacement flow meters are mentioned below:

Reciprocating Piston Meters

These are also known as oscillating piston flow meters. These are one of the oldest positive
displacement type flow meter designs. These types of meters are mainly of single or multiple-
piston types.
Other types available are double acting pistons and rotary pistons. Selection of a particular
type of piston meter depends on the range of flow rates necessary for an application.

Although piston meters are smaller in size and considered apt for handling only low flows of
viscous liquids, yet they are proficient enough to deal with an extensive range of liquids.
Major application areas of a reciprocating piston meter include viscous fluid services like oil
metering on engine test stands, specifically where turndown ratio is not considered much crucial.
Also these meters can be employed on residential water service where they tend to pass partial
quantities of dirt and fine sand along with water.

Oval-shaped gears
These types of meters consist of two rotating, oval-shaped gears constructed with
synchronized, close fitting teeth. In an oval gear meter, the rotation of gear shafts causes a fixed
amount of liquid to pass through the meter. By monitoring the number of shaft rotations, one
can calculate liquid flow rate.
These types of meters prove to be very accurate when slippage between the housing and the
gears is set very small. Turndown ratio of an oval gear meter gets influenced by the lubricating
properties of the process fluid.
Nutating disk Meters
These are the widely used positive displacement type flow meters. They consist of a movable
disk which is positioned on a concentric sphere situated inside a spherical side-walled unit.
Universally, they are employed as residential water meters.

They exist in various sizes and capacities and can be constructed from a wide range of materials.
Their typical size range varies from 5/8-in to 2-in sizes. They are ideal for pressure ranges around
150-psig with an upper limit of 300 psig.
Rotary vane Meters
These types of meters exist in different designs. However, they all work on the same operating
principle. These meters basically include uniformly divided rotating impellers with two or
more compartments inside the chamber. The number of rotations of the impeller are counted
and recorded in volumetric units. These types of meters are frequently employed in the petroleum
industry.

Based upon the construction material, maximum pressure and maximum temperature limits of
rotary vane meters are 350°F and 1,000 psig respectively. Their Viscosity limit ranges between 1
and 25,000 centipoises.

Helix Meters
These types of meters are made up of two radically pitched helical rotors which results in an
axial liquid displacement from one side of the chamber to the other side.

Both the rotors are geared together and there is a very small clearance between the rotors
and the casing.
Electromagnetic Flow Meter:

Electromagnetic Flow Meters are based on FARADAY’S LAW INDUCTION. These meters
are also called as Magnetic or Electromagnetic Flow Meters. A magnetic field is applied to
the metering tube, which results in a potential difference proportional to the flow velocity
perpendicular to the flux lines. The physical principle at work is electromagnetic induction
and mathematically,

E=k*B*D*
V where,

 E=Induced Voltage (Linear with velocity).

 k=Proportionality Constant.
 B=Magnetic Field Strength (Coil Inductance).
 D=Distance between electrodes.
 V=Velocity of process fluids.

The induced voltage (E) is directly proportional to the velocity (V) of the fluid moving through
the magnetic field (B). The induced voltage is carried to the transmitter through the electrode
circuit. The transmitter then converts this voltage into a quantifiable flow velocity. The
volumetric flow rate of the fluid is calculated using this known velocity along with the area of
the pipe.

When a flow meter is installed and activated, its operations begin with a pair of charged
magnetic coils. As energy passes through the coils, they produce a magnetic
field that remains perpendicular to both the conductive fluid being measured and the axis of
the electrodes taking measurements. The fluid moves along the longitudinal axis of the flow
meter, making any generated induced voltage perpendicular to the field and the fluid velocity.
An increase in the flow rate of the conductive fluid will create a proportionate increase in the
voltage level.

The meter features flanged construction and is available with a choice of liner and electrode
material. All meters consist of a sensor and a converter that may be mounted integral to the sensor
or remotely either with a field mount kit.

Advantages of Electromagnetic Flow Meter

(i) The obstruction to the flow is almost nil and therefore this type of meters can be used for
measuring heavy suspensions, including mud, sewage and wood pulp.

ii) There is no pressure head loss in this type of flow meter other than that of the length of
straight pipe which the meter occupies.

(iii) They are not very much affected by upstream flow disturbances.

(iv) They are practically unaffected by variation in density, viscosity, pressure and
temperature.

(v) Electric power requirements can be low (15 or 20 W), particularly with pulsed DC types.

(vi) These meters can be used as bidirectional meters.

(vii) The meters are suitable for most acids, bases, water and aqueous solutions because the lining
materials selected are not only good electrical insulators but also are corrosion resistant.

(viii) The meters are widely used for slurry services not only because they are obstruction
less but also because some of the liners such as polyurethane, neoprene and rubber have good
abrasion or erosion resistance.

(ix) They are capable of handling extremely low flows.

Disadvantages of Magnetic Flow Meter

(i) These meters can be used only for fluids which have reasonable electrical
conductivity.

(ii) Accuracy is only in the range of ± 1% over a flow rate range of 5%.

(iii) The size and cost of the field coils and circuitry do not increase in proportion to their
size of pipe bore. Consequently small size meters are bulky and expensive.

Applications of Magnetic Flow Meters

This electromagnetic flow meter being non intrusive type, can be used in general for any fluid
which is having a reasonable electrical conductivity above 10 microsiemens/cm.

Fluids like sand water slurry, coal powder, slurry, sewage, wood pulp, chemicals, water other
than distilled water in large pipe lines, hot fluids, high viscous fluids specially in food
processing industries, cryogenic fluids can be metered by the electromagnetic flow meter.

Ultrasonic Flow Meter:

An ultrasonic flow meter utilizes ultrasound to measure the velocity of a fluid and is used in
a variety of fluid applications. Ultrasonic flowmeters are ideal for water and other liquids.
Clamp-on ultrasonic flow meters achieve high accuracy at low and high flows, save time with
no pipe cutting or process shutdown, and are not affected by external noise.

Ultrasonic flow meters use sound waves at a frequency beyond the range of hearing (typically 0.5,
1, or 4 MHz). This ultrasound signal is sent into a stream of flowing liquid by using wetted
(insertion) transducers that make direct contact with the liquid or external (clamp-on) transducers
that send the ultrasound through the pipe wall. Clamp- on ultrasonic flow meters allow users to
measure the volumetric flow rate of a fluid in a pipe without having to penetrate the pipe which
decreases installation and maintenance costs.

A typical transit-time ultrasonic liquid flow meter utilizes two ultrasonic transducers that
function as both ultrasonic transmitter and receiver. The ultrasonic flow meter operates by
alternately transmitting and receiving a burst of ultrasound between the two transducers by
measuring the transit time that it takes for sound to travel between the two transducers in both
directions. The difference in the transit time (∆ time) measured is directly proportional to the
velocity of the liquid in the pipe.
Below is a drawing of a typical application using the most common, V (2 pass) mounting
method with clamp-on transducers. In this application, the ultrasound is transmitted from the first
transducer and travels through the pipe wall, through the liquid, then reflects off the back wall
of the pipe, then travels through the pipe wall, and is picked up by the second transducer.

The same process is then repeated in reverse as the second transducer transmits the ultrasound.
The time difference between the times of flight up and down is the ∆ Time. When the liquid
in the pipe is not moving, the ∆ Time would be zero.

To calculate the velocity of the liquid, you need to convert the raw ∆ Time into the velocity
of the liquid in the pipe. The angle of the ultrasound path is calculated by knowing the speed
of sound of the pipe and the liquid. This angle is used in a common trigonometry equation to
convert the ultrasound path into a straight line in the pipe. This will be the velocity of the
liquid in the pipe.
 Variable Area Flow Meters
Basic Principle
In the orifice meter, there is a fixed aperture and flow is indicated by a drop in differen-
tial pressure. In area meter, there is a variable orifice and the pressure drop is relatively
constant. Thus, in the area meter, flow is indicated as a function of the area of the annular
opening through which the fluid must pass. This area is generally readout as the position of a float
or obstruction in the orifice.
The effective annular area in area meter is nearly proportional to height of the float,
plummet or piston, in the body and relationship between the height of float and flow rate is
approximately linear one with linear flow curve as well as scale graduations.

Types of Variable Area Flow Meters

Area meters are of two general types :
1. Rotameters and
2. Piston type meter.
Rotameters. In this meter, a weighted float or plummet contained in an upright ta- pered
tube, is lifted to the position of equilibrium between the downward force of the plummet and the
upward force of the fluid in addition to the buoyancy effect of the fluid flowing past the float
through the annular orifice. The flow rate can be read by observing the position of the float.
Piston Type Meter. In this meter, a piston is accurately fitted inside a sleeve and is
lifted by fluid pressure until sufficient post area in the sleeve is uncovered to permit the pas-
sage of the flow. The flow is indicated by the position of the piston.

Fig. 1.35 shows the types of Variable area flow meter (a) Rotameter and (b) Piston Type
meter.
 (a) (b)
Fig. 1.35 Types of Variable area flow meter (a) Rotameter (b) Piston Type meter

Measurement of Density:

The density of material shows the denseness of that material in a specific given area. A material’s
density is defined as its mass per unit volume. Density is essentially a measurement of how
tightly matter is packed together. It is a unique physical property for a particular object. The
SI unit of density is kg/m³.

Hydrometer:

A hydrometer is an instrument used for measuring the relative density of liquids based on the
concept of buoyancy.

Continuous Weight measurement Hydrometer:

They are typically calibrated and graduated with one or more scales such as specific gravity. The
device consists essentially of a weighted, sealed, long-necked glass bulb that is immersed in
the liquid being measured; the depth of flotation gives an indication of liquid density, and the
neck can be calibrated to read density, specific gravity, or some other related characteristic.
In practice, the floating glass bulb is usually inserted into a cylindrical glass tube equipped
with a rubber ball at the top end for sucking liquid into the tube. Immersion
depth of the bulb is calibrated to read the desired characteristic. A typical instrument is the
storage-battery hydrometer, by means of which the specific gravity of the battery liquid can be
measured and the condition of the battery determined. Another instrument is the radiator
hydrometer, in which the float is calibrated in terms of the freezing point of the radiator
solution. Others may be calibrated in terms of “proof” of an alcohol solution or in terms of
the percentage of sugar in a sugar solution.
The Baumé hydrometer, named for the French chemist Antoine Baumé, is calibrated to measure
specific gravity on evenly spaced scales; one scale is for liquids heavier than water, and the other
is for liquids lighter than water.

Nuclear Densitometer (Gamma Ray):

There are so many instruments to measure density like hydrometers, Induction hydrometers,etc.
Nuclear devices can also used to measure density. They operate on the principle that the
absorption of gamma radiation increases with the density of the material being measured.

In the figure, a representative element for measuring the density of the radiation type is
represented. It consists of a source of constant gamma radiation (which can be radio, cesium or
cobalt), which is mounted on a wall of the pipe, and a radiation detector, which is mounted
on the opposite side. The gamma rays are emitted from the source, through the pipe and the
detector. The materials that flow through the pipe and between the source and the detector
absorb radioactive energy in proportion to their densities. The radiation detector measures the
radioactive energy that is not absorbed by the process material. The quantity that is measured
varies inversely with the density of the process stream. The unit of the radiation detector converts
this energy into an electrical signal, which is transmitted to an electronic module.
Viscosity:
Viscosity is defined as the measure of the resistance of a fluid to gradual deformation by shear or
tensile stress. In other words, viscosity describes a fluid’s resistance to flow. Simply put, we can
say that honey is thicker than water; in turn, honey is more viscous than water. Viscosity is
measured in Pascal seconds.

Saybolt Viscometer

A device used to measure the viscosity of a fluid. The saybolt viscometer controls the heat of
the fluid and the viscosity is the time is takes the fluid to fill a 60cc container.

The device used for measurement of viscosity is known as viscometer .

 The viscosity of a fluid is a measure of its resistance to gradual deformation by shear

stress or tensile stress.
 The units of viscosity are poise and centipoises.
 Specific viscosity is the ratio of the viscosity of fluid to the viscosity of water at 20
degree Celsius. Since the water has a viscosity of 1 cp at 20 degree Celsius.
 Kinematic viscosity is defined as ratio of dynamic viscosity to the density of the
fluid.

Efflux cup viscometers are most commonly used for fieldwork to measure the viscosity of
oils, syrups, varnish, paints and Bitumen emulsions. The testing procedure is quite similar to
the capillary-tube viscometers where efflux time of a specified volume of fluid is measured
through fixed orifice at the bottom of a cup to represent the viscosity of the fluid. Since the
viscosity of Newtonian liquid are independent of dimensions of
viscometer used, it is possible to convert the efflux times to kinematic viscosities by
conversion charts or by formulas suggested by the equipment manufacturers.
To obtain high accuracy the liquid holding vessel and orifice are temperature controlled by
immersing them in a thermostatically controlled bath. The saybolt viscometer, one of the efflux
cup viscometers is the standard instrument for testing petroleum products.

The furol and asphalt orifices, respectively, have an efflux time of approximately, one- tenth
and one-hundredth that of the universal orifice. The cup orifice combination should be
selected to provide an efflux time within the range of 20 to 100 seconds. Of these types, the
universal orifice (saybolt universal viscometer) is most commonly used and its efflux time is
designated as saybolt universal seconds (SUS).The universal viscometer measures the time
required for 60 cc of sample fluid to flow out through an orifice having dimensions of 0.176
cm in diameter and 1.225 cm in length. Saybolt universal seconds (t) can be converted to
kinematic viscosity (v) by the following equations:

When t < 100 secs, v = 0.226t – 195/t Centistokes When t

>100 secs, v = 0.220t – 135/t Centistokes

The viscosity determinations should be conducted in a room free from drafts and rapid changes
in temperature the highest degree of accuracy.

Advantages
 It has a digital meter to measure temperature and so reading is more accurate and
precise.
 The coils wrap around the container uniformly so uniform temperature can be
obtained.
 Viscosity can be directly compared for two or more liquids.
Disadvantages
 The main disadvantage of the capillary tube viscometer is the errors that arise due to the
variation in the head loss and other parameters.
 Efflux cup viscometer have some inherent inaccuracies
Application
 Efflux viscometer are most commonly used fieldwork to measure the viscosity of oil ,
syrups, varnish, paints.
 It is used for testing petroleum products.

Rotameter Type Viscometer:

Rotameter type viscometers are used both industrially and in the pilot plant to measure the
viscosity of the process fluids and continuously indicate or control the process. This type of
viscometer is used in a closed flow system. Viscometer has been successfully used to
maximize combustion efficiency by controlling the viscosity of fuel oils in marine boilers and
stationery
Operating principle of viscometer:

The operating principle is similar to that of the variable area flow meter, where the viscous
drag force on a float is proportional to the opening of the required orifice (between the float
and the conical tube) to move the fluid through that orifice at a constant flow rate.

In a flow meter type rotameter, the forces acting on the float are affected by the flow rate, by
the floating weight and the specific gravity of the liquid, and by the viscosity of the fluid being
measured.

For flow metering applications, the floats are designed so that the viscous drag area is
relatively small, so the float is relatively insensitive to viscosity. In the viscometer version of
this design, the flow rate through the variable area meter is held constant.

Construction and Working of Viscometer

To obtain accurate viscosity measurements with rotameter-type viscometers, the flow rate must
be constant. Because this required flow control can be obtained in three different ways, there are
three different designs: single float, double float and concentric float.

The simple float viscometer is a direct and continuous reading viscosity instrument. A positive
displacement pump (other flow control devices can also be used) provides the constant sample
flow rate through the instrument

The single float viscometer is also available as a transmitter that is used when screens or remote
controls are required. In this case, the position of the float is detected by the use of an armature
attached to the float extension bar with a magnetic detection device around its outer periphery.
The recommended flow rate is between 0.75 and 2.0 GPM (2.9 and 7.6 l/m). The glass tube
viscometer is rated for 450° F (232° C) temperature and for 90 PSIG (621 kPa) pressure.

Humidity:

Relative Humidity
The relative humidity is used for finding the water vapor content in the air. The relative humidity
is defined as the ratio between the amount of moisture in the air at a particular temperature
to the maximum moisture air can withstand at the same temperature. The relative humidity is
100% during rainy seasons.

Absolute Humidity
Absolute humidity which describes the water content of air is used to measure the weight of
water vapor per unit volume of air. The absolute humidity unit is given as g.m-3 which is units
of grams of water vapor per cubic meter of air. Since other factors constantly affect absolute
humidity, the results are less useful.
Specific Humidity
The specific humidity unit is the most reliable unit of measurement of humidity. This measures
the weight of water vapor per unit weight of air and it is expressed as grams of water vapor
per kilogram of air g.kg-1 is the specific humidity unit.

Different types of hygrometers and their applications Electrical

hygrometers
These hygrometers use resistance or capacitance to measure the amount of humidity in the air.
Electrical hygrometers can either be capacitive or resistive. Capacitive hygrometers have two
metals plates that have air between them; the moister the air is, the more it affects the plates’
ability to store a static electric charge. The amount of humidity is indicated by the metal plates’
ability to store the electric charge. Resistive hygrometers, electricity passes through a piece of
ceramic substance which is exposed to the air. The higher the humidity, the more water vapour
condenses inside the ceramic, leading to a change in resistance.

Psychrometer
A Psychrometer is a device used to measure the humidity of air. It accomplishes this by
comparing the difference in temperature between a dry thermometer bulb and a wet
thermometer bulb that has lost some of its moisture through evaporation.
When evaporation occurs in the wet bulb, the temperature drops to a lower level than that of
the dry bulb. This difference in temperature is caused by the humidity in the air. Psychrometer are
ideal for measuring outdoor humidity and areas which need dry storage conditions.
Wet and Dry Bulb Psychrometer
In order for a liquid to turn into gas, energy is required and this energy is called evaporation heat.
The thing which enabled it to measure humidity using this is a Psychrometer.
The Psychrometer is a hygrometer which measures humidity and temperature simultaneously
by measurement of dry-bulb temperature and wet-bulb temperature. In extreme high
temperature, low temperature, low humidity, and low pressure, an error becomes large by the
object for the measurement in general temperature and moisture environment. Consisting of
two thermometers, one side is a portion which makes a ball part always become wet with
water and which is called a wet bulb. A wet bulb shows a temperature usually lower than
another thermometer (dry bulb), in order that water may take evaporation heat by
evaporation in a ball part. However, since a wet bulb is covered in the layer of thin ice when
temperature is the freezing point, a temperature higher than a dry bulb may be shown.

In the case of precision measurement, relative humidity is calculated by the formula of Adolf
Sprung (1848 to 1909) from dry-bulb temperature or wet-bulb temperature, the difference in
temperature between a dry bulb and a wet bulb, and atmospheric pressure.

Dew point hygrometers

Dew point hygrometers are used to measure the saturation of moist air in a gas. These hygrometers
are used in areas where the smallest amounts of moisture need to be found. These devices
are the most precise of all the hygrometers. Hygrometers are useful devices that measure the
amount of moisture in the atmosphere. They can be used in homes, office buildings, and in
industrial areas. There are different types of hygrometers so you are guaranteed to find one that
is suitable for your requirements.
Application of Hair hygrometer

 These hydrometers are used in the temperature range of 0’C to 75’C.

 These hydrometers are used in the range of relative humidity (relative humidity) from
30 to 95%.
 Limitations of the hydrometer for the hair
 These hydrometers are slow in response
 If the hair hydrometer is used constantly, its calibration tends to change.

Thermal Conductivity Humidity Sensors

Thermal Conductivity Humidity Sensors are also known as Absolute Humidity (AH) Sensors
as they measure the Absolute Humidity. Thermal Conductivity Humidity Sensors measure the
thermal conductivity of both dry air as well as air with water vapor. The difference between
the individual thermal conductivities can be related to absolute humidity.

Working of Thermal Conductivity Humidity Sensors

The best component to accomplish thermal conductivity based humidity sensor is thermistor.
Hence, two tiny thermistors with negative temperature coefficient are used to for a bridge
circuit.
In that, one thermistor is hermetically sealed in a chamber filled with dry Nitrogen while the
other is exposed to open environment through small venting holes. When the circuit is powered
on, the resistance of the two thermistors is calculated and the difference between those two
values is directly proportional to Absolute Humidity (AH).

Advantages of Thermal Conductivity Humidity Sensors

 Suitable for high temperature environments and high corrosive situations.

 Very durable
 Higher resolution compared to other types

Disadvantage of Thermal Conductivity Humidity Sensors

 Exposure to any gas with thermal properties different than Nitrogen might affect
reading measurement.

Applications of Thermal Conductivity Humidity Sensors

 Drying kilns
 Pharmaceutical plants
 Owens
 Clothes dryers and drying machines
 Food dehydration
 Chilled mirror Dew point hygrometer
Dew point is the temperature at which a sample of moist air (or any other water vapor) at
constant pressure reaches water vapor saturation. At this saturation temperature, further cooling
results in condensation of water. Chilled mirror dew point hygrometers are some of the most
precise instruments commonly available. They use a chilled mirror and optoelectronic mechanism
to detect condensation on the mirror's surface. The temperature of the mirror is controlled by
electronic feedback to maintain a dynamic equilibrium between evaporation and condensation,
thus closely measuring the dew point temperature. An accuracy of 0.2 °C is attainable with
these devices, which correlates at typical office environments to a relative humidity accuracy of
about ±1.2%. These devices need frequent cleaning, a skilled operator and periodic calibration
to attain these levels of accuracy. Even so, they are prone to heavy drifting in environments
where smoke or otherwise impure air may be present.
More recently, spectroscopic chilled-mirrors have been introduced. Using this method, the
dew point is determined with spectroscopic light detection which ascertains the nature of the
condensation. This method avoids many of the pitfalls of the previous chilled-mirrors and is
capable of operating drift free.

BUOYANCY METHOD
A technique for measuring the bulk volume of a core sample by submerging it in a bath of mercury and
observing the increase in weight of the bath, following Archimedes principle. The bulk volume is
calculated from the increase in weight divided by the density of mercury at the temperature of the bath.

The experimental technique utilised in the determination of the densities was based on the Archimedes
principle (or buoyancy method), which states that a body immersed in a fluid apparently loses weight by
an amount equal to the weight of the fluid it displaces.

Archimedes' principle states that: “The upward buoyant force that is exerted on a body immersed in a
fluid, whether partially or fully submerged, is equal to the weight of the fluid that the body displaces and
acts in the upward direction at the center of mass of the displaced fluid”.
Buoyancy reduces the apparent weight of objects that have sunk completely to the sea floor. It is
generally easier to lift an object up through the water than it is to pull it out of the water. (This formula
is used for example in describing the measuring principle of a dasymeter and of hydrostatic weighing.)
 To calculate the buoyant force we can use the equation: F b = ρ V g where Fb is the buoyant force in
Newtons, is the density of the fluid in kilograms per cubic meter, V is the volume of displaced fluid in
cubic meters, and g is the acceleration due to gravity.

Buoyancy or a buoyant force can be defined as the tendency of the fluid to exert an upward force on an
object, which is wholly or partially immersed in a fluid. The S.I. unit of buoyant force is Newton.

Buoyancy, represented by the symbol B or F B. , refers to the upward force that a body experiences when
partially or fully submerged in a liquid. This upward force is a result of the pressure exerted by the
liquid. As a vector quantity, buoyancy possesses both magnitude and direction. It is measured in
Newton [N].

STRAINGAUGE LOAD CELL METHOD

A Strain gauge is a sensor whose resistance varies with applied force; It converts force, pressure,
tension, weight, etc., into a change in electrical resistance which can then be measure

Strain gauge load cells usually feature four strain gauges in a Wheatstone bridge configuration, which is
an electrical circuit that balances two legs of a bridge circuit. The force being measured deforms the
strain gauge in this type of load cell, and the deformation is measured as change in electrical signal.

A load cell, which is also known as a force sensor or force transducer, is a sensor that measures force by
converting the input of mechanical force into the output of an electrical signal. As the force is applied to
the sensor, its electrical output signal can be measured, converted, and standardized. The input force can
vary between load, weight, tension, compression, or pressure, and it can only be measured by a sensor
that is designed to calculate that type of force. (We will break down the different kinds of load cells/
force transducers in the section below.)

Strain gauges are electrical conductors that are tightly attached to a film in a zigzag shape. When stress is
transferred from the load cell flexure to the strain gauge, the resulting deformation or displacement of its
material causes strain that ultimately is converted into the load cell’s measurable output. For example,
when the film is pulled, it — and the conductors — stretches and elongates. When it is pushed, it is
contracted and gets shorter. This change in shape causes the resistance in the electrical conductors, what
we call strain gauge resistance, to also change. The strain gauge resistance increases with applied strain
and diminishes with contraction. The changes are converted into an electrical signal, which can then be
measured and captured using data acquisition.
 Understanding the Wheatstone bridge circuit
In order to measure the changes in resistance, the strain gauge must be connected to an electrical circuit
that is capable of accurately responding to the changes and creating a differential voltage variation.
Multiple strain gauges can be used in a divided bridge circuit that is called a Wheatstone bridge. In a
Wheatstone bridge configuration, an excitation voltage is applied across the circuit, and the output
voltage is measured across two points in the middle of the bridge. When there is no load acting on the
load cell, the Wheatstone bridge is balanced and there is zero output voltage. Any small change in the
material under the strain gauge results in a change in output.
 Measurement of Viscosity

The device used for measurement of viscosity is known as viscometer and it uses the basic laws of
laminar flow. The principles of measurement of some commonly used viscometers are discussed here;

Rotating Cylinder Viscometer: It consists of two co-axial cylinders suspended co- axially as shown
in the Fig. The narrow annular space between the cylinders is filled with a liquid for which the
viscosity needs to be measured. The outer cylinder has the provision to rotate while the inner cylinder
is a fixed one and has the provision to measure the torque and angular rotation. When the outer
cylinder rotates, the torque is transmitted to the inner stationary member through the thin liquid film
formed between the cylinders. Let r1 and r2 be the radii of inner and outer cylinders, h be the depth
of immersion in the inner cylinder in the liquid and t (= r2 −r1 ) is the annular gap between the
cylinders. This shear stress induces viscous drag in the liquid that can be calculated by measuring the
toque through the mechanism provided in the inner cylinder.

Fig: 5.11 Schematic nomenclature of a rotating cylinder viscometer

Falling Sphere Viscometer:
It consists of a long container of constant area filled with a liquid whose viscosity has to be measured.
Since the viscosity depends strongly with the temperature, so this container is kept in a constant
temperature bath .

Fig :5 Schematic diagram of a falling sphere viscometer

A perfectly smooth spherical ball is allowed to fall vertically through the liquid by virtue of its
own weight(W ). The ball will accelerate inside the liquid, until the net downward force is zero i.e.
the submerged weight of the ball (FB ) is equal to the resisting force (FR ) given by Stokes’ law. After
this point, the ball will move at steady velocity which is known as terminal velocity.;The constant fall
velocity can be calcul;ated by measuring the time taken by the ball to fall through a distance (L).It
should be noted here that the falling sphere viscometer is applicable for the Reynolds number below
0.1 so that wall will not have any effect on the fall velocity.

Capillary Tube Viscometer:

This type of viscometer is based on laminar flow through a circular pipe. It has a circular tube attached
horizontally to a vessel filled with a liquid whose viscosity has to be measured. Suitable head (hf ) is
provided to the liquid so that it can flow freely through the capillary tube of certain length (L) into a
collection tank as shown in Fig. 7.1.3. The flow rate (Q) of the liquid having specific weight wl can
be measured through the volume flow rate in the tank. The Hagen- Poiseuille equation for laminar
flow can be applied to calculate the viscosity (µ) of the liquid.

142
 Fig :5.13 Schematic diagram of a Capillary tube viscometer
Saybolt and Redwood Viscometer:

The main disadvantage of the capillary tube viscometer is the errors that arise due to the variation in
the head loss and other parameters. However, the Hagen-Poiseuille formula can be still applied by
designing a efflux type viscometer that works on the principle of vertical gravity flow of a viscous
liquid through a capillary tube. The Saybolt viscometer has a vertical cylindrical chamber filled with
liquid whose viscosity is to be measured It is surrounded by a constant temperature bath and a
capillary tube (length 12mm and diameter 1.75mm) is attached vertically at the bottom of the
chamber. For measurement of viscosity, the stopper at the bottom of the tube is removed and time for
60ml of liquid to flow is noted which is named as Saybolt seconds. So, Eq. can be used for the flow
rate (Q) is calculated by recording the time (Saybolt seconds) for collection of 60ml of liquid inthe
measuring flask. For calculation purpose of kinematic viscosity (ν), the simplified expression is

obtained as below;
ν = µ =0.002t − 1.8 ; where, ν in Stokes and t in seconds
ρ t
A Redwood viscometer is another efflux type viscometer that works on the same principle of
Saybolt viscometer. Here, the stopper is replaced with an orifice and Redwood seconds is defined for
collection of 50ml of liquid to flow out of orifice. Similar expressions can be written for Redwood
viscometer. In general, both the viscometers are used to compare the viscosities of different liquid.
So, the value of viscosity of the liquid may be obtained by comparison with value of time for the
liquid of known viscosity.

143
Fig 5.14: A Redwood viscometer