flow measurement lecture 1

7/27/2019 Flow Measurement Lecture 1

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Flow Meters

Flow meters are a device used to measure therate of fluid movement at a given point in thepipe or tube. The flow meter is usually secured

to a break in the pipe and the fluid is allowedto move through it.

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Types of flow encountered

Clean or dirty/opaque

Wet or dry

Hazardous/corrosive or safe

Single-phase, two phase or multiphase

Laminar or transitional or turbulent

Pressure may vary from vacuums to high pressure of many

atmospheres

Temperature may vary from cryogenic levels to hundreds of centigrade.

Flow rate may range from few drops per minute to thousands of liters

per minute.


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Measurement of Volume Flow Rate

Volumetric flow is given by:Q = A * v

Where, Q = Volumetric flow rate (m3/sec)

A = Cross-sectional Area (m2)

v = Average fluid velocity (m/sec) Differential Pressure flow meters

Differential pressure flow meters use Bernoulli'sequation to measure the flow of fluid in a pipe.

They are most widely used flow meters for liquids and

gases. A restriction is placed in the pipe and the differential

pressure developed across the restriction is measured.

The differential pressure output is calibrated in terms ofvolume flow rate.


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Differential Pressure Flow Meters


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Principle of Operation

Bernoulli's "Theory of Conservation of Mass" states that the sum of static energy

(pressure head), kinetic energy (velocity head) and potential energy (elevation head)

of the fluid are conserved in the flow across the constriction in a pipe and by

continuity. This may be defined as:

P/ + v2 /2 + Zg = Constant

Where, P = Pressure, N/m2

v = Average velocity, m/sec

= Fluid Density, kg/m3

A = Area of cross-section, m2

Z = Elevation above datum, m

Applying this equation in the figure shown in previous slide.

P1/ + v12 /2 + Z1g = P2/ + v2

2 /2 + Z2g ..(1)


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Assumptions made in calculating the

volume flow rate

The flow is frictionless. It means there is no loss of energy in the fluid itself or

between the fluid and the pipe walls.

There is no heat losses or gains due to heat transfer between the fluid and its

surroundings.

There is conservation of total energy (pressure + kinetic + potential) at any point of

liquid.

The fluid is incompressible, i.e. 1 = 2 =

The pipe is horizontal, i.e. Z1 = Z2. It means that equation (1) reduces to

v22v1

2/2 = P1 - P2/

Conservation of volume flow rate,

Q1 = Q2 = Q also, Q1 = A1v1 and Q2 = A2v2


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Assumptions (Contd.)

Since A2 < A1, it follows that v2 > v1 and P2 < P1.

Therefore, the theoretical value of volume flow

rate in a differential pressure flow meter (venturi

and Orifice) is :


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Reynolds's Number In many applications, the knowledge of type of flow is very important.

The flow can be turbulent or laminar.

All fluids have a force of friction, called viscosity, which tends to inhibit the

formation of turbulent eddies and vortices and maintain streamline flow.

Reynolds's number is given by:

Re

= d/

Where, Re = Reynolds's number

= velocity of flow; m/s

d = diameter of pipe throat or orifice; m

= density of fluid; kg/m3

= viscosity; Ns/m2


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Reynolds's Number (Contd.)

Reynolds's number is dimensionless.

It is used to compare the flows in geometrically similar installations

but with different flow conditions.

It provides information regarding where streamline flow ceases and

turbulent flow begins.

It has been found experimentally that the flow is streamline or

laminar for Reynolds's number less than 2000 and turbulent flow

increases as Reynolds's number increases from 2000.

Flow becomes complete turbulent for Reynolds's number greater

than 105.


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The theoretical value of volume flow rate always differs from the actual

flow rate due to two main reasons:

The frictionless flow is never occurred in pipe. It is true for turbulent flows

in smooth pipe where friction losses are small. The laminar and turbulence

flows are characterized by Reynolds's number.

A1 and A2 are the cross-sectional areas of the pipe and the restriction

respectively. The cross-sectional area of the pipe is D2/4 and the cross-

sectional area of the meter is d2/4, where D and d are the respective

diameters.

However the area of minimum cross-section will be given by:

A2 = 0.99 d2/4 for a venturi

A2 = 0.6 d2/4 for orifice plate


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Therefore the theoretical expression ofvolume flow rate is corrected as:

Where, C = discharge coefficient

= Flow meter pipe diameter ratio, d/D

A2 = Flow meter cross-sectional area d2/4


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Dependency of the values of discharge

co-efficient

Type of flow meter e.g. orifice or venturi.

Reynolds's Number, Re

Diameter ratio

Therefore, for a given flow meter C = f(Re, ).

Values of C are found out experimentally, for

several types of flow meters, over a wide range of

fluid velocities.


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General Features of Differential

Pressure Flow Meter

1. It has no moving parts and therefore it is robust, reliable and

easy to maintain and widely established.

2. There is always a permanent pressure loss and the extra

pumping energy is necessary to overcome it.

3. Both venturi and orifice meter are non-linear. Volumetric flow

rate is proportional to square root of pressure differential. This

limits the useful range of a meter in between 25% and 100%

of full scale output reading. At lower flows, the differential

pressure measurement is below 6% of full scale output reading

and is not accurate enough for measurement.


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Differential Pressure Distribution in the

Pipe


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Non Linearity of Flow Rate


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General Features (Contd.)

4. It can be used for turbulent flow.

A typical flow meter consists of the differential

pressure sensor and differential pressure transmitter,

Data Acquisition System (DAS) and a PC. The

transmitter gives a current output signal (4 to 20 mA).

The DAS consists of an amplifier, Current to Voltage

converter and Analog to Digital Converter (ADC).


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Orifice Meter

The thin plate square-edge orifice is the most

widely used differential pressure flow meter in

process industry, mainly because of its Simplicity

Low Cost

Moreover it is well established over the years and

the data are available for its behavior.


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Type of Orifice Plates


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Orifice Plates

The concentric orifice is the most widely used plate.

The eccentric and segmented orifices are employed to

measure the flows of fluids containing solids. In both

cases the bottom of the hole is located in a way that the

bottom of the hole is at the same level inside bottom of

the pipe installation. These two orifice plates need

separate calibration, because the discharge co-efficients

differ from that of concentric orifice.


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Orifice Plates (Contd.)

The concentric orifice plate is installed in the pipe with its hole concentric to

the pipe.

It is a flat metal circular plate made of steel, stainless steel, phosphor bronze.

Its thickness is only sufficient to withstand the buckling forces caused by the

differential pressure exists across the plate.

The circular hole is made with 90, square and sharp edge upstream.

Change of sharp edge will modify the discharge co-efficient of the orificemeter.

It is advisable to replace the orifice during routine maintenance of the plant

for better accuracy of the measurement.


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Orifice Pressure Taps

Flange Tap


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It is constructed so that taps for measuring

differential pressures are integral part of the

orifice plate assembly. The pressure taps are

usually located 2.5 cm either side of the orifice

plate. The advantage of the flange taps is that

the entire orifice assembly is easily replaceableand the pressure taps are accurately located.


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Orifice Pressure Taps (Contd.)

D and D/2 taps


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Orifice Pressure Taps (Contd.)

Vena-Contracta Tap


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Restrictions of the pipe fitting adjacent

to Orifice meter

The discharge co-efficient is experimentally determined on straight pipe.

Flow disturbances in the pipe line adjacent to orifice alter the value of

discharge co-efficient.

Therefore elbow, pipe bend, tee, valve are not allowed near the orifice.

There should be no fitting close to five pipe diameter from the orifice on the

downstream. There should not be any fittings closer than twenty pipe

diameters up stream. If the minimum distance is not feasible, specially in upstream, flow

straightners can be installed. The flow straightners are bundle of smaller

tubes welded inside the pipe.


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Flow Nozzle/Dall Tube

The flow nozzle, venturi tube and dall flow tube have the same principle

as the orifice.

Dall tube is a modified venturi tube and it has low permanent pressure loss.

The flow nozzle are more expensive than the orifice meter but cheaper than

venturi meter.

It is also a variation of venturi in which the exit section is omitted so that it

is similar to an orifice with a well rounded up stream edge. The upstream

tap is at about one pipe diameter from the entrance to the nozzle. The down

stream tap is made on the pipe opposite to the straight portion of the

nozzle.


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Flow Nozzle


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Dall Tube


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Flow Nozzle/Dall Tube (Contd.)

Flow nozzle are used for high velocity stream

flows and it is dimensionally more stable at

high temperature and velocity than an orifice.

The permanent pressure loss in the flow nozzle

is same as orifice.


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Venturi Tube


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Venturi Meter

Venturi Meter is an expensive instrument but offers very good accuracy ( 1%).

It has a lowest permanent pressure loss.

Construction of Venturi Tube:

It is made of cast iron or steel.

The large venturi tube is made of concrete.

Sometimes the throat is made of bronze.

Upstream section has an angle of 20 and downstream section has a pressure of

7.

The pressure taps are made of piezometer rings so as to average the measurement

around the periphery.


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Construction of Venturi Tube (Contd.)

The diameter ratio for the venturi typically lies between

0.25 and 0.50.

It has almost no maintenance requirement and its

working life is very long.

It is widely used in high flow situations such as

municipal water system where large savings of pumping

cost are possible due to low permanent pressure loss

across it.


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Venturi Tube (Contd.)

The smooth internal shape of the venturi tube

means it is unaffected by solid particles or

gaseous bubbles in flowing fluid and in fact it canmeasure the flow of liquid contain slurries.

Its range is extremely high. It is possible to

measure the water flow rate as high as 1.5 x 106

m3/hr.

flow measurement lecture 1

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