Momentum Transfer

(BCHE205L)

Module 3
Flow Measuring Devices
Dr. Mohammed Rehaan Chandan
School of Chemical Engineering,Vellore Institute of Technology,
Vellore
Flow Measuring Devices
 Importance of metering
 Classification flow measuring devices
 Principle and working of
 Orifice meter
 Venturi meter
 Pitot tube
 Variable area meters: Rotameter, Elbow meter

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Local way of measuring flow rate
 Liquid = Amount of volume collected/time
 Gases = Amount of volume collected/time (In case of
gases its difficult to measure the volume because of
low density.

The application: In process Industries

The control room is receiving the signal from the site.
And is monitored and controlled remotely.

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Flow meters and flow transmitter
 All flow meters are actually flow indicators
(the readings are indicated on a scale and not the
value on the electronic panel)
Flow transmitter: It converts the readings into a
electronic signal and sends to the control room for
monitoring and control of flow.
They have sensors with electrical transmission
output for indication of liquid flow rate.
A flow transmitter is an upgraded version of the flow
meter. It is a flow meter with an integrated electronic
circuit as an operational system.

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 Orifice meter and venturi meters – Flow
indicators and transmitters
 Rotameter – Flow indicator
 Pitot tube - Flow indicator and
transmitter
 Weirs and notches (for open channel
flow) - Flow indicator and transmitter

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Flow measurement
 Restriction flow meters
 Orifice meter
 Venturi meter
 Area flow meters
 Rotameter
 Target meters
 Turbine meters
 Local velocity measurement
 Pitot tube
 Open flow measurement
 Rectangular weirs and notches
 Triangular weirs and notches

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Measurement of Flow Rate Through Pipe
 Flow rate through a pipe is usually measured by
providing a coaxial area contraction within the pipe
and by recording the pressure drop across the
contraction.
 Therefore the determination of the flow rate from the
measurement of pressure drop depends on the straight
forward application of Bernoulli’s equation.
 Three different flow meters operate on this principle.
 Venturimeter
 Orificemeter
 Flow nozzle
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 Restriction flow meters
 This is used only for internal flow Streamlines

D1 V1
D2 V2

1 2
P1 P2
Vena Contracta
Assumptions;
1. Steady flow
2. Incompressible flow
3. Uniform velocity at (1) and (2)
4. No curvature of streamlines i.e. pressure at (1) and (2) are uniform
5. No frictional losses
6. z1 = z2
7. 𝛼1 = 𝛼2 ~ 1
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 Pressure at section (1) and (2), we observe a temporary pressure drop. At
section (3) we can observe a pressure recovery. But the pressure recovery
will not be 100%.

D1 V1
D2 V2

1 2 3
P1 P2

This drop in pressure between section (1) and (3) is permanent.

Permanent pressure drop is much higher in case of orifice meter as compared to
venturimeter.

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 In venturi meter the pressure recovery is around 98%
but the cost of instrument is very high as compared
to orifice meter.

 If pipe size is large – venturi meter is recommended.

 If pipe size is medium and small – orifice meter is

recommended.

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Orifice meter

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 Different pressure tappings:
1. D – D/2 type tapping (most common)
2. Flange type tapping (25 mm from plates)
3. Corner tapping

Typical value of CD for orifice meter

CD = 0.6 to 0.66

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Venturimeter

 To avoid flow separation long diffusor section is

maintained with low angle.
CD = 0.98-0.99
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Inclined venturimeter

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 Venturi meter
 Construction:
 A venturi meter is essentially a short pipe consisting of two conical
parts with a short portion of uniform cross-section in between.
 This short portion has the minimum area and is known as the throat.

 The two conical portions have the same base diameter, but one is
having a shorter length with a larger cone angle while the other is
having a larger length with a smaller cone angle.
 Such a constricted convergent-divergent passage was first
demonstrated by an Italian scientist Giovanni Battista Venturi in
1797.
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 Venturimeter

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 Working:
 The venturi meter is always used in a way that the upstream part
of the flow takes place through the short conical portion while the
downstream part of the flow through the long one.
 This ensures a rapid converging passage and a gradual diverging
passage in the direction of flow to avoid the loss of energy due to
separation.
 In course of a flow through the converging part, the velocity
increases in the direction of flow according to the principle of
continuity, while the pressure decreases according to Bernoulli’s
theorem.
 The velocity reaches its maximum value and pressure reaches its
minimum value at the throat. Subsequently, a decrease in the
velocity and an increase in the pressure takes place in course of
flow through the divergent part.

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 Measurement of Flow by a Venturi meter

Figure shows that a venturi meter is inserted in an inclined pipe line in a

vertical plane to measure the flow rate through the pipe.
Let us consider a steady, ideal and one dimensional (along the axis of the
venturi meter) flow of fluid. Under this situation, the velocity and pressure at
any section will be uniform.

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 The expression for flow rate, in terms of manometer deflection Δh, remains
the same irrespective of whether the pipe-line along with the venturi meter
connection is horizontal or not.
 Measured values of Δh, the difference in piezometric pressures between
Secs 1 and 2, for a real fluid will always be greater than that assumed in
case of an ideal fluid because of frictional losses in addition to the change in
momentum
 Therefore, Eq. (1) always overestimates the actual flow rate. In order to take
this into account, a multiplying factor Cd, called the coefficient of discharge,
is incorporated in the Eq.(1) as

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 Let the velocity and pressure at the inlet (Sec. 1) are V1 and p1
respectively, while those at the throat (Sec. 2) are V2 and p2.
Now, applying Bernoulli’s equation between Secs 1 and 2, we
get

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 The coefficient of discharge, Cd is always less than unity and
is defined as

 where, the theoretical discharge rate is predicted by the Eq. (1)

with the measured value of Δh, and the actual rate of discharge
is the discharge rate measured in practice.
 Value of Cd for a venturi meter usually lies between 0.95 to
0.98

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 Orifice meter

An orifice meter provides a simpler and cheaper arrangement for

the measurement of flow through a pipe.
An orifice meter is essentially a thin circular plate with a sharp edged
concentric circular hole in it.
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 Orifice meter

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 Working
 The orifice plate, being fixed at a section of the pipe, creates an
obstruction to the flow by providing an opening in the form of an
orifice to the flow passage.

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 The area A0 of the orifice is much smaller than the cross-sectional area of
the pipe. The flow from an upstream section, where it is uniform, adjusts
itself in such a way that it contracts until a section downstream the orifice
plate is reached, where the vena contracta is formed, and then expands to fill
the passage of the pipe.
 One of the pressure tapings is usually provided at a distance of one diameter
upstream the orifice plate where the flow is almost uniform (Sec. 1-1) and
the other at a distance of half a diameter downstream the orifice plate.
 Considering the fluid to be ideal and the downstream pressure taping to be
at the vena contracta (Sec. c-c), we can write, by applying Bernoulli’s
theorem between Sec. 1-1 and Sec.c-c,

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 where p1* and pc* are the piezometric pressures at Sec. 1-1 and c-c
respectively
 From the equation of continuity, A1V1 = AcVc where Ac is the area of the
vena contracta, we get

 (p1* - pc*) in Eq. is substituted by its measured value in terms of the

manometer deflection 'Δh‘

 where 'Δh' is the difference in liquid levels in the manometer and ρm is the
density of the manometric liquid.

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 The value of C depends upon the ratio of orifice to duct area, and the
Reynolds number of flow.
 The main job in measuring the flow rate with the help of an orifice meter, is
to find out accurately the value of C at the operating condition.
 The downstream manometer connection should strictly be made to the
section where the vena contracta occurs, but this is not feasible as the vena
contracta is somewhat variable in position and is difficult to realize.
 In practice, various positions are used for the manometer connections and C
is thereby affected. Determination of accurate values of C of an orifice
meter at different operating conditions is known as calibration of the
orifice meter.

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A comparison of the typical values of Cd, accuracy, and the cost
of three flow meters

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Venturi meter and orifice meter equation
 The basic equation is given by

𝐴1 𝐴2
𝑄= 2𝑔ℎ
2 2
𝐴1 − 𝐴2

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Example
 Water flows at the rate of 0.015 m3/s through a 100 mm
diameter orifice used in a 200 mm pipe. What is the difference
in pressure head between the upstream section and the vena
contracta section? (Take coefficient of contraction Cc=0.60 and
Cv=1.0).

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Static, Dynamic and Stagnation Pressure

Flow

P (static pressure)

Stagnation pressure: When the flow is decelerated to zero velocity, the

pressure of the fluid is stagnation pressure

1 2

V, P V=0, Pst

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 1 2

V, P V=0, Pst

Apply Bernoulli’s equation

𝑷 𝑽𝟐 𝑷𝒔𝒕
+ =
𝝆 𝟐 𝝆

𝟏 𝟐
𝑷𝒔𝒕 = 𝑷 + 𝝆𝑽
𝟐
Stagnation pressure
Static pressure Dynamic pressure

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Pitot Tube
Capillary tube
P, V

Pst

Standard Pitot tube

To manometer

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 P Pitot Static Tube

Pst

Pst
h
Pst > P
𝟏 𝟐
𝒉 𝝆𝒎 − 𝝆 𝒈 = 𝝆𝑽
𝟐

𝟐𝒉𝒈 𝝆𝒎 − 𝝆
𝑽=
𝝆
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 Pitot tube
 Static pressure:
 The thermodynamic or hydrostatic pressure caused by molecular collisions is
known as static pressure in a fluid flow and is usually referred to as the
pressure p.
 When the fluid is at rest, this pressure p is the same in all directions and is
categorically known as the hydrostatic pressure.
 For the real fluids it is the arithmetic average of the normal stress at a point.
 Static pressure is a parameter to describe the state of a flowing fluid.

Measurement of Static pressure (a) Single Wall tap (b) Multiple Wall Tap
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 Pitot Tube
 Construction:
 The principle of flow measurement by Pitot tube was adopted first
by a French Scientist Henri Pitot in 1732 for measuring velocities
in the river.
 A right angled glass tube, large enough for capillary effects to be
negligible, is used for the purpose.
 One end of the tube faces the flow while the other end is open to
the atmosphere as shown in Fig.

Simple Pitot Tube (a) tube for measuring the Stagnation Pressure
42 (b) Static and Stagnation
Dr. Mohammed tubes
R Chandan, together
SCHEME, VIT
 Pitot Tube

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 The liquid flows up the tube and when equilibrium is attained, the liquid
reaches a height above the free surface of the water stream
 Since the static pressure, under this situation, is equal to the hydrostatic
pressure due to its depth below the free surface , the difference in level
between the liquid in the glass tube and the free surface becomes the
measure of the dynamic pressure

 Where po, p and V are the stagnation pressure, static pressure and velocity
respectively at point A
Or

 Such a tube is known as Pitot tube and provides one of the most accurate
means of measuring fluid velocity

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 For an open stream of liquid with a free surface , this single
tube is sufficient to determine the velocity
 But for a liquid flowing through a closed duct, the pitot tube
measures only the stagnation pressure and so the static pressure
must be measured separately.
 Measurement of static pressure in this case is made at the
boundary of the wall
 The axis of the tube measuring the static pressure must be
perpendicular to the boundary and free from burrs

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Example
 Air flows through a duct, and the pitot-static tube measuring
the velocity is attached to a differential manometer containing
water. If the deflection of the manometer is 100 mm, calculate
the air velocity, assuming the density of air is constant and
equals to 1.22 kg/m3, and that the coefficient of the tube is
0.98.

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