Flow Measurement Techniques

FLOW MEASUREMENTS
A lecture by…
S.Raghubir Singh
(Lecturer Civil Engg.)
Pt. Jagat Ram Govt.
Polytechnic College,
Hoshiarpur.
Mobile No. 09501547500
Subject:-Fluid mechanics
3rd semester
(Civil Engg.)
Punjab Edusat Society Slide 1

CONTENTS
Discharge
 Flow measurement & it’s Importance
 Technical Terms related to Orifice, Notches and Weirs
 Hydraulic Co-efficients : Cc ,Cv ,Cd ,Cr
Devices for measuring rate of fluid flow
 Orifice :
 Mouthpiece
 Notches and Weirs
 Discharge Computations by Single Segment Method

DISCHARGE
 Discharge can be defined as the quantity of a fluid
flowing per second through a section of a pipe or
channel.
 It is generally denoted by Q.
 Let A = Cross-sectional area of the pipe.
V = Average velocity of the liquid.
Discharge, Q = Area x Average velocity
Q = A x V
 Units of Discharge : m3/sec ,cusec

Flow measurement & it’s Importance
• The rate of fluid flow or discharge through pipes,
rivers, open channels, large tanks has to be measured .
• This flow is measured for the following purposes:-
For designing various hydraulics structures.
To plan for the optimum utilization of river-valley
projects.
To make an accurate assessment of the available
water resources .
To design multi- purpose river valley projects.

TECHNICAL TERMS
JET
A jet is a continuous stream of a liquid that flows
out of an orifice.
VENA–CONTRACTA
Vena- Contracta is that section of a jet where the
cross- sectional area of the jet is minimum. This
cross section area is even less than that of orifice.
Vena –contracta is formed at a distance of 0.5d
from the wall of the tank.

JET VENA CONTRACTA
0.5 D
ORIFICE
D

TECHNICAL TERMS
VELOCITY OF APPROACH
• The velocity with which the liquid is approaching the
orifice in a tank is known as velocity of approach.
• The velocity of approach is negligible as compared to
the velocity at vena-contracta.
• Velocity at vena-contracta , V = 2gH where H is
the depth of the liquid above the centre of orifice.

HYDRAULIC CO-EFFICIENTS
There are mainly four hydraulic co-efficients or
Orifice co-efficients related to discharge through an
orifice :-
1. Co-efficient of Contraction Cc
2. Co-efficient of Velocity Cv
3. Co-efficient of Discharge Cd
4. Co-efficient of Resistance Cr

1. CO-EFFICIENT OF CONTRACTION
The co-efficient of contraction is defined as the
ratio of the area of jet at vena- contracta to the
area of the orifice. Mathematically,
Cc = Ac
Where Ac = Area of jet at vena- contracta
A = Area of the orifice
 The value of Cc varies from 0.61 to 0.69
(Average value is taken as 0.64)
A

2. CO-EFFICIENT OF VELOCITY
The co-efficient of velocity is defined as the ratio
of the actual velocity of jet at vena- contracta to
the theoretical velocity of the jet.
Mathematically,
Cv = V
 2gH
Where V = Actual velocity
H = Head under which the liquid flows out
of orifice.
 The value of Cv varies from 0.95 to 0.99

3. CO-EFFICIENT OF DISCHARGE
The co-efficient of discharge is defined as the ratio of the
actual discharge from an orifice to the theoretical
discharge from the orifice.Mathematically,
Cd = Q
a x  2gH
where Q = Actual Discharge
a x  2gH = Theoretical discharge
 The value of Cd varies from 0.61 to 0.65

4. CO-EFFICIENT OF RESISTANCE
The co-efficient of resistance is defined as the
ratio of the loss of head(or loss of kinetic
energy) in the orifice to the head of liquid
(actual kinetic energy) available at the exit of
the orifice. Mathematically,
Cr = Loss of Head in the orifice OR
Head of liquid
Cr = Loss of K.E in the orifice
Actual K.E of jet at vena-contracta

Co-efficient of Discharge, Cd = Actual Discharge
Theoretical Discharge
Cd = Actual Discharge
Theoretical Discharge
= Actual velocity x Actual Area
Theoretical velocity x Theoretical Area
= Actual velocity x Actual Area
Theoretical velocity Theoretical Area
Cd = Cv x Cc
RELATIONSHIP BETWEEN Cc , Cv , Cd

DEVICES FOR MEASURING DISCHARGE
• Orifice
• Mouthpiece
• Notches
• Weirs
• Venturimeter
• Orificemeter

ORIFICE
• An Orifice is a small
opening on the side or
bottom of a tank for
measuring the discharge.
• The top edge of the
orifice is always below
the free surface of liquid
in tank.

FUNCTIONS OFAN ORIFICE
 An Orifice is used to measure discharge of a
liquid from a reservoir or a tank.
 Orifice helps to find out the time required to
empty a tank.
 Orifice can be used to find out the time required
to fall liquid from a particular level to a desired
level.

CLASSIFICATION OF ORIFICE
1. ACCORDING TO SIZE
a) Small Orifice
b) Large Orifice
2. ACCORDING TO SHAPE
a) Rectangular Orifice
b) Circular Orifice
c) Triangular Orifice
d) Square Orifice

CLASSIFICATION OF ORIFICE
3. ACCORDING TO SHAPE OF THE EDGE
a) Sharp- Edged Orifice
b) Bell-mouthed Orifice ( Round cornered)
4. ACCORDING TO THE NATURE OF
DISCHARGE
a) Free discharging orifice
b) Submerged Orifice
(i) Fully Submerged Orifice
(ii) Partially Submerged Orifice

DISCHARGE THROUGH AN ORIFICE
Consider the case of a small,
rectangular, sharp-edged free
discharging orifice.
 An orifice is called a small
orifice if the head of the
liquid is more than 5 times
the depth of the orifice.
 The velocity in the entire
cross-section of the jet is
considered to be constant in
the case of small orifice. d
b

DISCHARGE THROUGH AN ORIFICE
Let a = Cross-sectional area of the orifice
h = Height of the liquid above the centre of the
orifice.
b = Width of the orifice
d = Depth of the orifice
Cd = Co-efficient of discharge for the orifice
Q = Cd x a x  2gh

MOUTHPIECES
 A mouthpiece is a short
length of a pipe(2 to 3
times its diameter)
connected to an orifice.
 Mouthpieces are used to
increase the amount of
discharge of liquid.
 The diameter at the exit
end of mouthpiece is
known as the diameter of
the mouthpiece.

CLASSIFICATION OF MOUTHPIECES
1. ACCORDING TO THE POSITION OF THE
MOUTHPIECE
a) Internal mouthpiece
b) External mouthpiece
a) Cylindrical mouthpiece
b) Convergent mouthpiece
c) Convergent-divergent mouthpiece
3. ACCORDING TO NATURE OF DISCHARGE
a) Running Full b) Running Free

EXTERNAL CYLINDERICAL
MOUTHPIECE
 A cylindrical
mouthpiece is a short
pipe having uniform
diameter.
 A mouthpiece
projecting outside the
body of vessel (tank) is
called an External
cylindrical mouthpiece.
FIG.A

DISCHARGE THROUGH AN EXTERNAL
CYLINDRICAL MOUTHPIECE
 Consider a tank with an
external cylindrical mouthpiece
The jet of liquid entering the
mouthpiece forms vena-
contracta at C-C. Let
a =area of mouthpiece
v = Velocity of liquid at outlet
ac =Area of flow at v.contracta
vc = velocity of liquid at
v.contracta
FIG.A

DISCHARGE THROUGH AN EXTERNAL
H =Height of the liquid above the centre of
mouthpiece.
w = Specific Weight of the liquid
Cc = Co-efficient of Contraction=0.855
Discharge ,Q = Cc x a x  2gH

DISCHARGE THROUGH AN INTERNAL
(RUNNING FREE)
 An internal mouthpiece is a
short cylindrical tube attached
to the orifice extending inside
the tank.
 When the length of the tube
is equal to its diameter, the jet
of liquid comes out without
touching the sides of
mouthpiece known as running
free.

(RUNNING FREE)
Let a = Area of mouthpiece
ac =Area of contracted jet
vc = velocity through mouthpiece
Cd = Co-efficient of discharge = 0.5
H = Height of the liquid above the centre of
mouthpiece
Discharge, Q = Cd x a x  2gH

(RUNNING FULL)
When the length of the
tube is about 3 times
its diameter, the jet of
liquid comes out with
its diameter equal to
the diameter of
mouthpiece at outlet
is known as running
full.

(RUNNING FULL)
Let a = Area of mouthpiece
ac =Area of contracted jet
vc = velocity through mouthpiece
Cd = Co-efficient of discharge = 0.707
H = Height of the liquid above the centre of
mouthpiece
Discharge, Q = Cd x a x  2gH

NOTCHES
 A Notch is an opening
in the vertical side of a
tank such that the free
surface of the liquid in
the tank is below the
top edge of the
opening.
 A Notch is used to
measure discharge
through a tank or an
open channel.

WEIRS
 A Weir is a masonry or
concrete structure (a
small dam of low ht.)
built across a river or
canal over which
water overflows.
 A weir is used to
measure the discharge
of water in rivers or
canals.

DIFFERENCE BETWEEN NOTCH AND WEIR
S.No. NOTCH WEIR
1. Water passes through
the notch.
Water flows over
the weir.
2. It is usually made up of
metallic plate.
It is usually made
up of concrete or
masonry.
3. It’s base length is
small.
It’s base length is
very large.

DIFFERENCE BETWEEN NOTCH AND WEIR
S.No. NOTCH WEIR
4. The edges of the notch
are sharp and thin.
The crest of the weir is
wide.
5. It is used for measuring
small discharges.
It is used for measuring
huge quantities of
discharges.
CREST OR SILL :- The Top edge of the weir over which the
water overflows is called crest or sill.

CLASSIFICATION OF NOTCHES
The notches can be classified according to the shape
of the opening as:
a) Rectangular Notch
Discharge,Q = 2 x Cd x L x 2g x H 3/2
3
Slide 34Punjab Edusat Society

a) Triangular Notch
Discharge,Q = 8 x Cd x 2g x H5/2 x tan
15 2

c) Trapezoidal Notch d) Stepped Notch

CLASSIFICATION OF WEIRS
1. ACCORDING TO THE WIDTH OF CREST
a) Narrow Crested Weir
b) Broad Crested Weir
a) Rectangular Weir
b) Triangular Weir
c) Trapezoidal Weir (Cippoletti Weir )
3. ACCORDING TO NATURE OF DISCHARGE
a) Free Weir b) Submerged Weir

DISCHARGE THROUGH TRAPEZOIDAL
WEIR (CIPPOLETTI WEIR)
Discharge,Q = 2 x Cd x L x 2g x H 3/2
3

DISCHARGE COMPUTATIONS BY
SINGLE SEGMENT METHOD
When the discharge in a river or channel is too
high,it can be calculated by Single segment
method in the following way:-
o The area of cross-section of the river is measured
by stretching a rope ar to the river or channel.
o The river is divided into small segments.
o The length of each segment is measured.

DISCHARGE COMPUTATIONS BY
SINGLE SEGMENT METHOD
o The depth of the river is
measured in the centre
of the segment.
o Area = L x d
o The velocity(V) in each
segment is calculated by
float,current meter etc.
o Discharge,Q =
L1d1V1+L2d2V2+…

CONCLUSION  Discharge
 Flow measurement & it’s
importance
 Technical Terms related to
orifice, notches and Weirs
 Hydraulic Co-efficients :
Cc ,Cv ,Cd ,Cr
Devices for measuring rate of
fluid flow
 Orifice :
 Mouthpiece
 Notches and Weirs
 Discharge Computations by
Single Segment Method Slide 41Punjab Edusat Society

Flow Measurement Techniques

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