flow measurementinpipe and open flow conditions

1. Flow Measurement

2. Why flow measurement?
• To quantify flows of
– water in streams in streams and rivers
– wastewater in sewers and wastewater drains
• To facilitate flow proportionated sampling of water
• To provide daily flow records required by regulatory agencies
• To determine
– Sizes of water and wastewater treatment plants and the
constituent treatment units
– Chemical dosage to the treatment units
• Interest may be to know instantaneous flow rates, cumulative
flows and variations in flow rates (peaking factor)
2

3. Flow proportionated sampling and
composite sample collection
Flow
Time
Base Flow
3

4. Basic requirements of flow meters
• Ability to calibrate
• Ability to integrate integrate flow fluctuations
• Ease of integration with piping system
• High accuracy
• High turn down ratio
• Low cost
• Low sensitivity to dust particles
• Low pressure loss
• Resistant to corrosion and erosion

5. Basic types of flow meters
• Differential pressure flow meters
• Velocity flow meters
• Positive displacement flow meters
• Mass flow meters
• Open channel flow measurement
• Miscellaneous type flow meters
5

6. Differential pressure flow meters
• Based on bernoullis equation
– Pressure drop over an obstruction inserted in the flow is used as
basis for flow measurement
• Used for flow measurement under pipeflow conditions
• Orifice meters, venturi meters and flow nozzles
– Orifice meter: a sharp edged orifice plate is introduced as
obstruction to flow – a simple and cheap but poorly accurate
specially at low flows - but can cause significant pressure drops
– Venturi meter: Flow cross section is gradually reduced to generate
pressure difference, and then increased for pressure recovery (low
pressure drops) – Preferred for accurate flow measurements and
for high turn-down rates (10:1)
– Flow nozzles: used usually for gas flow measurement - simple and
cheap - turn down rate and accuracy are comparable to orifice
plates - pressure drop across constricted area is maximum for
orifice plates & minimum for venturi tubes
6

7. Venturi meter
7
Consists of a conical contraction, a short cylindrical throat and a
conical expansion
P
1
P
2
V1 V2
Bernoulli equation between 1 and 2:
Continuity equation between 1 and 2: 2211 VAVAQ 
0
2
)VV()PP( 2
1
2
212





])/(A-[1
)(2
C 2
12
21
d,2
A
PP
V ideal


 Cd is discharge coefficient

8. Orifice Meter
A thin flat plate with a circular hole drilled in its center.
])/(A-[1
)(2
C 2
12
21
2
A
PP
V d


 Where Cd is the discharge
coefficient
P
1
P
2
A1, V1
1 2
Front view of
orifice plate
A2, V2

9. Nozzle Meter
P
1
P
2
])/(A-[1
)(2
C 2
12
21
2
A
PP
V d



• A Venturi meter without the diverging recovery section
• Less expensive than Venturi meter but higher head loss
• Accuracy: < ±1%; Range (turn-down ratio): 4:1
9
A1,V1 A2,V2

10. Velocity flow meters
• Flow is calculated by measuring flow velocity at one or more
points across the flow cross section
• Typical velocity flow meters
– Pitot tube
– Turbine flow meter (flow current meter)
– Electromagnetic flow meter
– Ultrasoic flow meter, etc.
• With the known flow velocity, flow rate is obtained using flow
cross sectional area

11. Turbine Flow meters
• Uses a multiple-bladed rotor
(turbine) mounted within a pipe,
perpendicular to flow
• The rotational speed is a direct
function of volume flow rate.
• The meter factor K is found by
direct calibration.
• Limited to pipes running full,
under pressure, and liquids low
in suspended solids
• Excellent accuracy (±0.25%)
and a good range of flows (turn
down ratio): 10:1

12. Measurement of flow rate
StageorDepth
Discharge, Q
Rating Curve
12

13. The Pitot Tube
P1 is a Static pressure: It is
measured by a device (static
tube) that causes no velocity
change to the flow. This is
usually accomplished by drilling
a small hole normal to a wall
along which the fluid is flowing.
P2 is a Stagnation pressure: It is
the pressure measured by an
open-ended tube facing the
flow direction. Such a device is
called a Pitot tube.
13
P1,V1 Stagnation
Point V2=0
1 2P2
2/1
12
1
)PP(2
V 















 

f
fm
XgV


21
ρm and ρf are fluid and manometic fluid densities
ΔX is manometric fluid level difference

14. Electromagnetic flow meter
Faraday’s law: Voltage produced by a
conducting fluid through a magnetic
field is proportional to fluid flow
velocity
• Advantages: Turn down ratio is quite
large (10:1); No head loss; and
Unaffected by temperature,
conductivity, viscosity, turbulence, &
suspended solids
• Problems: High initial cost and need
of trained personnel to handle
routine O&M
14
E=BDVx10-8
E=voltage, volts
B=magnetic flux density, gauss
D= length of the conductor, cm
V=velocity of the conductor, cm/sec

15. Ultrasonic flow meters
Ultrasonic Doppler flow meter:
• Frequency of a reflected signal is
modified by the velocity and
direction of the fluid flow
– If the fluid is moving towards a
transducer frequency of the
returning signal is increased and
otherwise it is decreased
– Frequency difference (reflected
frequency minus originating
frequency), known as ‘Doppler
effect’, is used to find flow velocity







C
V
FF SourceDoppler
‘V’ Flow velocity between source and receiver
‘C’ Speed of sound
‘Fsource‘ Transmitted frequency.

16. 16
Time-of-travel flow meters
Have 2 transducers mounted on each
side of the pipe
The transducers function as both as
sound wave transmitters and
receivers – operate alternatively as
transmitters and receivers
Sound wave is transmitted in the direction of the fluid flow and in the
opposite direction of flow and time of flight is measured
Differential in the time of flight is used to know the flow velocity and flow
measurement
Ultrasonic Flow meters

17. Positive displacement flow meters
Devices that isolate fixed volumes of fluid flowing into them in
sealed compartments and discharge to the outlet.
These may be passive (operate on the power from flowing fluid) or
active (metering pumps - driven by external power source)
Leakage and pressure loss are two problems associated with the PD
flow meters
Volume flow rate is calculated from the size and number of
compartments delivered per unit time
PD meters can be classified as rotary, reciprocating, or nutating
PD meters for liquids: Nutating disk meters, reciprocating-piston
meters, rotary-piston meters, rotary-vane meters, rotor meters
PD meters for gases: Roots-type meters, diaphragm-type meters,
liquid-sealed drum-type meters

18. Nutating disk meters
(a disk nutates in a dual conical housing)
Reciprocating – single piston meters
Plunger or piston is driven by a cam

19. Rotary-vane flow meters
Flat vanes are inserted into matching
slots around the perimeter of a
cylindrical drum.
Cylindrical drum is located eccentrically
within the housing
Rotary-(oscillating) piston flow meters
A cylindrical drum mounted
eccentrically inside a cylindrical
housing

20. Rotor meters: Oval Gear Meters
Rotor meters: Gear flow meters

21. Rotor meters: Helical gear flow meter
Roots-type flow meters
Lobe Rotary Piston

22. Diaphragm-type meters
Liquid-sealed wet gas flow meters (liquid provides sealing action)
Liquid ring pump

23. Mass flow meters
• These are also known as inertial flow meters
• If density is variable (temperature, pressure and fluid
composition influence density) mass flow rate can not be
obtained from volumetric flow rate
• Includes
– Coriolis flow meters
– Thermal flow meters
• Capillary tube type thermal mass flow meter
• Constant temperature differential method
• Constant current method
densityfluid
rateflowmass
rateflowvolumetric 

24. Coriolis mass flow meters
• with the help of an actuator the
inlet arm and the outlet arm are
vibrated at the same frequency
• when there is fluid flow, the inlet
arm and the outlet arm vibrate
differently and a phase shift
occurs
• The (measured) degree of phase
shift is proportional to the mass
flow in the tube


2
2
2Kd
IK
Q uu
m


Qm is fluid mass flow rate
Ku is temperature dependent tube stiffness
K is shape dependent factor
‘d’ is width, τ is time lag
ω is vibration frequency
Iu is inertia of the tube

25. Thermal mass flow meters
• Thermal dispersion or immersible mass flow meters
– Fluid mass flow rate is measured through measuring the heat
convected from a heated surface to the flowing fluid
– Commonly used for the gas flow measurement
– Heat is introduced into the flow stream and the heat dissipated is
measured by sensors
– Heat dissipated depends on the sensor design and the thermal
properties of the fluid
• Constant temperature differential method: two sensors, a heated
sensor and a gas temperature sensor are used - Power required for
maintaining constant temperature difference between the two sensors
is measured and used
• Constant current method: also have two sensors – power used to heat
the sensor is kept constant – temperature difference between the two
sensors is measured and used for flow measurement
• Capillary tube type of thermal mass flow meter
– Heat is transferred to the flowing fluid from a small heated
capillary tube carrying fluid
– Used for measuring smaller flows of cleaner gases and liquids

27. Rotameter, variable area flow meter
Fluid flowing moves the float/bob
upwards and maintains in a equilibrium
position when
 










tan2
1
.
.Re
min
2
22
22
hmor
D
DD
mwhere
gm
RnoRuppel
DU
Rnoynold
gVgVgVF
flowturbulentforUDCF
flowarlaforUDCF
buoyancyBobweightBobforceDrag
b
b
b
b
u
bin
e
bbbbbd
bTd
bLd
















Fd is drag force
ρb and ρ are bob density and fluid density
Vb is volume of the bob
Db is maximum bob diameter
D is tube diameter at the bob height
U is flow velocity at the annular gap around the bob

28.  
 
 
 
 
4
4
4
4
4
44
2
2
2
2
2
222
b
T
bb
b
bTbb
L
bbb
b
bLbb
b
bb
mD
C
gV
Q
mD
Q
DCgV
C
mDgV
Q
mD
Q
DCgV
mD
Q
U
UmDUDDQ
























 Q is volumetric flow rate
--- for laminar flow conditions
--- for turbulent flow conditions
Rotameter, variable area flow meter

29. Flow meters for open channel flow
Weirs and flumes: used as flow meters for open channel flow
Weirs:
• Elevated structures in open channels used for flow
measurement
• Can be sharp crested weirs (thin plates set vertically across
the width of the channel) and board crested weirs
• Can be contracted weirs or suppressed weirs
– Contracted weirs: Nappe is open to atmosphere at the edges; Nappe
width is slightly lesser than the weir width
– Suppressed weirs: Channels sides are also the sides of the weir
opening; Nappe is not open to atmosphere, but usually some type of
air vent is provided beneath the nappe)
• Weirs for flow measurement
– Rectangular weirs
– Cipolletti weirs
– Triangular (V-notch) weirs

30. Rectangular weirs
  2
3
2
3
2
3
2.083.1
83.1
075.0611.0
2
3
2
HHbQ
bHQ
H
H
C
HbgCQ
w
d
d




Discharge for suppressed rectangular weir
Discharge for contracted rectangular weir
Applicable for H/Hw is <5
‘b’ is width at the weir crest
H is water depth above the crest at 4H to 5H
distance upstream side
Cd according to Rouse (1946) & Bievins (1984)
Hw is weir crest height from channel bottom
For H/Hw <0.4 Cd is 0.62 & Q is
Acceptable for b≥3H

31. Cipoletti weir and V-notch weir
Cipoletti or trapezoidal weir
• Side slope is 1:4 (H:V)
• Corrections for end contractions not needed
• Can be used when the H is >6 mm (for <6
mm the nappe does not spring free of crest)
V-Notch weir
• Has V shaped opening with θ = 10° to 90°
• Cd value decreases with increasing angle
• Minimum Cd value is 0.581
• 0.58 can be used as Cd for θ = 20° to 100°
2
3
859.1 HbQ  ‘b’ is bottom weir width
2
5
2
tan2
15
8
HgCQ d 







Weirs cause high head losses and suspended
solids tend to accumulate behind the weirs

32.   













3
2
2
3
2
97.4
5.0
5.0
a
hgabCQ
a
hbaQ
d














 
5.0
1
tan
2
1
a
y
bx

.max
.max
.min
5.0
.max
.min5.1
.max
.max
262.0
H
Q
Q
a
Q
Q
gH
Q
b








Cd value is 0.6 to 0.65
b is taken as ‘channel width – 150 mm’!
Proportional weir (Sutro weir)

33. Broad crested weirs
• Very robust flow measurement device used in rivers/canals
• A broad rectangular weir with a level crest and rounded edges
• Works on the principle that the flow over the weir occurs at
critical depth
– Flow at critical depth occurs when the weir height is above a
specific value
– Uptill critical depth occurs, raising the crest level will not affect
the upstream water level
– Once critical depth is achieved, any further rise of crest height
also rises the upstream water level
• For a proper broad crested weir used for flow measurement
– Upstream flow is sub-critical
– Flow over the crust is critical flow
– Super critical on the downstream side
– On the downstream side a super critical flow turns back to a sub-
critical flow after a hydraulic jump
• Hydraulic jump in the downstream side is in fact an evidence
for critical flow on the crest

35. Broad crested weirs
• Problems associated with broad crested weirs
– Accumulation of silt and debris in the region of dead water on the
upstream side
– Loss of energy from the downstream side hydraulic jump formation
• A solid weir has no hydraulic jump (!)
• Crump weir can to a great extent solve the above problems
– Crump weirs have an upstream slope of 1 in 2 and a
downstream slope of 1 in 5 to reduce the region of dead water
on the upstream side
• For critical depth of flow over the crest of the weir, unique
relationship exists between the head above the crest and the
flow rate/discharge

36. Broad crested weir
Discharge equation/formula
5.1
5.1
5.1
705.1
6.1
LHQ
LHQ
CLHQ



L is weir length
H is head over the crest
H is actually height of the total energy line
from the crest of the weir
It is measured usually in a stilling chamber a
few meters upstream the weir where the
water level is affected by draw-down
C is weir coefficient, its value is taken as 1.6
C is estimated from the total energy or bernouli’s equation as 1.705
From this the coefficient of discharge can be calculated as 0.94
Critical depth of flow should occur on the crest for the discharge
formula to work
The discharge formula is based on the critical flow on the crest and
does not be influenced by the weir shape
Value of ‘C’ however can be influenced by the weir shape

38. Flumes
• Flumes are specially shaped fixed hydraulic structures that
force flow to accelerate through in such a way that the flow
rate becomes related to the liquid level
– Converging side walls or raising bottom or both are used in
shaping the special hydraulic structures
• Flumes usually have 3 sections: converging section, throat
section and diverging section
– All the sections do not necessarily be present in all the flumes -
Cutthroat flume has no throat
• Compared to weirs, head loss for flumes is lesser (it is just
1/4th of a sharp crested weir)
• Flumes have no dead zones on the upstream side where
sediment and debris can accumulate
• Types of flumes commonly used:
– Parshall flumes
– Palmer-Bolus flumes

39. Parshall flume
• Consists of a converging section, a throat section and a
diverging section
– Crest of the throat section is tilted to the downstream side
– In channels of < 2.44 m width, inlet of the converging section
may be rounded
• Parshall flumes are constructed for standard dimensions
defined by the width of the constriction
• Parshall flumes operate on the venturi principle
– Narrow throat causes water level to raise on the upstream side
• Flow rate is obtained by measuring water depth in the
converging section of the parshall flume
n
KHQ 
H is water depth at point h1
K is a constant (function of the constriction and of the
units chosen for the measurement – value increases with
the increasing flume width)
‘n’ is a constant of exponent (function of the constriction’s
dimensions – value is between 1.522 - 1.607

40. Standard dimensions
W 305±0.8
A 1372
2/3A 914
B 1343
C 610
D 845
E 914
F 610
G 914
H ----
K 76
M 381
N 229
P 1492
R 508
X 51
Y 76Parshall flume of standard dimensions

41. Parshall flume (submerged conditions)
• When downstream water depth is higher than the crest level
of the flume (floor level of the converging section), a second
water depth measurement (h2) is needed for the flow
measurement
• If h2/h1 is crossing 50% to 80% (50% for smaller flumes and
80% for larger flumes) then flow is said to be submerged
• Flow measurement for submerged flow conditions is possible
when h2/h1 is <0.95
 
2
1
1
2
211
log
n
n
h
h
hhC
Q









C1 is a constant – its value increases with the
increasing width of the flume
‘n1’ and ‘n2’ are constants – their values also
increase with increasing flume width
‘h1’ and ‘h2’ are water depths against a
reference level in the converging section and
at the downstream of the throat

42. Parshall flume
• Parshall flume must be located in the straight section of the
channel for flow measurement
• Crest level of the flume must be higher than the channel
bottom
– The crest level is raised at 1 in 4 slope from the channel
• Parshall flume is extremely effective for flow measurement
when the water contains suspended solids
• Parshall flume creates very little head loss
• Turndown ratio is >100
– A feet wide standard parshall flume can measure a minimum
flow of 0.00439 m3/sec. (h1 is 31 mm) and a maximum flow of
0.4568 m3/sec. (h1 is 762 mm)
• Margin of error is ±3%

43. Palmer-Bolus flume
• It is a venturi type flume
– High velocity critical flow is produced in the throat by flow
constriction
• Usually prefabricated - designed to install in existing channels
– Installed in sewers or in manholes or in open, round or
rectangular bottom channels
• Advantages
– Easy to install
– Minimum restriction to flow, less energy loss, less cost and low
maintenance
– Less sensitive to upstream disturbances
– Can be used in submerged flow conditions (80-90%
submergence is no problem
– Does not require upstream or downstream crest differential
– Water containing solids can be measured

44. Palmer-Bolus flume
• Size may range from 100 mm to 1000 mm
– Dimensions of the flume depend on the diameter or size of the
channel in which installed
• Throat is trapezoidal in shape
– Has a flat bottom and inclined sides (20°)
– Length of the throat is usually equal to the diameter
• The flume is elevated from the channel bottom by D/6
• Inclined section from channel to flume has 1 in 3 slope
• Length of the base of the flume is D+2P where P is length of
the inclined section (D/2)
• Turndown ratio is relatively small (9 or 10:1)
– Difference between the minimum flow and the maximum flow
that can be measured is relatively small
– For a 12’’ flume (D=12’’) the minimum and the maximum flow
measured is 0.0056 m3/Sec. and 0.0158 m3/Sec. respectively

45. t = D/6
B = W = D/2 or 5D/12
m = D/4
mm

46. PALMER-BOWLUS FLUME – STANDARD DIMENSIONS

47. Palmer-Bolus flume
 
 mz
mzgz
DQ
8.41
4.21
12
5
33
2
5



Q is flow rate
D is diameter of the channel
‘g’ is acceleration due to gravity
‘z’ is dc/D where ‘dc’ is depth of flow
‘m’ is vertical constrictions base projection (D/4)
Flow measurement equation
Flow rate is determined by measuring water depth upstream
from the flume
Liquid depth is measured at a point D/2 distance from the
flume on the upstream side
Within the normal range of flow (10% to 90% of the flume
capacity) error in flow measurement is <3%

48. Acoustic Meter
• Use sound waves to measure
the flow rates
• Sonic meter or ultrasonic meter
depending on whether the
sound waves are in or above
audible frequency range
• Determine the liquid levels,
area, and actual velocity
• Advantages: low head loss,
excellent accuracy (2~3%),
usable in any pipe size, no
fouling with solids, and wide
flow ranges (10:1)
• Disadvantages: High initial cost
and need for trained personnel
to handle routine O&M 48

49. Miscellaneous Flow
Measurement Devices
• Depth Measurement
– Need to measure the flow depth and sewer slope and use
Manning equation for flow estimation
– Frequently used for interceptor flow estimation
• Open Flow Nozzle
– Crude devices used to measure flow at the end of freely
discharging pipes.
– Must have a section of pipe that has a length of at least six
times the diameter with a flat slope preceding the discharge.
– Examples: Kennison nozzle and the California pipe
49