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Flow Measurementand Screens
CE 547
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Flow Meters
Flow Meters: are devices used to measure theflow rate of a fluid
In Water, all types of flow meters can be used
In Wastewater, the choice is critical due to solidcontent:
Solids can be removed
Flow has enough energy to be self-cleaning
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Rectangular Weirs
Fully-contracted weir
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Suppressed weir: weir extends to the channelvertical sides
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P = weir height
H = head over the weir
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The energy equation between (1) and (2)
V = velocity (average) P = pressure y = height above bottom of channel Z = height of bottom above a datum
hl = head loss between (1) and (2) g = gravitational constant = specific weight of water
22222
11121
22ZyP
gVhZyP
gV
l
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In the figure:
Z1 = Z2 = 0
V2 >> V1P1 = P2 = atmospheric pressure
If hl was neglected, then:
y1 = H + P
y2 = yc + P
Substitute in the energy equation and change V2 to Vc
(critical velocity)
)(2
cc
yHZgV
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Specific energy equation states that:
The critical depth, yc, occurs at minimum specificenergy
Differentiate E with respect to y and equate to zero
Use ( Q = VA ) Q = flow rate
V = velocity
A = cross-sectional area
gVyE2
2
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A/T = hydraulic depth, D
D is simply equals to yc
dy
dAT
gD
V
TgA
V
TgA
V
gA
TQ
1
/1
2
3
2
c
c
gyV
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Substitute for yc in:
To get:
)(22 cc yHgV
gHVc 23
1
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If L = length of the weir, then
and
Use
cyLA
ccc
yLVAVQ
32385.0
23
1
1
HLgQ
then
VforgHV
and
yforgy
V
cc
c
c
c
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Remember
hl and V1 were neglected
y2 was assumed to be (yc = P)
L must be corrected depending upon whetherthe equation to be used for fully contracted or
suppressed weirs
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To make the equation more practical
For fully contracted weirs
P
HK
PHfor
HLgKQ
05.040.0
10
2 3
HLLweircontractedfully
2.0
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Example
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To measure the flow rate of wastewater, arectangular weir was used. The flow rate is 0.33
m3/s. Design the weir. The width of therectangular channel to be connected to the weir is2.0 m and the available head (H) is 0.2 m.
Solution
Use a fully suppressed weir and assume length,
L = 2.0 m
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Then, the dimensions of the weir are: L = 2.0 m
P = 0.6 m
mP
PP
HK
KK
HLgKQ
6.0
2.005.040.005.040.0417.0
792.0)2.0()2()81.9(233.0
2
3
3
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Triangular Weir (V-notch weir)
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For low flow rates, triangular weirs are moreaccurate than the rectangular ones.
The hydraulic profile in channels measured bytriangular weirs is exactly similar to that measuredby rectangular weirs
K is obtained from the Figure 3.4 and multipliedby (8/15) as a correction factor.
25
25
2
22tan
22
tan525
162
tan
HgKQ
HgQ
yA c
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Example
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Solve previous example for v-notch weir if:
Q = 0.33 m3/s
Channel width = 2.0 m
H = 0.2 m
Solution
16.4
2
tan
15
8
2.02
tan15
833.0
22
tan15
8
25
25
K
K
HgKQ
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From Figure 3.4 at H = 0.2 m
Values of [ K(8/15) tan (/2) ],in the table, is near 4.16
For > 90 , K = 0.58
then,
4.16 = 0.58 (8/15) tan (/2)tan (/2) = 13.45
so, = 171
K K(8/15) tan (/2)
90 0.583 0.31
60 0.588 0.18
45 0.592 0.13
20 0.609 0.06
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Trapezoidal Weirs
Flow is contracted in trapezoidalweirs
The equation for suppressed weirscan be used:
In this case = 28
32 HLgKQ
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Venturi Meters
Used to measure flow rate in pipes
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21
212
2
2
1
2
2211
21
2
22
2
11
2
1
2
4/4/
sin
22
PPgKAQ
D
d
where
PPgV
VdVD
VAVA
QQce
g
VP
g
VP
t
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Example
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Parshall Flumes
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Can be used with Parshall Flumes
Replace L with W (width of throat)
Replace H with Ha (water surface elevation above flume floor
level in the converging zone)
Then,
K can be obtained from Figure 3.7. Also Table 3.1 showsstandard Parshall flume dimensions.
32385.0 HLgQ
32 aHWgKQ
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Example
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Miscellaneous Flow Meters
Magnetic Flow Meter
(measures flow by producing
magnetic fields)
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What is a Magnetic Flow Meter?
A magnetic flow meter (magnetic flow meter) is avolumetric flow meter which does not have anymoving parts and is ideal for wastewater
applications or any dirty liquid which is conductiveor water based. Magnetic flow meters will generallynot work with hydrocarbons, distilled water andmany non-aqueous solutions). Magnetic flowmeters are also ideal for applications where lowpressure drop and low maintenance are required.
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Principle of Operation
The operation of a magnetic flowmeter or mag meter is
based upon Faraday's Law, which states that the voltageinduced across any conductor as it moves at right anglesthrough a magnetic field is proportional to the velocityof that conductor.
Faraday's Formula:
E is proportional to V B D where:
E = The voltage generated in a conductor
V = The velocity of the conductor
B = The magnetic field strength
D = The length of the conductor
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To apply this principle to flow measurement with a magneticflowmeter, it is necessary first to state that the fluid beingmeasured must be electrically conductive for the Faraday
principle to apply. As applied to the design of magneticflowmeters, Faraday's Law indicates that signal voltage (E) isdependent on the average liquid velocity (V) the magnetic fieldstrength (B) and the length of the conductor (D) (which in thisinstance is the distance between the electrodes).In the case of
wafer-style magnetic flowmeters, a magnetic field is establishedthroughout the entire cross-section of the flow tube (Figure 1). Ifthis magnetic field is considered as the measuring element of themagnetic flowmeter, it can be seen that the measuring element isexposed to the hydraulic conditions throughout the entire cross-section of the flowmeter. With insertion-style flowmeters, the
magnetic field radiates outward from the inserted probe (Figure2).
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Magnetic Meter Selection
The key questions which need to be answered before
selecting a magnetic flowmeter are: Is the fluid conductive or water based? Is the fluid or slurry abrasive? Do you require an integral display or remote display?
Do you require an analog output? What is the minimum and maximum flow rate for the
flow meter? What is the minimum and maximum process pressure? What is the minimum and maximum process
temperature? Is the fluid chemically compatible with the flow meter
wetted parts? What is the size of the pipe? Is the pipe always full?
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Turbine Flow Meters
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Rotameters or Variable Area Flow Meters
Variable area flow meters, orrotameters, use a tube andfloat to measure flow. As thefluid flows through the tube,
the float rises. Equilibriumwill be reached whenpressure and the buoyancy ofthe float counterbalancegravity. The float's height in
the tube is then used toreference a flow rate on acalibrated measurementreference.
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Important Information on Rotameters
The Variable-Area type flowmeter, or Rotameter, is oneof the most economical and reliable of flowmeasurement instruments. In various configurations itcan be designed to withstand high pres sures, corrosive
fluids, high temperatures, and is completelyindependent of factors influencing electronic meters.
They can be calibrated to measure nearly any gas orliquid, because their principles of operation are simple
and well understood. The flow indication is obtainedfrom a balance of the fluid forces underneath the float
with gravity.
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Important Information on Rotameters
This is done using a uniformly tapered tube, a floatwhose diameter is nearly identical to the tube ID at theinlet, and a scale to correlate float height. The flow tube
is traditionally placed in a vertical position and fluidenters from the bottom, forcing the float up in the tubeuntil a sufficient annular opening exists between thefloat and tube to allow the total volume of fluid to flow
past the float. At this point the float is in an equilibriumposition and its height is proportional to the flow rate.
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Important Information on Rotameters
With this in mind, many simple factors influencingrotameter performance are easily understood. Forexample, increasing the density and weight of the float
will require a higher flow rate to force the ball up to anyheight in the tube. In addition, it is easy to see that anychanges in the fluid caused by temperature or pressure
will affect the float's position. This is particularly true
for gases which are compressible, and are therefore,greatly affected by operating pressures. Studies over theyears have resulted in many
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Screening
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Is a unit operation that separates materials intodifferent sizes using screens
Bar Racks or Bar Screen (Fig 5.1)
Are composed of large bars spaced at 2580 mmapart
Used to exclude large particles
Used in water intakes at shores and wastewater
treatment plants Hand cleaned or mechanically cleaned
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Traveling Screens (Fig 5.2)
Used to remove smaller particles in watertreatment plants (following bar screens) such asleaves, small fish and other materials that pass the
bar screen.
Mi t i (Fi 5 3)
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Micro-strainer (Fig 5.3)
Made of very fine fabric or screen wound around a drum
75% of the drum is submerged Rotates at 5 to 45 rpm
Influent is introduced from the underside of the drum andexits into the outside
Strained materials (solids) are retained inside of the drum andremoved by jets of water through a trough inside the drum
Flow of influent is sometimes from the outside to the inside
Used to remove high concentrations of algae (effluent from
stabilization ponds) or treatment of effluents from biologicaltreatment processes
The pore size of micro-strainers range between 2060 m
Material used in micro-strainers include stainless steel andpolyester
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Head Loss in Bar Racks
Apply Bernoulli equation(Fig 5.2)
P = pressure
V = velocity (V1 = approachvelocity)
h = elevation head
g = acceleration due to gravity
2
2
221
2
11
22hg
VPhg
VP
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Approach velocity should be maintained at self-
cleaning velocity ( 0.76 m/s)
Since, P1 = P2 = atmospheric pressure
Then, From continuity equation
122
2
2
1 2 hhgVV
1
22
1
2
12222
1
221
1
2
1
2
A
A
hgA
A
A
hhgAVAQ
thus
A
VAV
B lli i f i i l fl
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Bernoulli equation assumes frictionless flow, to correctfor this, a coefficient of discharge must be added to theequation, thus:
Solve for h
Cd is determined experimentally or a value of 0.84 may beused. As the screen clogs, the value of A2 will decrease.
1
22
1
2
A
A
hgACQ d
22
2
1
22
2
1
AgC
A
AQ
hd
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Head Loss in Micro-strainers
The flow turns at right angle (90) as it enters the openingsof the micro-strainer cloth. Therefore, the approach
velocity (V1) is equal to ZERO. Thus:
Similarly, Cd can be determined experimentally or a valueof 0.60 can be used. The above equation can be applied toscreens where the approach velocity is negligible.
2
2
2
2
2 AgC
Qh
d
D i P t d C it i f
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Design Parameters and Criteria for
Bar Screens
Parameter MechanicallyCleaned ManuallyCleaned
Bar Size
Width, mm
Thickness, mm
520
20
80520
20
80
Bar Clear Spacing, mm 2050 1580Slope from Vertical, degree 3045 030Approach Velocity, m/s 0.30.6 0.61.0
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