Transcript Flow meters

CE 547
Flow Measurement
and Screens
Flow Meters



Flow Meters: are devices used to measure the
flow rate of a fluid
In Water, all types of flow meters can be used
In Wastewater, the choice is critical due to solid
content:
Solids can be removed
 Flow has enough energy to be self-cleaning

Rectangular Weirs
Fully-contracted weir
Suppressed weir:
vertical sides
weir extends to the channel
P = weir height
H = head over the weir
The energy equation between (1) and (2)
2
1
2
2
V
P1
V
P2
  y1  Z1  hl 
  y2  Z 2
2g 
2g 







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
In the figure:
Z1 = Z 2 = 0
V2 >> V1
P1 = 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)
V  Zg ( H  yc )
2
c

Specific energy equation states that:
2
V
E  y
2g



The critical depth, yc, occurs at minimum specific
energy
Differentiate E with respect to y and equate to zero
Use ( Q = VA )



Q = flow rate
V = velocity
A = cross-sectional area
Q 2T
1
3
gA
V

gA T
T


V2
gA / T
V
1
gD
dA
dy
A/T = hydraulic depth, D
D is simply equals to yc
Vc
gy c
Substitute for yc in:
V  2 g ( H  yc )
2
c
To get:
1
Vc 
2 gH
3
If L = length of the weir, then
A  L  yc
and
Q  Vc  A  Vc  L  yc
Use
Vc
gyc
1
for
yc
and
Vc 
1
2 gH
3
for
then
Q  0.385 2 g L H 3
Vc
Remember
 hl and V1 were neglected
 y2 was assumed to be (yc = P)
 L must be corrected depending upon whether
the equation to be used for fully contracted or
suppressed weirs
To make the equation more practical
Q  K 2g L H
for
3
H P  10
H
K  0.40  0.05
P
For fully contracted weirs
L fully
contracted
weir
 L  0.2H
Example
To measure the flow rate of wastewater, a
rectangular weir was used. The flow rate is 0.33
m3/s. Design the weir. The width of the
rectangular channel to be connected to the weir is
2.0 m and the available head (H) is 0.2 m.
Solution
Use a fully suppressed weir and assume length,
L = 2.0 m
Q  K 2g L H 3
0.33  K 2(9.81) (2) (0.2)  0.792
3
K
H
 0.2 
K  0.417  0.40  0.05  0.40  0.05

P
 P 
P  0.6
m
Then, the dimensions of the weir are:
L = 2.0 m
 P = 0.6 m

Triangular Weir (V-notch weir)
For low flow rates, triangular weirs are more
accurate than the rectangular ones.
The hydraulic profile in channels measured by
triangular weirs is exactly similar to that measured
by rectangular weirs
A  y tan
2
c

2
16

Q
tan
2g H 5 2
2
25 5
Q  K tan

2
2g H 5 2
K is obtained from the Figure 3.4 and multiplied
by (8/15) as a correction factor.
Example
Solve previous example for v-notch weir if:
Q = 0.33 m3/s
 Channel width = 2.0 m
 H = 0.2 m

Solution
8 
Q  K   tan
2g H 5 2
2
 15 
8 
52
0.33  K   tan 0.2
2
 15 
8 
K   tan  4.16
2
 15 
From Figure 3.4 at H = 0.2 m

K
K(8/15) tan (/2)
90
0.583
0.31
For  > 90 , K = 0.58
60
0.588
0.18
then,
4.16 = 0.58 (8/15) tan (/2)
tan (/2) = 13.45
so,  = 171
45
0.592
0.13
20
0.609
0.06
Values of [ K(8/15) tan (/2)
], in the table, is near 4.16
Trapezoidal Weirs


Flow is contracted in trapezoidal
weirs
The equation for suppressed weirs
can be used:
Q  K 2g L H

In this case  = 28
3
Venturi Meters

Used to measure flow rate in pipes
V12 P2 V22

 
 2g  2g
sin ce
Q1  Q2
P1
A1V1  A2V2
D / 4V  d
2
1
2

/ 4 V2
2 g P1  P2 
V2 
 1   
where
d

D
Q  KAt
2 g P1  P2 

Example
Parshall Flumes
Q  0.385 2 g L H
3
 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,
Q  K 2 gW H
3
a
K can be obtained from Figure 3.7. Also Table 3.1 shows
standard Parshall flume dimensions.
Example
Miscellaneous Flow Meters
Magnetic Flow Meter
(measures flow by producing
magnetic fields)
What is a Magnetic Flow Meter?
A magnetic flow meter (magnetic flow meter) is a
volumetric flow meter which does not have any
moving parts and is ideal for wastewater
applications or any dirty liquid which is conductive
or water based. Magnetic flow meters will
generally not work with hydrocarbons, distilled
water and many non-aqueous solutions). Magnetic
flow meters are also ideal for applications where
low pressure drop and low maintenance are
required.
Principle of Operation
The operation of a magnetic flowmeter or mag meter is
based upon Faraday's Law, which states that the voltage
induced across any conductor as it moves at right angles
through a magnetic field is proportional to the velocity
of 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
To apply this principle to flow measurement with a magnetic
flowmeter, it is necessary first to state that the fluid being
measured must be electrically conductive for the Faraday
principle to apply. As applied to the design of magnetic
flowmeters, Faraday's Law indicates that signal voltage (E) is
dependent on the average liquid velocity (V) the magnetic field
strength (B) and the length of the conductor (D) (which in this
instance is the distance between the electrodes).In the case of
wafer-style magnetic flowmeters, a magnetic field is established
throughout the entire cross-section of the flow tube (Figure 1). If
this magnetic field is considered as the measuring element of the
magnetic flowmeter, it can be seen that the measuring element is
exposed to the hydraulic conditions throughout the entire crosssection of the flowmeter. With insertion-style flowmeters, the
magnetic field radiates outward from the inserted probe (Figure
2).
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?
Turbine Flow Meters
Rotameters or Variable Area Flow Meters
Variable area flow meters, or
rotameters, use a tube and
float to measure flow. As the
fluid flows through the tube,
the float rises. Equilibrium
will be reached when
pressure and the buoyancy
of the float counterbalance
gravity. The float's height in
the tube is then used to
reference a flow rate on a
calibrated
measurement
reference.
Important Information on Rotameters


The Variable-Area type flowmeter, or Rotameter, is one
of the most economical and reliable of flow
measurement instruments. In various configurations it
can be designed to withstand high pres sures, corrosive
fluids, high temperatures, and is completely
independent of factors influencing electronic meters.
They can be calibrated to measure nearly any gas or
liquid, because their principles of operation are simple
and well understood. The flow indication is obtained
from a balance of the fluid forces underneath the float
with gravity.
Important Information on Rotameters

This is done using a uniformly tapered tube, a float
whose diameter is nearly identical to the tube ID at the
inlet, and a scale to correlate float height. The flow tube
is traditionally placed in a vertical position and fluid
enters from the bottom, forcing the float up in the tube
until a sufficient annular opening exists between the
float and tube to allow the total volume of fluid to flow
past the float. At this point the float is in an equilibrium
position and its height is proportional to the flow rate.
Important Information on Rotameters

With this in mind, many simple factors influencing
rotameter performance are easily understood. For
example, increasing the density and weight of the float
will require a higher flow rate to force the ball up to any
height in the tube. In addition, it is easy to see that any
changes 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 the
years have resulted in many
Screening
Is a unit operation that separates materials into
different sizes using screens
Bar Racks or Bar Screen (Fig 5.1)
Are composed of large bars spaced at 25 – 80 mm
apart
 Used to exclude large particles
 Used in water intakes at shores and wastewater
treatment plants
 Hand cleaned or mechanically cleaned

Traveling Screens (Fig 5.2)
Used to remove smaller particles in water
treatment plants (following bar screens) such as
leaves, small fish and other materials that pass the
bar screen.
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 and
exits into the outside
Strained materials (solids) are retained inside of the drum and
removed 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 biological
treatment processes
The pore size of micro-strainers range between 20 – 60 m
Material used in micro-strainers include stainless steel and
polyester
Head Loss in Bar Racks
Apply Bernoulli equation
(Fig 5.2)
V12
P2 V22

 h1  
 h2
 2g
 2g
P1




P = pressure
V = velocity (V1 = approach
velocity)
h = elevation head
g = acceleration due to gravity
Approach velocity should be maintained at selfcleaning velocity (  0.76 m/s)
Since, P1 = P2 = atmospheric pressure
V  V  2 g h2  h1 
2
1
2
2
Then, From continuity equation
A2V2
V1 
A1
thus
Q  A2V2  A2
2 g h2  h1 
2 gh
 A2
A2
A2
1
1
A1
A1
Bernoulli equation assumes frictionless flow, to correct for
this, a coefficient of discharge must be added to the
equation, thus:
Q  Cd A2
2 gh
A2
1
A1
Solve for h
 A2 
Q 1  
A1 

h 
2 gCd2 A22
2
Cd is determined experimentally or a value of 0.84 may be
used. As the screen clogs, the value of A2 will decrease.
Head Loss in Micro-strainers
The flow turns at right angle (90) as it enters the
openings of the micro-strainer cloth. Therefore, the
approach velocity (V1) is equal to ZERO. Thus:
2
Q
h 
2 2
2 gC d A2
Similarly, Cd can be determined experimentally or a value
of 0.60 can be used. The above equation can be applied
to screens where the approach velocity is negligible.
Design Parameters and Criteria for
Bar Screens
Parameter
Mechanically
Cleaned
Manually
Cleaned
Bar Size
 Width, mm
 Thickness, mm
5 – 20
20 – 80
5 – 20
20 – 80
Bar Clear Spacing, mm
20 – 50
15 – 80
Slope from Vertical, degree
30 – 45
0 – 30
Approach Velocity, m/s
0.3 – 0.6
0.6 – 1.0