Flow Measurement Flow Measurement and Screensand Screens

CE 547CE 547

Flow MetersFlow Meters

Flow Meters: are devices used to Flow Meters: are devices used to measure the flow rate of a fluidmeasure the flow rate of a fluid

In Water, all types of flow meters In Water, all types of flow meters can be usedcan be used

In Wastewater, the choice is critical In Wastewater, the choice is critical due to solid content:due to solid content: Solids can be removedSolids can be removed Flow has enough energy to be self-Flow has enough energy to be self-

cleaningcleaning

Rectangular WeirsRectangular Weirs

Fully-contracted weirFully-contracted weir

Suppressed weir: weir extends to the Suppressed weir: weir extends to the channel vertical sides channel vertical sides

P = weir heightP = weir height

H = head over the weirH = head over the weir

The energy equation between (1) and (2)The energy equation between (1) and (2)

V = velocity (average)V = velocity (average) P = pressureP = pressure y = height above bottom of channely = height above bottom of channel Z = height of bottom above a datumZ = height of bottom above a datum hhll = head loss between (1) and (2) = head loss between (1) and (2) g = gravitational constantg = gravitational constant = specific weight of water= specific weight of water

222

22

111

21

22Zy

P

g

VhZy

P

g

Vl

In the figure:In the figure:

ZZ11 = Z = Z22 = 0 = 0

VV22 >> V >> V11

PP11 = P = P22 = atmospheric pressure = atmospheric pressure

If hIf hll was neglected, then: was neglected, then:

yy11 = H + P = H + P

yy22 = y = ycc + P + P

Substitute in the energy equation and Substitute in the energy equation and change Vchange V22 to V to Vcc (critical velocity) (critical velocity)

)(2cc yHZgV

Specific energy equation states that:Specific energy equation states that:

The critical depth, yThe critical depth, ycc, occurs at minimum , occurs at minimum specific energyspecific energy

Differentiate E with respect to y and Differentiate E with respect to y and equate to zeroequate to zero

Use ( Q = VA )Use ( Q = VA ) Q = flow rateQ = flow rate V = velocityV = velocity A = cross-sectional areaA = cross-sectional area

g

VyE

2

2

A/T = hydraulic depth, DA/T = hydraulic depth, D D is simply equals to yD is simply equals to ycc

dy

dAT

gD

V

TgA

V

TgA

V

gA

TQ

1

/1

2

3

2

c

c

gy

V

Substitute for ySubstitute for ycc in: in:

To get:To get:

)(22cc yHgV

gHVc 23

1

If L = length of the weir, thenIf L = length of the weir, then

and and

UseUse

cyLA

ccc yLVAVQ

32385.0

23

1

1

HLgQ

then

VforgHV

and

yforgy

V

cc

c

c

c

RememberRemember hhll and V and V11 were neglected were neglected

yy22 was assumed to be (y was assumed to be (ycc = P) = P) L must be corrected depending L must be corrected depending

upon whether the equation to be upon whether the equation to be used for fully contracted or used for fully contracted or suppressed weirssuppressed weirs

To make the equation more practicalTo make the equation more practical

For fully contracted weirsFor fully contracted weirs

P

HK

PHfor

HLgKQ

05.040.0

10

2 3

HLLweircontractedfully

2.0

ExampleExample

To measure the flow rate of wastewater, a To measure the flow rate of wastewater, a rectangular weir was used. The flow rate rectangular weir was used. The flow rate is 0.33 mis 0.33 m33/s. Design the weir. The width /s. Design the weir. The width of the rectangular channel to be of the rectangular channel to be connected to the weir is 2.0 m and the connected to the weir is 2.0 m and the available head (H) is 0.2 m. available head (H) is 0.2 m.

SolutionSolution

Use a fully suppressed weir and assume Use a fully suppressed weir and assume length, length,

L = 2.0 mL = 2.0 m

Then, the dimensions of the weir are:Then, the dimensions of the weir are: L = 2.0 mL = 2.0 m P = 0.6 mP = 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

Triangular Weir (V-notch Triangular Weir (V-notch weir)weir)

For low flow rates, triangular weirs are For low flow rates, triangular weirs are more accurate than the rectangular ones.more accurate than the rectangular ones.The hydraulic profile in channels The hydraulic profile in channels measured by triangular weirs is exactly measured by triangular weirs is exactly similar to that measured by rectangular similar to that measured by rectangular weirsweirs

K is obtained from the Figure 3.4 and K is obtained from the Figure 3.4 and multiplied by (8/15) as a correction factor.multiplied by (8/15) as a correction factor.

25

25

2

22

tan

22

tan525

162

tan

HgKQ

HgQ

yA c

Example Example

Solve previous example for v-notch Solve previous example for v-notch weir if:weir if:

Q = 0.33 mQ = 0.33 m33/s/s Channel width = 2.0 mChannel width = 2.0 m H = 0.2 mH = 0.2 m

SolutionSolution

16.42

tan15

8

2.02

tan15

833.0

22

tan15

8

25

25

K

K

HgKQ

From Figure 3.4 at H = From Figure 3.4 at H = 0.2 m0.2 m

Values of [ K(8/15) tan Values of [ K(8/15) tan ((/2) ], in the table, is near /2) ], in the table, is near 4.164.16

For For > 90 > 90 , K = 0.58 , K = 0.58

then,then,

4.16 = 0.58 (8/15) tan 4.16 = 0.58 (8/15) tan ((/2)/2)

tan (tan (/2) = 13.45/2) = 13.45

so, so, = 171 = 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

Trapezoidal WeirsTrapezoidal Weirs

Flow is contracted in Flow is contracted in trapezoidal weirstrapezoidal weirs

The equation for The equation for suppressed weirs can be suppressed weirs can be used:used:

In this case In this case = 28 = 28

32 HLgKQ

Venturi MetersVenturi Meters

Used to measure flow rate in pipesUsed to measure flow rate in pipes

21

212

22

12

2211

21

222

211

2

1

2

4/4/

sin

22

PPgKAQ

D

d

where

PPgV

VdVD

VAVA

QQ

ce

g

VP

g

VP

t

ExampleExample

Parshall FlumesParshall Flumes

Can be used with Parshall FlumesCan be used with Parshall FlumesReplace L with W (width of throat)Replace L with W (width of throat)Replace H with HReplace H with Haa (water surface elevation (water surface elevation

above flume floor level in the converging zone)above flume floor level in the converging zone)

Then,Then,

K can be obtained from Figure 3.7. Also K can be obtained from Figure 3.7. Also Table 3.1 shows standard Parshall flume Table 3.1 shows standard Parshall flume dimensions.dimensions.

32385.0 HLgQ

32 aHWgKQ

ExampleExample

Miscellaneous Flow Miscellaneous Flow Meters Meters

Magnetic Flow Meter Magnetic Flow Meter

(measures flow by (measures flow by producing magnetic producing magnetic fields)fields)

What is a Magnetic Flow Meter?What is a Magnetic Flow Meter?

A magnetic flow meter (magnetic flow A magnetic flow meter (magnetic flow meter) is a volumetric flow meter which meter) is a volumetric flow meter which does not have any moving parts and is does not have any moving parts and is ideal for wastewater applications or any ideal for wastewater applications or any dirty liquid which is conductive or water dirty liquid which is conductive or water based. Magnetic flow meters will generally based. Magnetic flow meters will generally not work with hydrocarbons, distilled not work with hydrocarbons, distilled water and many non-aqueous solutions). water and many non-aqueous solutions). Magnetic flow meters are also ideal for Magnetic flow meters are also ideal for applications where low pressure drop and applications where low pressure drop and low maintenance are required. low maintenance are required.

Principle of OperationPrinciple of Operation

The operation of a magnetic flowmeter or mag meter is The operation of a magnetic flowmeter or mag meter is based upon Faraday's Law, which states that the voltage based upon Faraday's Law, which states that the voltage induced across any conductor as it moves at right angles induced across any conductor as it moves at right angles through a magnetic field is proportional to the velocity through a magnetic field is proportional to the velocity of that conductor.of that conductor.

Faraday's Formula:Faraday's Formula:

E E is proportional to is proportional to V V B B D D where:where:

E E = The voltage generated in a conductor= The voltage generated in a conductor V V = The velocity of the conductor= The velocity of the conductor B B = The magnetic field strength= The magnetic field strength D D = The length of the conductor= The length of the conductor

To apply this principle to flow measurement with a magnetic To apply this principle to flow measurement with a magnetic flowmeter, it is necessary first to state that the fluid being flowmeter, it is necessary first to state that the fluid being measured must be electrically conductive for the Faraday measured must be electrically conductive for the Faraday principle to apply. As applied to the design of magnetic principle to apply. As applied to the design of magnetic flowmeters, Faraday's Law indicates that signal voltage flowmeters, Faraday's Law indicates that signal voltage (E)(E) is is dependent on the average liquid velocity dependent on the average liquid velocity (V) (V) the magnetic field the magnetic field strength strength (B)(B) and the length of the conductor and the length of the conductor (D)(D) (which in this (which in this instance is the distance between the electrodes).In the case of instance is the distance between the electrodes).In the case of wafer-style magnetic flowmeters, a magnetic field is established wafer-style magnetic flowmeters, a magnetic field is established throughout the entire cross-section of the flow tube (Figure 1). If throughout the entire cross-section of the flow tube (Figure 1). If this magnetic field is considered as the measuring element of the this magnetic field is considered as the measuring element of the magnetic flowmeter, it can be seen that the measuring element is magnetic flowmeter, it can be seen that the measuring element is exposed to the hydraulic conditions throughout the entire cross-exposed to the hydraulic conditions throughout the entire cross-section of the flowmeter. With insertion-style flowmeters, the section of the flowmeter. With insertion-style flowmeters, the magnetic field radiates outward from the inserted probe (Figure magnetic field radiates outward from the inserted probe (Figure 2).2).

Magnetic Meter SelectionMagnetic Meter Selection

The key questions which need to be answered The key questions which need to be answered before selecting a magnetic flowmeter are:before selecting a magnetic flowmeter are:

Is the fluid conductive or water based?Is the fluid conductive or water based? Is the fluid or slurry abrasive?Is the fluid or slurry abrasive? Do you require an integral display or remote Do you require an integral display or remote

display?display? Do you require an analog output?Do you require an analog output? What is the minimum and maximum flow rate What is the minimum and maximum flow rate

for the flow meter?for the flow meter? What is the minimum and maximum process What is the minimum and maximum process

pressure?pressure? What is the minimum and maximum process What is the minimum and maximum process

temperature?temperature? Is the fluid chemically compatible with the Is the fluid chemically compatible with the

flow meter wetted parts?flow meter wetted parts? What is the size of the pipe?What is the size of the pipe? Is the pipe always full?Is the pipe always full?

Turbine Flow MetersTurbine Flow Meters

Rotameters or Variable Area Flow Rotameters or Variable Area Flow

MetersMeters Variable area flow Variable area flow meters, or rotameters, meters, or rotameters, use a tube and float to use a tube and float to measure flow. As the measure flow. As the fluid flows through the fluid flows through the tube, the float rises. tube, the float rises. Equilibrium will be Equilibrium will be reached when pressure reached when pressure and the buoyancy of the and the buoyancy of the float counterbalance float counterbalance gravity. The float's gravity. The float's height in the tube is height in the tube is then used to reference a then used to reference a flow rate on a calibrated flow rate on a calibrated measurement reference.measurement reference.

Important Information on Important Information on RotametersRotameters

The Variable-Area type flowmeter, or Rotameter, The Variable-Area type flowmeter, or Rotameter, is one of the most economical and reliable of flow is one of the most economical and reliable of flow measurement instruments. In various measurement instruments. In various configurations it can be designed to withstand configurations it can be designed to withstand high pres sures, corrosive fluids, high high pres sures, corrosive fluids, high temperatures, and is completely independent of temperatures, and is completely independent of factors influencing electronic meters.factors influencing electronic meters.

They can be calibrated to measure nearly any gas They can be calibrated to measure nearly any gas or liquid, because their principles of operation or liquid, because their principles of operation are simple and well understood. The flow are simple and well understood. The flow indication is obtained from a balance of the fluid indication is obtained from a balance of the fluid forces underneath the float with gravity. forces underneath the float with gravity.

Important Information on Important Information on RotametersRotameters

This is done using a uniformly tapered tube, a This is done using a uniformly tapered tube, a float whose diameter is nearly identical to the float whose diameter is nearly identical to the tube ID at the inlet, and a scale to correlate tube ID at the inlet, and a scale to correlate float height. The flow tube is traditionally float height. The flow tube is traditionally placed in a vertical position and fluid enters placed in a vertical position and fluid enters from the bottom, forcing the float up in the from the bottom, forcing the float up in the tube until a sufficient annular opening exists tube until a sufficient annular opening exists between the float and tube to allow the total between the float and tube to allow the total volume of fluid to flow past the float. At this volume of fluid to flow past the float. At this point the float is in an equilibrium position point the float is in an equilibrium position and its height is proportional to the flow rate. and its height is proportional to the flow rate.

Important Information on Important Information on RotametersRotameters

With this in mind, many simple factors With this in mind, many simple factors influencing rotameter performance are easily influencing rotameter performance are easily understood. For example, increasing the density understood. For example, increasing the density and weight of the float will require a higher flow and weight of the float will require a higher flow rate to force the ball up to any height in the rate to force the ball up to any height in the tube. In addition, it is easy to see that any tube. In addition, it is easy to see that any changes in the fluid caused by temperature or changes in the fluid caused by temperature or pressure will affect the float's position. This is pressure will affect the float's position. This is particularly true for gases which are particularly true for gases which are compressible, and are therefore, greatly affected compressible, and are therefore, greatly affected by operating pressures. Studies over the years by operating pressures. Studies over the years have resulted in many have resulted in many

ScreeningScreening

Is a unit operation that separates Is a unit operation that separates materials into different sizes using materials into different sizes using screensscreens

Bar Racks or Bar Screen (Fig 5.1)Bar Racks or Bar Screen (Fig 5.1) Are composed of large bars spaced at Are composed of large bars spaced at

25 – 80 mm apart25 – 80 mm apart Used to exclude large particlesUsed to exclude large particles Used in water intakes at shores and Used in water intakes at shores and

wastewater treatment plantswastewater treatment plants Hand cleaned or mechanically cleanedHand cleaned or mechanically cleaned

Traveling Screens (Fig 5.2)Traveling Screens (Fig 5.2)

Used to remove smaller particles in Used to remove smaller particles in water treatment plants (following bar water treatment plants (following bar screens) such as leaves, small fish and screens) such as leaves, small fish and other materials that pass the bar other materials that pass the bar screen.screen.

Micro-strainer (Fig 5.3)Micro-strainer (Fig 5.3)

Made of very fine fabric or screen wound around a Made of very fine fabric or screen wound around a drumdrum

75% of the drum is submerged75% of the drum is submerged Rotates at 5 to 45 rpmRotates at 5 to 45 rpm Influent is introduced from the underside of the drum Influent is introduced from the underside of the drum

and exits into the outsideand exits into the outside Strained materials (solids) are retained inside of the Strained materials (solids) are retained inside of the

drum and removed by jets of water through a trough drum and removed by jets of water through a trough inside the druminside the drum

Flow of influent is sometimes from the outside to the Flow of influent is sometimes from the outside to the insideinside

Used to remove high concentrations of algae (effluent Used to remove high concentrations of algae (effluent from stabilization ponds) or treatment of effluents from stabilization ponds) or treatment of effluents from biological treatment processesfrom biological treatment processes

The pore size of micro-strainers range between 20 – 60 The pore size of micro-strainers range between 20 – 60 mm

Material used in micro-strainers include stainless steel Material used in micro-strainers include stainless steel and polyesterand polyester

Head Loss in Bar RacksHead Loss in Bar Racks

Apply Bernoulli Apply Bernoulli equation (Fig 5.2)equation (Fig 5.2)

P = pressureP = pressure V = velocity (V1 = V = velocity (V1 =

approach velocity)approach velocity) h = elevation headh = elevation head g = acceleration due to g = acceleration due to

gravitygravity

2

222

1

211

22h

g

VPh

g

VP

Approach velocity should be Approach velocity should be maintained at self-cleaning velocity maintained at self-cleaning velocity ( ( 0.76 m/s) 0.76 m/s)

Since, PSince, P11 = P = P22 = atmospheric pressure = atmospheric pressure

Then, From continuity equationThen, From continuity equation

122

22

1 2 hhgVV

1

22

1

2

12222

1

221

1

2

1

2

A

Ahg

A

A

Ahhg

AVAQ

thus

A

VAV

Bernoulli equation assumes frictionless flow, Bernoulli equation assumes frictionless flow, to correct for this, a coefficient of discharge to correct for this, a coefficient of discharge must be added to the equation, thus:must be added to the equation, thus:

Solve for Solve for hh

CCdd is determined experimentally or a value of is determined experimentally or a value of 0.84 may be used. As the screen clogs, the 0.84 may be used. As the screen clogs, the value of Avalue of A22 will decrease. will decrease.

1

22

1

2

A

Ahg

ACQ d

22

21

22

2

1

AgC

A

AQ

hd

Head Loss in Micro-Head Loss in Micro-strainersstrainers

The flow turns at right angle (90The flow turns at right angle (90) as it enters the ) as it enters the openings of the micro-strainer cloth. Therefore, openings of the micro-strainer cloth. Therefore, the approach velocity (Vthe approach velocity (V11) is equal to ZERO. Thus:) is equal to ZERO. Thus:

Similarly, CSimilarly, Cdd can be determined experimentally or can be determined experimentally or a value of 0.60 can be used. The above equation a value of 0.60 can be used. The above equation can be applied to screens where the approach can be applied to screens where the approach velocity is negligible.velocity is negligible.

22

2

2

2 AgC

Qh

d

Design Parameters and Design Parameters and Criteria for Bar ScreensCriteria for Bar Screens

Parameter Mechanically Cleaned

Manually Cleaned

Bar Size Width, mm Thickness, mm

5 – 2020 – 80

5 – 2020 – 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