04 flow control

8/6/2019 04 Flow Control

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Monroe L. Weber-ShirkSchool ofCiviland

Environmental Engineering

Flow ControlFlow Control

Creativity without a trip

Variations on a dripGiving head loss the slip
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Overview

Why is constant flow desirable? If you had electricity

Hypochlorinators in Honduras Hole in a BucketConstant head devicesOverflow tanksMarriot bottleFloatsFloat valve

Orifices and surface tensionFlow Measurement


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Why is constant flow desirable for

POU treatment devices?

Why is constant flow desirable for

POU treatment devices?

Slow constant treatment can use a smallerreactor than intermittent treatment

It isnt reasonable to expect to treat ondemand in a householdFlow variations are huge (max/average=_____)

System would be idle most of the timeUse a mini clearwell so that a ready supply

of treated water is always available

40


5/38

If you had electricityIf you had electricity

Metering pumps (positive displacement)Pistons

Gears

Peristaltic

Valves with feedback from flow sensors

So an alternative would be to raise the per capitaincome and provide electrical service to everyone

But a simpler solution would be better!


6/38

Constant Head: Floats

(variation on hypochlorinator)

Constant Head: Floats

(variation on hypochlorinator)

orifice

VERY Flexible hose

Head can be

varied bychanging

buoyancy of

float

Supercriticalopen channel

flow!

Unaffected by downstream conditions!

2orifice orifice

Q K A g h=

h


7/38

Floating BowlFloating Bowl

Adjust the flow by changing the rocks

Need to make

adjustments (INSIDE)the chemical tank

Rocks are submerged in

the chemical

Safety issues


8/38

Chemical Metering

(Hypochlorinator)

Chemical Metering

(Hypochlorinator)

Transparent

flexible tube

(0.5)

1.0 m

1.05 m1.78 m

1.5 PVC

overflow tube

Float

PVC needle

valve 0.5 PVC tube

Water in the distribution tank

What is the simplest

representation that

captures the fluid

mechanics of this

system?


9/38

Hole in a BucketHole in a Bucket

Vena contracta

0.6vc orificeA A

Orifice

2orifice orifice

Q K A g h=

h

0.6orificeK


10/38

Transparent

flexible tube

(0.5)

1.0 m

1.05 m1.78 m

1.5 PVC

overflow tube

Float

PVC needle

valve 0.5 PVC tube


Transparent

flexible tube

(0.5)

1.0 m

1.05 m1.78 m

1.5 PVC

overflow tube

Float

PVC needle

valve 0.5 PVC tube


Use Control Volume Equation:

Conservation of Mass

h0orcv

Q dVt=

2or or or Q K A gh=

2 0res or or dh

A K A ghdt + =

resor

A dhdVQ

dt dt = =

cs cv

dA dV t

r r

=-

Vn

Orifice in the PVC valve

Integrate to get h as f(t)

volume

2V gh=


11/38

Finding the chlorine depth as f(t)

0 02

h t

res

hor or

A dhdt

K A g h

=

( )1/2 1/2022

res

or or

Ah h t

K A g

=

0 22

oror

res

Ah h tK g A=

Integrate

Solve for height

Separate variables


12/38

Finding Q as f(t)Finding Q as f(t)

2or orQ K A gh=

02 2

2

or or or or

res

tK AQ K A g h g

A

=

0

02

or

or

QA

K gh

=

Find Aor as function of initial target flow rate

Set the valve to get desired dose initially

0 22

oror

res

Ah h tK g

A=


13/38

Surprise Q and chlorine dose

decrease linearly with time!

Surprise Q and chlorine dose

decrease linearly with time!

0 0

1

1 2

res

design

hQ t

Q t h=

0

02or

or

QA

K gh=

02 22

or or or or

res

tK AQ K A g h g

A

=

Relationship between Q0 and Ares ?

Assume flow at Q0 for time (tdesign ) would empty reservoir0 design res resQt A h=

0 res

res design

Q h

A t=

2

200

1

1 2

Cl res

Cl design

C ht

C t h

=

0

0 01 2 res

tQQ

Q A h= Linear decrease in flow


14/38

Effect of tank height above valveEffect of tank height above valve

2

02

0

Qh h

Q=

0 2 4 6 80

0.2

0.4

0.6

0.8

0

0.2

0.4

0.6

0.8

Qratio t tdesign, hres, h0,( )

h t tdesign, hres, h0,( ) h0 hres( )

hres

t

day

Depth in

reservoir

Case 1, h0=50 m,

hres = 1 m,

tdesign =4 days

0 2 4 6 80

0.2

0.4

0.6

0.8

0

0.2

0.4

0.6

0.8

Qratio t tdesign, hres, h0,( )h t tdesign, hres, h0,( ) h0 hres( )

hres

t

day

Case 1, h0=1 m,hres = 1 m,

tdesign =4 days


15/38


16/38

Constant Head:

Marriot bottle

Constant Head:

Marriot bottle

A simple constant head device

Why is pressure at the top ofthe filter independent of waterlevel in the Marriot bottle?

What is the head loss for thisfilter?

Disadvantage? ___________

2 2

2 2

in in out out in in P out out T L

p V p V z h z h hg g

+ + + = + + + +

Lh

batch system


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Constant Head: Float ValveConstant Head: Float Valve

Float adjusts opening

to maintain relativelyconstant water level in

lower tank

(independent of uppertank level)

NOT Flow Control!?

Describe sequence of events after filling


18/38

Flow Control Valve (FCV)

Limits the ____ ___

through the valve to a

specified value, in aspecified direction

Calculate the sizes of

the openings and thecorresponding

pressures for the

flows of interest

flow rate Expensive Work best with large

Q and large head loss


19/38

Raw water reservoir and SSF

Flow control device

Clean water reservoir

Small diameter tubing

Float valve and small

tube

Float valve and small

tube


20/38

Floating Ball ValveFloating Ball Valve

Float valve

Small

diameter

tube


21/38

Float valve with IV dripFloat valve with IV drip

. cm83. cm110

. cm05

. cm44

. cm65

mm2

. cm23

. cm91

mm2

. cm56

. cm15

cm2

. cm52 Housing Dimensions:

ID = . cm785

OD = . cm88

Floatmass:

grams6

IV roller

clamp

Rubber tip

Barb tubing

adapter

PVC

stem

IV tubing(~ drops/10 mL)

. cm83. cm110

. cm05

. cm44

. cm65

mm2

. cm23

. cm91

mm2

. cm56

. cm15

cm2

. cm52 Housing Dimensions:

ID = . cm785

OD = . cm88

Floatmass:

grams6

IV roller

clamp

Rubber tip

Barb tubing

adapter

PVC

stem

IV tubing(~ drops/10 mL)


22/38

Floating Bowl with OrificeFloating Bowl with Orifice


23/38

Sandcolumn

HJR

Holding container

(bucket or glass

column)

Pong pipe

Sealing pipe

Driving pressure for sand column

Upflow prevents trapped air

(keyword: prevent)!


24/38

Flow Control Competition Results

from CEE 454 in 2004

Flow Control Competition Results

from CEE 454 in 2004

What are the two essential elements of

gravity powered flow control?

Constant head (float valve wins!)

Head loss elements

____________________________________

________________________________________________________

Can use flexible tube to facilitate adjusting the

head

Orifice i.e.. small hole or restriction

Long small diameter tubePorous media


25/38

Flow control device

Small diameter tubing

Float valve and small tube

(Gravity dosing system)

Float valve and small tube

(Gravity dosing system)

hlf 2 4

32 128 LV LQh

gD g D

= =

4

l

128

h g DQ

L

=

chemical stock tank

If laminar flow!

2 2

2 2

in in out out in in P out out T L

p V p V z h z h h

g g

+ + + = + + + +

L in out h z z= Neglecting minor losses


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Long small tube head lossLong small tube head loss

Laminar flow

Turbulent Flow

f 2 4

32 128 LV LQh

gD g D

= =

2

f 2 5

8

f

LQ

h g D=2

0.9

0.25f

5.74log3.7 ReD

= + D

Q4Re =

Flow proportional to hf


27/38

Orifice flowOrifice flow

2

42

8

v

QD K

g h=

2orQ K A gh=2

2 2 4

1 8

or

Qh

K g D=

2

1

or

KK

=

Solve for h and substitute

area of a circle to obtain same

form as minor loss equationKor = 0.63 therefore K=2.5

2.5 d 8 d

d

h

D


28/38

Porous Media Head Loss: Kozeny

equation

Porous Media Head Loss: Kozeny

equation

f 2

32 pore

pore

LVh

gd

=

apore

VV

= Velocity of fluid above the porous media

Laminar flow assumption

( ) 2f3 2

136 a

sand

Vhk

L gd

=

k= Kozeny constant

Approximately 5 for

most filtration conditions


29/38

Tube vs. OrificeTube vs. Orifice

Clogging

Adjustability

0 50 100 150 2000

1

2

3

Dtube Q 20cm, 1m, ,( )

mm

Dorifice2.5 Q, 20cm,( )

mm

Q

mL

min

Dtube Q hf, L, ,( )128 L Q

g hf

1

4

:=Dorifice K Q, he,( ) K8 Q

2

g 2 he

1

4

:=

Minor losses Major losses


30/38

Surface TensionSurface Tension

hIs the force of gravity stronger than surface tension?

34

3 2g

rF g

=

2 rF =

Fp=( )

324 2 r

3 2

rg g h r

+ =

( )2 g h r

Will the droplet drop?


31/38

Surface Tension can prevent flow!Surface Tension can prevent flow!

0.050

0.0550.0600.0650.0700.075

0.080

0 20 40 60 80 100

Temperature (C)

S

urfacetens i

on(N

/m)

( )3

24 2 r3 2

rg g h r

+ =

( )

3

2

42 r

3 2

rg

h g r

=

Solve for height of waterrequired to form droplet

2 2

3

rh

gr

=


32/38

Design constraint for flow control

devices: Surface Tension

Design constraint for flow control

devices: Surface Tension

0.1 1 101

10

100

h r( )mm

r

mm

2 2

3

rh

gr

=

Delineates the

boundary between

stable and unstable

No droplets form to left of line

Flow control devices

need to be designed

to operate to the

right of the red line!


33/38

Hypochorinator FixHypochorinator Fix

http://web.mit.edu/d-lab/honduras.htm

What is good?

How could you improve this system?

What might fail?Safety hazards?


34/38

Modular Flow

Control

Modular Flow

Control


35/38

Identify the Flow Controller Failure

Modes

Identify the Flow Controller Failure

Modes

Moving parts

Wear

Corrosion (especially with corrosive chemicals) Precipitation (e.g. calcium carbonate)

Incompatible materials

Dont forget sunlight has UV rays!Clogging

Design errors


36/38

Flow Measurement DevicesFlow Measurement Devices

Orifice in the side of a pipe

Pipe vented through water

surface Jet of water must free fall

inside the pipe

Korifice

is due to the vena

contracta and has a value

of approximately 0.6.

hgAKQ orificeorifice = 2

h


37/38

Free Surface with Orifice limitationsFree Surface with Orifice limitations

The head loss from making themeasurement is wasted (likely on theorder of 20 cm)

Ability to include this type of flow

measurement depends on availability ofexcess potential energy The useable measurement range doesnt

include the range where the orifice isonly partially submerged

Thus large diameter orifices arent ideal

because they limit the measurementrange For reasonably small head loss the flow

per orifice cant be much greater than100 Lpm

Use multiple orifices for larger flow

rates

Qplant d h,( ) Korifice

d2

4 2 g h:=

40 60 80 100 120 1400

5

10

15

20

25

h

cm

Qplant d h,( )

L

min


38/38

Alternative Flow MeasurementsAlternative Flow Measurements

Block the effluent port from a small tank and measurethe rate of depth increaseThe grit chamber at the head of a water treatment plant could

be used for this purpose

But this causes a major flow disturbance for the plant

open channel weirs for very large flow ratemeasurements

Orifice plates in a pipe (use manometer to measure

pressure drop) If you have access to electricity, then there are a large

number of measurement techniques available

04 flow control

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