Flow Control
Creativity without a trip
Variations on a drip
Giving head loss the slip
Monroe L. Weber-Shirk
School of Civil and
Environmental Engineering
Overview
 Why is constant flow desirable?
 If you had electricity
 Hypochlorinators in Honduras – Hole in a Bucket
 Constant head devices
 Overflow tanks
 Marriot bottle
 Floats
 Float valve
 Orifices and surface tension
 Flow Measurement
Applications of Constant Flow
 POU treatment devices (Point of Use)
 UV disinfection
 clay pot filters
 SSF (slow sand filters)
 arsenic removal devices
 Reagent addition for community treatment
processes
 Alum for ____________
coagulation
 Calcium or sodium hypochlorite for ____________
disinfection
 Sodium carbonate for _____________
pH control
 Could you make a flow control device that
increased the dose in proportion to the main flow?
Why is constant flow desirable for
POU treatment devices?
Slow constant treatment can use a smaller
reactor than intermittent treatment
It isn’t reasonable to expect to treat on
demand in a household
40
Flow variations are huge (max/average=_____)
System would be idle most of the time
Use a mini clearwell so that a ready supply
of treated water is always available
If 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 capita
income and provide electrical service to
everyone…
 But a simpler solution would be better!
Constant Head: Floats
(variation on hypochlorinator)
Q  Korifice Aorifice 2 g h
Head can be
varied by
changing
buoyancy of
float
h
orifice
Supercritical
open channel
flow!
VERY Flexible hose
Unaffected by downstream conditions!
Floating Bowl
Adjust the flow by changing the rocks
Need to make
adjustments
(INSIDE) the
chemical tank
Rocks are
submerged in
the chemical
Safety issues
Chemical Metering
(Hypochlorinator)
Float
What is the simplest
representation that
captures the fluid
mechanics of this
system?
PVC needle
valve
1.0 m
1.5” PVC
overflow tube
Transparent
flexible tube
1.78 m
(0.5”)
1.05 m
0.5” PVC tube
Water in the distribution tank
Hole in a Bucket
h
Orifice
Avc  0.6 Aorifice
K orifice  0.6
Q  Korifice Aorifice 2 g h
Vena contracta
Use Control Volume Equation:
Conservation of Mass
Float
¶
r V ×n
ˆ dA = r dV
ò
ò
¶t cv
cs
Qor
Qor


dV

t cv
Ares dh
dV


dt
dt
V 
dh
 K or Aor
dt
1.5” PVC
overflow tube
Transparent
flexible tube
1.78 m
(0.5”)
1.05 m
h0
PVC needle
valve
0.5” PVC tube
Water in the distribution tank
Orifice in the PVC valve
2 gh
Qor  K or Aor
Ares
volume
1.0 m
2 gh
2 gh  0
Integrate to get h as f(t)
Finding the chlorine depth as f(t)
 Ares
K or Aor
h
2g
 Ares
K or Aor
h 
2g

h0
dh

h
t
 dt
Separate variables
0
2  h1/ 2  h01/ 2   t
h0  tK or
Aor
2 Ares
2g
Integrate
Solve for height
Finding Q as f(t)
Q  K or Aor
Q  K or Aor
2 gh

2g 

h 
tK or Aor
h0 
2 Ares
h0  tK or
Aor
2 Ares
2g

2g 

Find Aor as function of initial target flow rate
Aor 
K or
Q0
2 gh0
Set the valve to get desired dose initially
Surprise… Q and chlorine dose
decrease linearly with time!
Q  K or Aor

2g 

tQ0
Q
 1
Q0
2 Ares h0
tK or Aor
h0 
2 Ares

2g 

Aor 
Q0
K or 2 gh0
Linear decrease in flow
Relationship between Q0 and Ares?
Assume flow at Q0 for time (tdesign) would empty reservoir
Q0tdesign  Ares hres
Q
1 t hres
 1
Q0
2 tdesign h0
Q0
hres

Ares
tdesign
CCl2
CCl2
0

1 t hres
 1 

2 tdesign h0





Effect of tank height above valve
Case 1, h0=50 m,
hres = 1 m,
tdesign=4 days
Q2
h  2 h0
Q0


0.8
0.8
0.6
0.6 h t t
design hres h0  h0 hres
0.4
0.4
0.2
0.2

Qratio t t design hres h0
0
0
2
4
6

hres
Depth in
reservoir
0
8
t
Case 1, h0=1 m,
hres = 1 m,
tdesign=4 days
day


0.8
0.8
0.6
0.6 h t t
design hres h0  h0 hres
0.4
0.4
0.2
0.2

Qratio t t design hres h0
0
0
2
4
t
day
6
0
8


hres

Constant Head: Overflow Tanks
h
Aorifice
Surface tension
effects here
What controls
the flow?
Q  Korifice Aorifice 2 g h
Constant Head:
Marriot bottle
hL
 A simple constant head
device
 Why is pressure at the top of
the filter independent of
water level in the Marriot
bottle?
 What is the head loss for this
filter?
batch system
 Disadvantage? ___________
2
Vin2
pout
Vout
 zin   in
 hP 
 zout   out
 hT  hL

2g

2g
pin
Constant Head: Float Valve
Float adjusts opening
to maintain relatively
constant water level in
lower tank
(independent of upper
tank level) ?
NOT Flow Control!
Describe sequence of events after filling
Flow Control Valve (FCV)
flow rate
Limits the ____
___
through the valve to a
specified value, in a
specified direction
Calculate the sizes of
the openings and the
corresponding
pressures for the
flows of interest
• Expensive
• Work best with large
Q and large head loss
Raw water reservoir and SSF
Float valve and small
tube
Flow control device
Small diameter tubing
Clean water reservoir
Floating Ball Valve
Float valve
Small
diameter
tube
Float valve with IV drip
2 cm
2.3 cm
1.5 cm
2 mm
0.5 cm
Rubber tip
4.4 cm
PVC
stem
11.0 cm
8.3 cm
Float
mass:
6 grams
6.5 cm
5.2 cm
Barb tubing
adapter
5.6 cm
9.1 cm
IV roller
clamp
Housing Dimensions:
ID = 7.85 cm
OD = 8.8 cm
IV tubing
(~10 drops/mL)
2 mm
Floating Bowl with Orifice
Holding container
(bucket or glass
column)
Sealing pipe
Pong pipe
Driving pressure for sand column
Sand column
HJR
Upflow prevents trapped air
(keyword: “prevent”)!
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
Orifice i.e.. small hole or restriction
____________________________________
Long small diameter tube
____________________________
Porous media
____________________________
Can use flexible tube to facilitate adjusting the
head
Float valve and small tube
(Gravity dosing system)
chemical stock tank
Flow control device
If laminar flow!
32 LV 128 LQ
hf 

2
 gD
 g D 4
hl  g D 4
Q
128 L
hl
Small diameter tubing
2
Vin2
pout
Vout
 zin   in
 hP 
 zout   out
 hT  hL

2g

2g
pin
hL  zin  zout
Neglecting minor losses
Long small tube head loss
Laminar flow
32 LV 128 LQ
hf 

2
 gD
 g D 4
Flow proportional to hf
Turbulent Flow
Re 
4Q
D
f 
0.25
5.74

 
log


0.9

 3.7 D Re




2
hf  f
8
g 2
LQ 2
D5
Orifice flow
Q  K or A 2 gh
1
8Q 2
h 2
K or g 2 D 4
1
K 
2
K or
Solve for h and substitute
area of a circle to obtain same
form as minor loss equation
Kor = 0.63 therefore K=2.5
8d
2.5 d
h
D
4
8Q 2
K
g 2 hv
D
d
Porous Media Head Loss: Kozeny
equation
V pore 
hf 
Velocity of fluid above the porous media
Va

32 LV pore
 gd
Laminar flow assumption
2
pore
1     Va
hf
 36k
2
L
 3 gd sand
2
k = Kozeny constant
Approximately 5 for
most filtration conditions
Tube vs. Orifice
Clogging
Adjustability
Minor losses
2

8 Q 

Dorifice K Q h e  K
 g  2 h 
e

Major losses
1
4
128  L Q 
Dtube Q h f L  
g   hf 


1
4
3
Dtube( Q 20cm 1m  )
2
mm
Dorifice( 2.5 Q 20cm)
mm
1
0
0
50
100
Q
mL
min
150
200
Surface Tension
Will the droplet drop?
Is the force of gravity stronger than surface tension?
4 r 3
Fg 
g
3 2
Fs= 2rs
4 r 3
 g   g h  r 2   2 rs
3 2
2

g

h

r


F p=
h
4 r 3
 g   g h  r 2   2 rs
3 2
Solve for height of water
required to form droplet
4 r 3
2 rs 
g
3 2
h 
 g  r 2 
2s 2r
h 

 gr 3
Surface tension (N/m)
Surface Tension can prevent flow!
0.080
0.075
0.070
0.065
0.060
0.055
0.050
0 20 40 60 80 100
Temperature (C)
Design constraint for flow control
devices: Surface Tension
100
2s 2r
h 

 gr 3
Delineates the
boundary between
stable and unstable
Flow control devices
need to be designed
to operate to the
right of the red line!
h ( r)
mm
10
1
0.1
1
10
r
mm
No droplets form to left of line
Hypochorinator Fix
http://web.mit.edu/d-lab/honduras.htm
What is good?
How could you improve this system?
What might fail?
Safety hazards?
Modular Flow
Control
Identify the Flow Controller Failure
Modes
 Moving parts
 Wear
 Corrosion (especially with corrosive chemicals)
 Precipitation (e.g. calcium carbonate)
 Incompatible materials
 Don’t forget sunlight has UV rays!
 Clogging
 Design errors…
Flow Measurement Devices
 Orifice in the side of a pipe
 Pipe vented through water
surface
 Jet of water must free fall h
inside the pipe
 Korifice is due to the vena
contracta and has a value
of approximately 0.6.
Q  K orifice Aorifice 2 gh
Free Surface with Orifice limitations
 The head loss from making the
measurement is wasted (likely on the
order of 20 cm)
 Ability to include this type of flow
measurement depends on availability of
excess potential energy
 The useable measurement range doesn’t
include the range where the orifice is
only partially submerged
 Thus large diameter orifices aren’t ideal
because they limit the measurement
range
 For reasonably small head loss the flow
per orifice can’t be much greater than
100 Lpm
 Use multiple orifices for larger flow
rates
2
 d
Qplant ( d h )  Korifice
 2 g  h
4
25
20
15
h
cm
10
5
0
40
60
80
100
Qplant ( d h)
L
min
120
140
Alternative Flow Measurements
 Block the effluent port from a small tank and
measure the rate of depth increase
 The 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 rate
measurements
 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