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h1. |
Theory,
...
Design,
...
and
...
Application
...
of
...
Gravity
...
Powered
...
Flow
...
Controller
...
Authors:
...
Monroe
...
Weber-Shirk
...
...
and
...
Nicole
...
Ceci
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...
...
of Contents
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TOC:maxLevel=2} {cloak} h2. Abstract Development of robust sustainable drinking water treatment technologies requires improved methods of metering aqueous chemical solutions. Existing technologies either required contact with the chemical solution when adjusting the flow rate or they didn't provide a calibrated method for setting the flow to the target value. The AguaClara team at Cornell University developed a low cost flow control module based on laminar pipe flow. The flow control module features a variable calibrated flow. The range of design flow rates is a function of the viscosity of the solution. For dilute solutions with viscosities similar to pure water the flow control modules can be designed in the range of 10 to 500 mL/min. The flow control module has been field tested for metering chlorine and aluminum sulfate for AguaClara water treatment plants in Honduras. h3. Keywords: Flow Controller, Laminar, Variable, Calibrated, AguaClara h2. Introduction The lack of robust and sustainable technologies for chemical dosing and flow control that don't require electrical power continues to adversely affect the ability to reliably provide safe drinking water. Conventional municipal water treatment plants often use variable speed peristaltic pumps or other positive displacement pumps to meter coagulant solutions and chlorine. Many potential water treatment plant sites in the Global South don't have ready access to electricity and frequently the electrical grid is unreliable. The AguaClara team at Cornell University recognized the need for an improved gravity powered flow control device and began evaluating the available technologies and ultimately developed and tested an improved flow control module. |
Abstract
Development of robust sustainable drinking water treatment technologies requires improved methods of metering aqueous chemical solutions. Existing technologies either required contact with the chemical solution when adjusting the flow rate or they didn't provide a calibrated method for setting the flow to the target value. The AguaClara team at Cornell University developed a low cost flow control module based on laminar pipe flow. The flow control module features a variable calibrated flow. The range of design flow rates is a function of the viscosity of the solution. For dilute solutions with viscosities similar to pure water the flow control modules can be designed in the range of 10 to 500 mL/min. The flow control module has been field tested for metering chlorine and aluminum sulfate for AguaClara water treatment plants in Honduras.
Keywords: Flow Controller, Laminar, Variable, Calibrated, AguaClara
Introduction
The lack of robust and sustainable technologies for chemical dosing and flow control that don't require electrical power continues to adversely affect the ability to reliably provide safe drinking water. Conventional municipal water treatment plants often use variable speed peristaltic pumps or other positive displacement pumps to meter coagulant solutions and chlorine. Many potential water treatment plant sites in the Global South don't have ready access to electricity and frequently the electrical grid is unreliable. The AguaClara team at Cornell University recognized the need for an improved gravity powered flow control device and began evaluating the available technologies and ultimately developed and tested an improved flow control module.
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{float:right|border=2px solid black|width=650px}
{anchor:Hypochlorinator}[!flow controller theory^Hypochlorinator.jpg!|width=640px|flow controller theory^Hypochlorinator.jpg]
h5. Hypochlorinator design as implemented in hundreds of communities in Honduras. Frequently the float components are not included.
{float}
|
The
...
AguaClara
...
team
...
first
...
recognized
...
the
...
need
...
for
...
an
...
improved
...
flow
...
control
...
module
...
during
...
site
...
visits
...
of
...
community
...
water
...
supply
...
systems
...
in
...
Honduras
...
in
...
2004.
...
The
...
standard
...
Honduran
...
design
...
for
...
community
...
water
...
supply
...
systems
...
consists
...
of
...
a
...
surface
...
water
...
source
...
that
...
is
...
piped
...
to
...
a
...
distribution
...
tank
...
and
...
then
...
distributed
...
via
...
a
...
pipe
...
network
...
to
...
homes.
...
The
...
only
...
water
...
treatment
...
is
...
the
...
addition
...
of
...
hypochlorite.
...
Most
...
communities
...
use
...
granular
...
calcium
...
hypochlorite
...
to
...
prepare
...
a
...
concentrated
...
chlorine
...
solution
...
in
...
a
...
small
...
tank
...
that
...
is
...
located
...
on
...
top
...
of
...
the
...
distribution
...
tank.
...
The
...
original
...
design
...
of
...
the
...
hypochlorinators
...
called
...
for
...
a
...
floating
...
frame
...
that
...
held
...
a
...
flexible
...
tube
...
with
...
a
...
submerged
...
orifice.
...
This
...
system
...
theoretically
...
provided
...
a
...
constant
...
flow
...
through
...
the
...
submerged
...
orifice.
...
The
...
orifice
...
flow
...
is
...
set
...
by
...
the
...
size
...
of
...
the
...
orifice
...
and
...
the
...
distance
...
between
...
the
...
water
...
(or
...
chlorine)
...
surface
...
and
...
the
...
center
...
of
...
the
...
orifice.
...
| Include Page | ||||
|---|---|---|---|---|
|
where the orifice coefficient, K orifice has a value of approximately 0.6.
...
In
...
practice
...
the
...
orifices
...
clog
...
quickly
...
due
...
to
...
the
...
precipitation
...
of
...
calcium
...
carbonate,
...
the
...
flow
...
rate
...
adjustment
...
is
...
by
...
trial
...
and
...
error,
...
and
...
maintenance
...
and
...
operation
...
requires
...
contact
...
with
...
the
...
concentrated
...
chlorine
...
solution.
...
Perhaps
...
due
...
to
...
these
...
difficulties
...
the
...
design
...
evolved
...
and
...
a
...
1/2"
...
PVC
...
valve
...
was
...
installed
...
on
...
the
...
exit
...
pipe
...
at
...
the
...
bottom
...
of
...
the
...
chlorine
...
tank,
...
the
...
floating
...
orifice
...
was
...
removed,
...
and
...
the
...
flow
...
is
...
now
...
adjusted
...
by
...
a
...
trial
...
and
...
error
...
setting
...
of
...
the
...
valve
...
position.
...
This
...
modification
...
created
...
a
...
system
...
that
...
was
...
easier
...
to
...
maintain,
...
but
...
the
...
valve
...
was
...
still
...
subject
...
to
...
frequent
...
clogging
...
and
...
the
...
hydraulic
...
design
...
no
...
longer
...
provided
...
a
...
constant
...
flow.
...
The
...
flow
...
decreases
...
as
...
the
...
reservoir
...
drains.
...
The
...
decrease
...
in
...
flow
...
rate
...
over
...
time
...
can
...
be
...
obtained
...
by
...
combining
...
mass
...
conservation
...
and
...
the
...
orifice
...
equation
...
and
...
integrating
...
to
...
find
...
the
...
reservoir
...
depth
...
as
...
a
...
function
...
of
...
time.
...
If
...
the
...
operator
...
sets
...
the
...
valve
...
to
...
deliver
...
a
...
flow
...
rate
...
such
...
that
...
the
...
reservoir
...
would
...
drain
...
in
...
t
...
design if
...
the
...
flow
...
remained
...
constant,
...
then
...
the
...
flow
...
rate
...
will
...
decrease
...
significantly
...
over
...
the t design and by the end of the design period the theoretical flow is given by
| Include Page | ||||
|---|---|---|---|---|
|
where h res is the initial depth of chemical solution in the reservoir, h 0 is the vertical distance between the initial free surface and the orifice (the valve), t design is the duration that the chemical supply was supposed to last, and Q 0 is the initial flow rate from the valve. Thus if the valve is located at almost the same elevation as the bottom of the reservoir, then when t = t design the flow will be approximately one half of the design flow. If the operator allows the entire tank to drain without adjusting the flow rate there will be an even larger flow variation. The large fluctuation in chlorine flow rate increases the difficulty of maintaining an appropriate chlorine residual.
| Wiki Markup |
|---|
t ~design~ and by the end of the design period the theoretical flow is given by [{include:Hypochlorinator Q vs t}|Hypochlorinator Q vs t] where h ~res~ is the initial depth of chemical solution in the reservoir, h ~0~ is the vertical distance between the initial free surface and the orifice (the valve), t ~design~ is the duration that the chemical supply was supposed to last, and Q ~0~ is the initial flow rate from the valve. Thus if the valve is located at almost the same elevation as the bottom of the reservoir, then when t = t ~design~ the flow will be approximately one half of the design flow. If the operator allows the entire tank to drain without adjusting the flow rate there will be an even larger flow variation. The large fluctuation in chlorine flow rate increases the difficulty of maintaining an appropriate chlorine residual. {float:right|border=2px solid black|width=540px} {anchor:floating bowl }[!flow controller theory^floating bowl.jpg|width=530px!|flow controller theory^floating bowl.jpg] h5. Floating bowl constant flow device. {float} |
Another
...
design
...
for
...
a
...
constant
...
flow
...
device
...
is
...
called
...
a
...
floating
...
bowl
...
...
...
...
...
.
...
It
...
is
...
conceptually
...
similar
...
to
...
the
...
hypochlorinators
...
used
...
in
...
Honduras,
...
but
...
the
...
flow
...
is
...
adjusted
...
by
...
varying
...
the
...
submergence
...
of
...
the
...
bowl
...
instead
...
of
...
by
...
sliding
...
the
...
tube
...
with
...
the
...
orifice
...
relative
...
to
...
the
...
floating
...
frame.
...
The
...
submergence
...
is
...
varied
...
by
...
adding
...
or
...
removing
...
pebbles
...
from
...
the
...
bowl.
...
The
...
floating
...
bowl
...
also
...
requires
...
reaching
...
into
...
the
...
chemical
...
solution
...
to
...
adjust
...
the
...
pebbles.
...
Adjustments
...
to
...
the
...
flow
...
rate
...
can
...
be
...
calibrated
...
to
...
eliminate
...
the
...
need
...
for
...
trial
...
and
...
error.
...
Both
...
the
...
floating
...
bowl
...
and
...
the
...
floating
...
frame
...
have
...
to
...
be
...
installed
...
inside
...
each
...
chemical
...
tank
...
that
...
is
...
used
...
for
...
chemical
...
dosing.
...
The
...
difficulties
...
of
...
using
...
the
...
current
...
flow
...
control
...
devices
...
prompted
...
us
...
to
...
develop
...
a
...
list
...
of
...
characteristics
...
required
...
for
...
the
...
next
...
generation
...
of
...
gravity
...
powered
...
flow
...
control
...
devices.
...
An
...
ideal
...
flow
...
control
...
device
...
would
...
have
...
the
...
following
...
characteristics:
...
- calibrated
...
- to
...
- easily
...
- vary
...
- the
...
- flow
...
- rate
...
- maintain
...
- a
...
- constant
...
- flow
...
- rate
...
- independent
...
- of
...
- the
...
- chemical
...
- level
...
- in
...
- the
...
- stock
...
- tank
...
- handle
...
- corrosive
...
- chemicals
...
- incorporate
...
- a
...
- linear
...
- scale
...
- to
...
- facilitate
...
- setting
...
- the
...
- flow
...
- without
...
- need
...
- to
...
- use
...
- trial
...
- and
...
- error
...
- be
...
- resistant
...
- to
...
- clogging
...
- be
...
- easy
...
- to
...
- maintain
...
- and
...
- operate
...
- be
...
- economical,
...
- small,
...
- and
...
- easily
...
- used
...
- to
...
- replace
...
- existing
...
- flow
...
- control
...
- devices
...
- be
...
- easily
...
- adapted
...
- for
...
- a
...
- range
...
- of
...
- flow rates
Theory
Maintaining a constant flow of chemical is difficult because of the fluctuations in the level of the chemical in the stock tank. The variable head means that any restrictions used to regulate the flow will cause a decreasing flow rate as the tank empties. One simple solution to this problem would be to use an elevated tank with a large head driving the fluid through the flow restriction. Then the small variation in the driving head as the tank emptied would not be as significant. The disadvantages of this approach are the construction and operation difficulties of the elevated tank and the clogging of the flow restriction. Thus we need a solution that isolates the flow restriction from the variable head of the stock tank and we need a flow restriction that is as large as possible to minimize clogging.
Creation of a constant flow requires a constant driving force coupled with a constant pressure coefficient or loss coefficient. Recent advances in small low cost chemical resistant float valves have made it possible to use float valves even with corrosive chlorine solutions. The float valve can be used to maintain a constant liquid level in a small tank. The constant liquid level can then be used to develop a constant flow when coupled with a constant pressure or loss coefficient. Many float valves are designed to cycle between full on and full off to minimize wear on the valve mechanism. These float valves wait for the water level to drop a significant amount (often more than 1 cm) before cycling on again. Thus these more sophisticated float valves would be a poor choice for a constant head tank. The ideal constant head tank float valve consists of a float on a lever that pushes a soft surface against an opening to close the opening.
There are many methods of creating a constant loss coefficient including flow through a valve, porous media, a long tube, or an orifice. Selection of an appropriate mechanism for producing the loss coefficient can be based on the desired characteristics of the flow control device. We have tested the use of a sand column to provide a loss coefficient for flow regulation. The sand column has the advantage of being able to handle some particle accumulation with minimal affect on the loss coefficient. The disadvantages of the sand column are that it must filled using up flow to prevent air entrapment and the cost of the assembly.
Clogging due to precipitation of calcium carbonate in the case of hypochlorinators, insoluble contaminants of aluminum sulfate, and particulate matter that may be present in the water used to prepare the chemical stocks is a significant problem. In the case of hypochlorinators clogging is a common failure mode. To reduce the risk of clogging the flow passage diameter should be as large as possible. The loss coefficient for valves and orifices are both due to the expansion losses that occur downstream from the flow restriction and thus the flow area is similar for valves and orifices given the same loss coefficient. The relationship between the orifice diameter and flow rate is derived from energy conservation. This equation is valid for both turbulent and laminar flow if the orifice or valve discharges to the atmosphere.
| Include Page | ||||
|---|---|---|---|---|
|
The laminar flow relationship between head loss due to shear on the pipe walls (h f), pipe length (L), pipe diameter (D), and kinematic viscosity (¿) is given by the Hagen-Poiseuille equation.
| Include Page | ||||
|---|---|---|---|---|
|
The maximum flow that can be sent through a tube while maintaining laminar flow is based on eliminating diameter from the Hagen-Poiseuille equation by using the maximum laminar flow Reynolds number constraint of 2100.
| Include Page | ||||
|---|---|---|---|---|
|
| Wiki Markup |
|---|
rates h2. Theory Maintaining a constant flow of chemical is difficult because of the fluctuations in the level of the chemical in the stock tank. The variable head means that any restrictions used to regulate the flow will cause a decreasing flow rate as the tank empties. One simple solution to this problem would be to use an elevated tank with a large head driving the fluid through the flow restriction. Then the small variation in the driving head as the tank emptied would not be as significant. The disadvantages of this approach are the construction and operation difficulties of the elevated tank and the clogging of the flow restriction. Thus we need a solution that isolates the flow restriction from the variable head of the stock tank and we need a flow restriction that is as large as possible to minimize clogging. Creation of a constant flow requires a constant driving force coupled with a constant pressure coefficient or loss coefficient. Recent advances in small low cost chemical resistant float valves have made it possible to use float valves even with corrosive chlorine solutions. The float valve can be used to maintain a constant liquid level in a small tank. The constant liquid level can then be used to develop a constant flow when coupled with a constant pressure or loss coefficient. Many float valves are designed to cycle between full on and full off to minimize wear on the valve mechanism. These float valves wait for the water level to drop a significant amount (often more than 1 cm) before cycling on again. Thus these more sophisticated float valves would be a poor choice for a constant head tank. The ideal constant head tank float valve consists of a float on a lever that pushes a soft surface against an opening to close the opening. There are many methods of creating a constant loss coefficient including flow through a valve, porous media, a long tube, or an orifice. Selection of an appropriate mechanism for producing the loss coefficient can be based on the desired characteristics of the flow control device. We have tested the use of a sand column to provide a loss coefficient for flow regulation. The sand column has the advantage of being able to handle some particle accumulation with minimal affect on the loss coefficient. The disadvantages of the sand column are that it must filled using up flow to prevent air entrapment and the cost of the assembly. Clogging due to precipitation of calcium carbonate in the case of hypochlorinators, insoluble contaminants of aluminum sulfate, and particulate matter that may be present in the water used to prepare the chemical stocks is a significant problem. In the case of hypochlorinators clogging is a common failure mode. To reduce the risk of clogging the flow passage diameter should be as large as possible. The loss coefficient for valves and orifices are both due to the expansion losses that occur downstream from the flow restriction and thus the flow area is similar for valves and orifices given the same loss coefficient. The relationship between the orifice diameter and flow rate is derived from energy conservation. This equation is valid for both turbulent and laminar flow if the orifice or valve discharges to the atmosphere. [{include:D orifice}|D orifice] The laminar flow relationship between head loss due to shear on the pipe walls (h ~f~), pipe length (L), pipe diameter (D), and kinematic viscosity (¿) is given by the Hagen-Poiseuille equation. [{include:D Hagen-Poiseuille}|D Hagen-Poiseuille] The maximum flow that can be sent through a tube while maintaining laminar flow is based on eliminating diameter from the Hagen-Poiseuille equation by using the maximum laminar flow Reynolds number constraint of 2100. [{include:Maximum laminar flow}|Maximum laminar flow] {float:right|border=2px solid black|width=363px} {anchor:Tube vs Orifice Diameter}[!flow controller theory^Tube vs Orifice Diameter.JPG|width=353px!|flow controller theory^Tube vs Orifice Diameter.JPG] h5. Tube vs orifice diameter given a head loss of 20 cm and tube length of 1 m (need to confirm the flow conditions) {float} [ |
...
...
...
...
...
...
...
...
...
...
...
...
...
reveal
...
that
...
the
...
tube
...
diameter
...
is
...
approximately
...
1
...
mm
...
larger
...
than
...
the
...
orifice
...
or
...
valve
...
opening
...
for
...
the
...
entire
...
range
...
of
...
laminar
...
flow.
...
Although
...
a
...
1
...
mm
...
increase
...
in
...
diameter
...
may
...
not
...
appear
...
significant,
...
the
...
risk
...
of
...
clogging
...
is
...
substantially
...
reduced
...
because
...
the
...
sedimentation
...
velocity
...
for
...
small
...
particles
...
is
...
proportional
...
to
...
their
...
projected
...
area.
...
The
...
larger
...
particles
...
required
...
to
...
clog
...
the
...
tube
...
are
...
more
...
easily
...
removed
...
by
...
sedimentation
...
in
...
the
...
stock
...
tank
...
or
...
in
...
the
...
constant
...
head
...
tank.
...
A
...
flexible
...
tube
...
can
...
be
...
used
...
to
...
regulate
...
the
...
flow
...
from
...
a
...
constant
...
head
...
tank
...
by
...
simply
...
raising
...
or
...
lowering
...
the
...
end
...
of
...
the
...
tube
...
that
...
discharges
...
to
...
the
...
atmosphere.
...
Under
...
conditions
...
of
...
laminar
...
flow
...
and
...
neglecting
...
entrance
...
and
...
exit
...
losses,
...
the
...
flow
...
rate
...
is
...
directly
...
proportional
...
to
...
the
...
difference
...
in
...
elevation
...
between
...
the
...
liquid
...
level
...
in
...
the
...
constant
...
head
...
tank
...
and
...
the
...
discharge
...
end
...
of
...
the
...
tube.
...
The
...
flow
...
rate
...
can
...
be
...
easily
...
calibrated
...
so
...
that
...
a
...
particular
...
flow
...
can
...
be
...
reliably
...
obtained
...
by
...
setting
...
the
...
elevation
...
difference.
...
The
...
simple
...
laminar
...
flow
...
tube
...
is
...
a
...
significant
...
improvement
...
over
...
a
...
valve
...
because
...
the
...
valve
...
setting
...
can
...
not
...
be
...
easily
...
replicated
...
unless
...
it
...
has
...
a
...
dial
...
indicating
...
the
...
valve
...
position.
...
The
...
high
...
cost
...
of
...
valves
...
with
...
position
...
indicators
...
in
...
comparison
...
with
...
the
...
cost
...
of
...
a
...
short
...
length
...
of
...
flexible
...
tubing
...
gives
...
a
...
strong
...
advantage
...
to
...
the
...
laminar
...
flow
...
tube.
...
It
...
is
...
likely
...
possible
...
to
...
design
...
a
...
flow
...
control
...
module
...
using
...
turbulent
...
pipe
...
flow.
...
However,
...
we
...
anticipate
...
unfavorable
...
flow
...
fluctuations
...
in
...
the
...
transition
...
region
...
between
...
laminar
...
and
...
fully
...
turbulent
...
flow.
...
A
...
turbulent
...
flow
...
design
...
would
...
not
...
have
...
a
...
linear
...
response,
...
but
...
it
...
could
...
still
...
be
...
calibrated.
...
We
...
have
...
not
...
yet
...
explored
...
the
...
use
...
of
...
turbulent
...
flow
...
designs
...
because
...
the
...
flow
...
rates
...
that
...
we
...
have
...
needed
...
for
...
the
...
AguaClara
...
can
...
be
...
accommodated
...
using
...
laminar
...
flow.
...
Design
...
of
...
a
...
flow
...
control
...
module
...
initially
...
appears
...
difficult
...
because
...
of
...
the
...
flexibility
...
to
...
choose
...
tube
...
length,
...
tube
...
diameter,
...
and
...
head
...
loss.
...
Appropriate
...
selection
...
of
...
the
...
parameters
...
to
...
obtain
...
a
...
practical
...
design
...
is
...
subject
...
to
...
a
...
series
...
of
...
constraints.
...
A
...
clear
...
physical
...
constraint
...
is
...
set
...
by
...
the
...
goal
...
of
...
maintaining
...
laminar
...
flow
...
in
...
the
...
tube.
...
The
...
continuity
...
equation
...
(Q
...
=
...
VA)
...
and
...
the
...
equation
...
for
...
the
...
area
...
of
...
a
...
circle
...
can
...
be
...
substituted
...
into
...
the
...
Reynolds
...
number
...
definition
...
to
...
obtain
...
the
...
minimum
...
diameter
...
required
...
to
...
obtain
...
laminar
...
flow
...
for
...
a
...
given
...
maximum
...
design
...
flow
...
rate.
| Include Page | ||||
|---|---|---|---|---|
|
The laminar flow constraint dictates that the tube diameter must increase as the maximum design flow increases. A second constraint on the tube diameter can be obtained based on the requirement that the tube must be long enough so that the end of the tube can reach the various elevations required to set the desired head loss. In subsequent analysis we assume that the end of the tube can reach high enough so that the flow can be set to zero and that it can reach low enough to obtain the maximum design flow. At absolute minimum the tube length would have to be longer than 1/2 the maximum head loss and given the need to have gentle curves in the tube a more reasonable constraint might be 1.5 times the maximum head loss. A desired relationship between head loss and tube length can be substituted into the Hagen-Poiseuille equation to give a second constraint on the tube diameter.
| Include Page | ||||
|---|---|---|---|---|
|
| Wiki Markup |
|---|
[{include:Minimum Diameter for Laminar Flow}|Minimum Diameter for Laminar Flow] The laminar flow constraint dictates that the tube diameter must increase as the maximum design flow increases. A second constraint on the tube diameter can be obtained based on the requirement that the tube must be long enough so that the end of the tube can reach the various elevations required to set the desired head loss. In subsequent analysis we assume that the end of the tube can reach high enough so that the flow can be set to zero and that it can reach low enough to obtain the maximum design flow. At absolute minimum the tube length would have to be longer than 1/2 the maximum head loss and given the need to have gentle curves in the tube a more reasonable constraint might be 1.5 times the maximum head loss. A desired relationship between head loss and tube length can be substituted into the Hagen-Poiseuille equation to give a second constraint on the tube diameter. [{include:D Hagen-Poiseuille}|D Hagen-Poiseuille] {float:right|border=2px solid black|width=394px} {anchor:Tube Diameter}[!flow controller theory^Tube Diameter.jpg|width=384px!|flow controller theory^Tube Diameter.jpg] h5. Minimum tube diameter given the three constraints of laminar flow, tube length sufficient to accommodate the head loss range, and a series of available tubing diameters. The constraints used were a maximum head loss of 20 cm, a minimum tube length of 30 cm, available tubing sizes in increments of 1 mm, and solution viscosity of pure water. The blue dot represents a design solution for a 200 mL/min flow rate. {float} |
The
...
minimum
...
diameter
...
that
...
can
...
be
...
used
...
is
...
the
...
maximum
...
diameter
...
obtained
...
from
...
the
...
previous
...
two
...
equations.
...
The
...
design
...
diameter
...
of
...
the
...
tubing
...
is
...
obtained
...
by
...
selecting
...
the
...
smallest
...
diameter
...
tubing
...
that
...
is
...
larger
...
than
...
the
...
minimum
...
diameter.
...
The
...
...
...
...
shows
...
that
...
the
...
head
...
loss
...
constraint
...
dominates
...
for
...
low
...
flows
...
and
...
the
...
laminar
...
flow
...
constraint
...
dominates
...
for
...
higher
...
flows.
...
It
...
is
...
important
...
to
...
note
...
that
...
a
...
single
...
tube
...
diameter
...
can
...
provide
...
a
...
wide
...
range
...
of
...
maximum
...
flow
...
rates
...
and
...
that
...
all
...
designs
...
have
...
the
...
capability
...
of
...
varying
...
the
...
flow
...
from
...
zero
...
to
...
the
...
maximum
...
design
...
flow
...
rate
...
by
...
simply
...
raising
...
the
...
discharge
...
end
...
of
...
the
...
tube
...
to
...
the
...
liquid
...
level
...
height
...
in
...
the
...
constant
...
head
...
tank.
...
The
...
next
...
step
...
in
...
the
...
design
...
process
...
is
...
to
...
determine
...
the
...
length
...
of
...
tubing.
...
The
...
tubing
...
length
...
is
...
obtained
...
by
...
solving
...
the
...
Hagen-Poiseuille
...
for
...
tubing
...
length
...
given
...
the
...
design
...
tube
...
diameter,
...
maximum
...
design
...
flow
...
rate,
...
and
...
maximum
...
design
...
head
...
loss.
...
The
...
maximum
...
design
...
head
...
loss
...
also
...
is
...
governed
...
by
...
several
...
constraints.
...
The
...
minimum
...
value
...
for
...
the
...
maximum
...
head
...
loss
...
for
...
a
...
flow
...
control
...
device
...
must
...
be
...
large
...
enough
...
so
...
that
...
it
...
is
...
easy
...
for
...
the
...
operator
...
to
...
accurately
...
adjust
...
the
...
tube
...
position
...
to
...
set
...
the
...
flow
...
rate.
...
The
...
accuracy
...
of
...
the
...
flow
...
rate
...
is
...
also
...
affected
...
by
...
any
...
fluctuations
...
in
...
the
...
fluid
...
level
...
in
...
the
...
"constant"
...
head
...
tank.
...
Although
...
the
...
fluid
...
level
...
is
...
controlled
...
by
...
a
...
float
...
valve,
...
the
...
float
...
valve
...
does
...
not
...
completely
...
isolate
...
the
...
constant
...
head
...
tank
...
from
...
variations
...
in
...
the
...
level
...
of
...
the
...
stock
...
tank.
...
The
...
hydrostatic
...
pressure
...
exerted
...
by
...
the
...
liquid
...
in
...
the
...
stock
...
tank
...
must
...
be
...
resisted
...
by
...
the
...
float
...
valve
...
and
...
ultimately
...
the
...
force
...
must
...
be
...
provided
...
by
...
the
...
buoyancy
...
of
...
the
...
float.
...
Thus
...
the
...
extent
...
of
...
submergence
...
of
...
the
...
float
...
decreases
...
as
...
the
...
stock
...
tank
...
empties
...
and
...
the
...
liquid
...
level
...
in
...
the
...
constant
...
head
...
tank
...
decreases
...
slightly
...
as
...
well.
...
We
...
tested
...
the
...
attenuation
...
ratio
...
(the
...
change
...
in
...
the
...
constant
...
head
...
tank
...
liquid
...
level
...
divided
...
by
...
the
...
change
...
in
...
the
...
stock
...
tank
...
level
...
for
...
the
...
modified
...
float
...
valve
...
that
...
we
...
use
...
The
...
attenuation
...
ratio
...
can
...
be
...
obtained
...
by
...
a
...
moment
...
balance
...
about
...
the
...
float
...
valve
...
hinge
...
pin
...
required
...
to
...
cause
...
the
...
valve
...
to
...
close.
...
| Include Page | ||||
|---|---|---|---|---|
|
where
| Latex |
|---|
$\Delta h_{flow controller}$ |
...
...
the
...
change
...
in
...
depth
...
of
...
the
...
liquid
...
level
...
in
...
the
...
constant
...
head
...
tank
...
and
...
| Latex |
|---|
...
$A_{float}$ |
...
...
the
...
cross
...
sectional
...
area
...
of
...
the
...
cylindrical
...
float.
...
Thus
...
| Latex |
|---|
...
$\Delta h_{flow controller} A_{float}$ |
...
...
the
...
submerged
...
volume
...
of
...
the
...
float
...
that
...
when
...
multiplied
...
by
...
the
...
density,
...
| Latex |
|---|
...
$\rho$ |
...
...
by
...
acceleration
...
due
...
to
...
gravity
...
is
...
equal
...
to
...
the
...
total
...
buoyant
...
force
...
acting
...
on
...
the
...
float.
...
The
...
lever
...
arm
...
for
...
the
...
float
...
has
...
a
...
length
...
| Latex |
|---|
...
$L_{float\;lever\;arm}$ |
...
...
The
...
moment
...
acting
...
to
...
open
...
the
...
valve
...
is
...
provided
...
by
...
the
...
pressure
...
of
...
liquid
...
from
...
the
...
stock
...
tank,
...
| Latex |
|---|
...
$\rho g\Delta h_{stock}$ |
...
...
acting
...
over
...
the
...
area
...
of
...
the
...
valve
...
opening
...
| Latex |
|---|
...
$A_{orifice}$ |
...
...
The
...
lever
...
arm
...
for
...
the
...
opening
...
moment
...
is
...
| Latex |
|---|
...
$L_{valve\;lever\;arm}$ |
The float valve attenuation can be obtained by rearranged the previous equation and solving for the ratio of the change in height of the stock tank divided by the change in height of the constant head tank.
| Include Page | ||||
|---|---|---|---|---|
|
The theoretical attenuation factor for the miniature PVC adjustable float valve modified with a 5 cm diameter polypropylene float is approximately 2000. The attenuation factor was also measured. A peristaltic pump was connected to the inlet of the flow controller, along with a pressure sensor. The outlet tube of the flow controller was plugged. The peristaltic pump was then used to pump water into the flow controller. The pressure of the water in the inlet tube, or the pressure the float valve could resist, was then measured using process controller. The maximum inlet pressure was determined using three orientations, with the float straight down giving the lever arm a 90 degree angle, partially down for a 45 degree angle, and straight out at zero degrees. This was to determine which orientation provided the greatest resistance. The pressure was also measured as a function of the height of the water level inside the flow controller. The results indicate that the attenuation factor is similar for the different orientations of the float valve and thus we selected the orientation with float axis vertical to the water surface since that is the most compact orientation for installation inside a 1 liter bottle. The measured attenuation factor is approximately 900. Thus a change in liquid level of 1 m in the stock tank is expected to only produce a change of approximately 1 mm in the flow controller.
| Wiki Markup |
|---|
{latex}. The float valve attenuation can be obtained by rearranged the previous equation and solving for the ratio of the change in height of the stock tank divided by the change in height of the constant head tank. [{include:Float valve attenuation}|Float valve attenuation]\\ The theoretical attenuation factor for the miniature PVC adjustable float valve modified with a 5 cm diameter polypropylene float is approximately 2000. The attenuation factor was also measured. A peristaltic pump was connected to the inlet of the flow controller, along with a pressure sensor. The outlet tube of the flow controller was plugged. The peristaltic pump was then used to pump water into the flow controller. The pressure of the water in the inlet tube, or the pressure the float valve could resist, was then measured using [process controller]. The maximum inlet pressure was determined using three orientations, with the float straight down giving the lever arm a 90 degree angle, partially down for a 45 degree angle, and straight out at zero degrees. This was to determine which orientation provided the greatest resistance. The pressure was also measured as a function of the height of the water level inside the flow controller. The results indicate that the attenuation factor is similar for the different orientations of the float valve and thus we selected the orientation with float axis vertical to the water surface since that is the most compact orientation for installation inside a 1 liter bottle. The measured attenuation factor is approximately 900. Thus a change in liquid level of 1 m in the stock tank is expected to only produce a change of approximately 1 mm in the flow controller. {float:right|border=2px solid black|width=250px} {anchor:chartmacrodemo} {chart:type=scatter| ylabel=Stock tank depth (m)| xlabel=Change in flow controller depth (mm)| displayData=false| dataOrientation=vertical| width=250| height=200| legend=false} || Stock tank depth (m)|| Change in constant head tank depth (mm)|| |0.559 | 0| |1.604 | 3| |2.85 | 5| |5.19 | 7| |6.88 | 9| {chart} h5. Attenuation factor for the float valve with the 5 cm diameter polypropylene float installed with its axis vertical. {float} |
In
...
addition
...
the
...
desired
...
increments
...
in
...
flow
...
settings
...
must be
| Wiki Markup |
|---|
be {float:right|border=2px solid black|width=391px} {anchor:Tube Length}[!flow controller theory^Tube Length.jpg|width=381px!|flow controller theory^Tube Length.jpg] h5. Tube Length. {float} h2. Application The AguaClara project team began using the [flow control module design webpage|http://eswserver.cee.cornell.edu/mas/ |
Application
The AguaClara project team began using the
flow control module design webpage
| Wiki Markup |
|---|
worksheets/knowledgebase/flow controllerdesign.xmcd?TemplatePath=worksheets/mathweb.mlt] {float:right|border=2px solid black|width=588px} {anchor:Flow controller schematic}[!flow controller theory^flow controller schematic.jpg|width=578px!|flow controller theory^flow controller schematic.jpg] h5. Flow controller schematic. {float} |
Flow
...
control
...
modules
...
will
...
generate
...
a
...
linear
...
response
...
between
...
head
...
loss
...
and
...
chemical
...
flow
...
rate
...
as
...
long
...
as
...
expansion
...
losses
...
are
...
small
...
relative
...
to
...
shear
...
losses
...
and
...
as
...
long
...
as
...
the
...
flow
...
is
...
laminar.
...
Design
...
of
...
the
...
flow
...
control
...
module
...
consists
...
of
...
choosing
...
a
...
maximum
...
head
...
loss
...
corresponding
...
to
...
the
...
maximum
...
design
...
flow
...
rate,
...
and
...
then
...
determining
...
the
...
diameter
...
and
...
length
...
of
...
the
...
tubing.
...
Cost
...
...
...
...
Conclusion
Acknowledgments
The development of the Flow Controller began as a class project in the course Sustainable Small Scale Water Supplies in the fall of 2004. The entire class contributed by testing various flow control ideas and the simple float valve and tube became the clear favorite for further investigation. The first field implementation of the flow controller was by Roslyn Odum in the Honduran community of La 34, the site of the first AguaClara water treatment plant. A number of AguaClara team members tested various float valve configurations before we discovered the manufactured PVC float valve that we now use. The manufactured PVC float valve was tested in the laboratory by Nicole Ceci, Cherish Scott, and ???. The 1 liter bottle version of the flow controller was first tested on aluminum sulfate and chlorine feed systems in the Honduran community of Ojojona, site of the second AguaClara water treatment plant. The Ojojona plant operators, ?? took the initiative to use the flow controller to upgrade an existing chlorine feed system and thus began the first replacement of the traditional hypochlorinators. The Sanjuan Fund generously supported the research and testing of the flow controller.
References
| Anchor | ||||
|---|---|---|---|---|
|