Flow Control Report
Team DHMO
Barry Schnorr
Haixian Huang
Justin Ferrentino
David Harrison
Abstract
A slow-sand filter works best when water is added at a constant rate. However, the flow rate from a gravity-fed storage tank changes over time due to the change in head.
That is why a device that can regulate the flow to a constant rate is needed. We made constant flow from a floating ball valve. Water enters a soda bottle through a vertical pipe at the top, while a floating racquetball pushes back against the pipe, limiting the rate that water can flow through. The water exits the bottle through a long section of very thin plastic tubing, creating head loss that determines the flow rate. This device is very cheap to make; it is made out of a plastic soda bottle, a racquetball, about a meter of thin
PVC tubing, and a small section of metal pipe that only needs to be a few centimeters long. An advantage of this device is that it does not require any initial setup, except to make sure that the ball is flushed with the pipe. Another advantage is that the flow rate can be changed by raising and lowering the free end of the tubing, which changes the head loss. The biggest advantage of this device is that dirty water does not clog it, because there are no small orifices.
Goal
The purpose of this project is to design and build a flow control device so that it can be used to improve the performance of Point of Use (POU) water treatment systems.
Many POU systems, such as slow-sand filters and drip chlorinators, are designed on the

assumption that the flow rate of water is constant. However, this is often not the case.
Water turbidity and surface tension can easily disrupt the constant flow and thus lead to failures and poor performances in many of the POU devices that are being use today. Our objective is to build a purely mechanical and self-sustainable device that can provide a constant flow rate of 20 L/day. The ultimate goal is to come up with an inexpensive, user-friendly, and reliable technology that can be distributed in the global south, where the quality of drinking water is still an everyday concern.
Literature Review
During the brainstorming process, we researched various topics involving constant flow, such as IVs and waterclocks; however, in our final design we did not incorporate any of those components, and only relied on our knowledge of fluid mechanics and the guidance of Professor Weber-Shirk in building our device. We consulted a fluid mechanics textbook, Engineering Fluid Mechanics by Crowe, et. al for the headloss equation used in our design calculations.
Design Calculations
A floating ball blocks the top of a container into which water flows from above.
Air holes are placed near the top of the container (but not blocked by the ball) to keep the pressure atmospheric at the level of the float. If the water level drops, water leaks in from above the float to raise it again. Thus the head in the container remains roughly constant.

θ
d f
ρ f
ρ water d f
2
θ
θ d f
2 sin

A c


4 d t
2
Figure 1: Floating ball valve and contact
Float constraint: F buoyant
– F gravity
> F pressure
when float is submerged

6 d f
3 g

 water
  float

  water g h t

A c

6 d f
3 h t


 water

 water
 float



A c
A c
A c





 d
2 f max


  sin
4 d
 f
2


 2 sin 2

,

4 d t
2



depending on whether contact is at the lip of the tube or with the top walls of the container
For: d f
= 5cm, h t
= 50 cm, ρ float
= 0.3ρ water
 0.916 cm 2 > A c d t
< 1.1 cm with d t
constraint on A; this looks attainable.
Leak constraint: When the ball is at its maximum height, leaks from above < design flow.
This is much harder to estimate since it depends on the roughness and imperfections of

the ball and container. We hope to limit the leak constraint by making the ball and/or the lip of the tube deformable, so that when the water level is high, the float or an o-ring compresses and improves the contact of the ball/surface interface to limit leaking.
This system should be able to produce a controllable head loss of less than 10cm
(on the order of the diameter of the float). If the head loss device relies on major losses due to flow in a thin tube, flow will always be laminar for any reasonably sized tube.
Re

Dv



D

Q /(

D

2
/ 4 )

4

Q

D

With 20 L/day of water, Re < 2.8 for all tubes with D > 1 mm. We can use the results for laminar Poiseuille flow to predict the tube length necessary to produce a given flow rate, assuming fully developed steady flow. f
Moody

2 gD
 h

Lv
2
64
Re
L

2 gD f
Moody v
2
 h


D
4 g

128 Q

 h
Based on this equation we see that using a 1/16 inch (0.00159m) inner diameter tubing will give us about 17 cm of headloss in 1m tubing.
Decision Process
The most important reason for choosing the floating ball valve is its ability to control the flow through a slow sand filter with a head loss device after filter. Head loss mechanisms, whether valves, tubes, or orifices, are vulnerable to clogging—by controlling the flow of water after its turbidity has been reduced, the reliable lifetime of the head loss device is increased. Most constant head devices, however, cannot be used

after the slow sand filter and still control the flow through the filter. A constant head device with a water level that changes as the original container drains would not control the flow rate through the filter.
For instance, placing a floating orifice device in a tank after the slow sand filter appears to work over one run. The water level in A will be h f
above that in B, and will gradually drop as the floating orifice drains them both at constant flow into C. However, when tank A is filled again with dirty water, it will rapidly flow through the slow sand filter until the levels equilibrate to within h f
of each other, making roughly half of the filter run almost untreated water. h f A
B
C
Figure 2: Floating orifice design
A constant head device which only controls the flow leaving, rather than entering, can only be placed after the SSF without allowing massive startup flows through the SSF if there is supercritical flow leaving the SSF—which would make it impossible to control the relevant flow. Thus, the choices for flow control devices after the SSF are essentially limited to the floating valves, float-controlled valves controlling entering flow (such as

used in the MIT Honduras hypochlorinator project), and valves controlled by clockwork or electric timers. Of these, we chose the floating ball valve because it is simple and contains only one moving part (the ball).
This device does contain a small amount of space which empties after the flow from above stops, and which refills rapidly at the beginning of a filter run, but this space is only on the order of 10 mL, much smaller than the volume of the SSF.
Schematics
Figure 3: Floating ball valve
A major advantage of this device is that it is inexpensive and easy to build. Using a 1 L soda bottle, a racquetball and various diameter tubes we were able to construct our device. The water comes in from the SSF and into the bottle through the steel tubing and then flows out through the PVC tube into the clearwell. The most critical component of our design is to ensure that the steel tubing will create a sufficient seal with the rubber ball to maintain constant head within the bottle. Below is a cost table of our materials.

Table 1: Materials Costs
Approximate Material Costs for Flow Control Device
Item Cost
Soda bottle
Racquet ball
1/4 inch steel tube
$ 0.05
$ 0.50
$ 0.15
1/16 inch PVC tubing bucket (reservoir)
$ 0.25
$ 2.00
Total $ 2.95
Test Results
After many short-term and long-term trial runs using both clean and dirty water, we were able to conclude that our device can successfully produce constant flow. By varying the distance between the water surface inside the bottle and the outlet of the tube, we can change the flow rate of our device. There was a linear relationship between the difference in height and the flow rate produced, as expected from our design calculations.
We measured the water by mass because it is more accurate than measuring by volume.
We assumed a density of exactly 1 g/mL for both clean and dirty water.
Table 2: Flow Rates Measured from Different Reservoir Water Levels
Changing Water Level in
Reservoir
Water Height Mass Empty
(+0.5cm) Container
(cm)
7.5
16.5
27.5 varied varied
(g)
64.22
64.17
42.1
527.2
531.6
Mass w/
Water
(g)
89.64
89.45
67.53
2151.2
2933.4
Mass of
Water
(g)
25.42
25.28
25.43
1624
2401.8
Time
Flow
Rate
Flow
Rate
(s)
115
113
113
(g/s)
0.221
0.224
0.225
7380 0.220
10980 0.219
(L/day)
19.1
19.3
19.4
19.0
18.9

Table 3: Flow Rates Measured From Different Tube Heights
Changing Outlet Height
Tube Height
(+0.5cm)
(cm)
2.5 (4.5)
8.5 (9.5)
17
19
29.5 rose to
Mass Empty
Container
(g)
41.9
41.9
41.2
41.9
41.9
44.5 41.9
** ( ) indicates height water
Mass w/
Water
(g)
54.7
62.4
73.0
70.2
78.4
90.8
Mass of
Water
(g)
12.8
20.5
31.8
28.3
36.5
48.9
Time
(s)
233
165
132
109
95
88
Flow
Rate
Flow
Rate
(g/s) (L/day)
0.055 4.7
0.124
0.241
0.260
10.7
20.8
22.4
0.384
0.556
33.2
48.0
Table 4: Comparison of Flow Rates of Clean and Dirty Water
Clean vs. Dirty Water(~120 NTU)
Tube
Height
(+0.5cm)
Mass Empty
Container
Mass w/
Water
(cm) clean 18
(g)
42.0
(g)
96.7 clean 17.5 dirty 17.5
42.1
41.9
69.1
65.6 dirty 17.5 dirty 17.5 dirty** 17.5
529.1
41.9
41.9
4181.6
69.4
64.3
** 4.5 hours after previous test
Mass of
Water
(g)
54.7
27.0
23.7
3652.5
27.5
22.4
Time
(s)
221
111
100
Flow
Rate
Flow
Rate
0.248 21.4
0.243 21.0
0.237 20.5
15810 0.231 20.0
Time
Running in
Device
(g/s) (L/day) (min)
-
1
5
268.5
120
97
0.229 19.8
0.231 20.0
273.5
543.5

19.5
19.5
19.4
19.4
19.3
19.3
19.2
19.2
19.1
19.1
0 5 10 15
Water Height (cm)
20
Figure 4: Graph of Flow Rate vs. Reservoir Water Level
25 30

50
40
30
20
10
0
0 5 10 15 20 25
Tube Height (cm)
30 35 40 45
Figure 5: Graph of Flow Rate vs. Tube Height (Range of Flow Rates Produced)
50

21.2
21.0
20.8
20.6
20.4
20.2
20.0
19.8
19.6
0 100 200 300
Time Running in Device (min)
400 500
Figure 6: Flow Rates of Dirty Water over Time
600
Clean Water
Dirty Water

Photos of the Prototype
Figure 7: The setup for testing

Figure 8: Close up of the flow control device

Figure 9: Various parts of our device
Figure 10: The 1/16” ID headloss tubing

Operator Instructions
One drawback of this device is that air fills the head loss tubing after a filter run when the ball has dropped. When the water level rises above the tubing again, it usually does not force the bubbles out and automatically restore flow. The user needs to suck on the end of the tubing until water comes out. Since what comes out is filtered drinking water, this may be acceptable, but it would be better for the user to refill the feed container more often so that it never drains.
After the ball has dropped, it must rise back into position to make an adequate seal. In earlier tests using a PVC tube and O-ring to contact the ball, it often required several attempts and readjustments to make proper contact. When we used our steel tubing to contact the ball, the ball rose into position to make a seal every time without any effort on our part. As constructed, the device appears to be robust enough that it would not require user effort to make the ball.
The head loss device itself should require little to no maintenance. Some particles that make it through the SSF may settle at the bottom of the container but this is likely harmless. If the water leaving the SSF still contains enough nutrients to support biological growth of a slime in the device, it may be necessary for the user to clean it to avoid clogging the head loss tubing. This could be accomplished by removing the cap, scrubbing out the inside of the container with a small brush or toothbrush, and rinsing with clean water. However, controlling water that has passed through a SSF makes it most likely that no maintenance will be required.

Recommendations for Further Research
Further research for this device should focus on durability, ease of production, and ease of maintenance. Durability could be achieved by using a sturdier bottle and using an adhesive to fix the steel tube to the bottle cap. Ease of production could be achieved with standard parts, finding a quick and easy way to arrange the head loss tubing around the bottle, and using a less expensive plastic tube to replace the steel one.
Ease of maintenance would be best accomplished if the bottle could be screwed together.
This would make it possible to open the device to replace the ball or to clean settled particles. It would also be more durable than the putty seal we used.