Liquid Metering System
Submitted November 21st, 2013 by
Kanchan Bhattacharyya
Matthew Stevens
Ting Zhang
Xie Zheng
Background
Liquid Metering Systems are used all throughout the world for a
variety of purposes.
From manufacturing and filling of liquids to dispensing
beverages in restaurants, there will always be a need for a
machine to deliver specific amounts of liquids in specific
amounts of time.
Objective
Using a budget of 100 develop a simple system capable of delivering 1000cc of water.
Motivations
Using a limited budget and relatively limited resources, develop a simple system capable of delivering 1000cc of
water. Considering the relatively small volumes of water being dispensed, the limited budget, and sheer
simplicity, we designed a system operating with a small submersible constant flow rate water pump, a solenoid
valve connected to a timed DAQ input, and other simple items found at the local hardware store. Using a pump
to ensure constant flow rate through a small system would allow for easy calibration of the volume flow rate of
the system and subsequently would provide the necessary criteria to be able to deliver specific volumes.
Basic Working Principle
∙ Constant flow rate water pump placed in a small reservoir of water
connected to 12V Solenoid Valve via polyethylene tubing
∙ As implied, pump will supply a constant flow rate of water through the
polyethylene tubing discharging through the valve/nozzle assembly to a
container
∙ The normally closed solenoid valve will be controlled via LabVIEW
programming to deliver water from the reservoir.
∙ When opened, the water will be delivered at the same flow rate allowing
for calibration of the system’s discharge volume flow rate as a function of
time.
∙ Having developed the relationship between the dispensed volume and
elapsed time, derive a relation for time as a function of volume
∙ Use the function t(V) to control system’s valve timing to produce any
desired volume of water
∙
3D Renderings of our proposed design
Theoretical Perspective
and Design Considerations
𝑉𝑜𝑙𝑢𝑚𝑒
𝑄=
𝑡𝑖𝑚𝑒
∙Utilizing a pump greatly simplifies the problem; as we
know the Volume Flow Rate is given by
t=
∙ If the pump displaces a finite amount of volume at a specific flow rate,
we can find the required time at this flow rate to produce the volume.
∙ Because water is an incompressible fluid with a known density of
1gram/cc, we also know that any mass of water (in grams) will have a
volume of equal value in cc.
ρ𝐻20
𝑉𝑜𝑙𝑢𝑚𝑒
𝑄
𝑚𝑎𝑠𝑠
1.0 g
=
=
𝑉𝑜𝑙𝑢𝑚𝑒
cc
mass g → Volume(cc)
∙ Therefore, we can also say that for water any volume flow rate in cc/sec
will have an equivalent mass flow rate in grams/sec.
𝑚 g/s → Q(cc/s)
Theoretical Perspective
and Design Considerations
∙ Therefore, if our system were to displace a mass of water m in a time t,
we can determine the volume of the displaced water in that time.
∙ Considering the results of successive flow times, we can use linear
regression analysis to find the relationship that exists between the
volume of water dispersed by the system
And the time taken for the system to displace that water.
∙ Specifically, we can use the experimental results of volume dispensed
per time to calculate a true volume flow rate for our system.
𝑚𝑎𝑠𝑠(𝑔) = 𝑣𝑜𝑙𝑢𝑚𝑒(𝑐𝑐) = 𝑄 ∗ 𝑡
𝑚 𝑡 = 𝑚0 + 𝑚 ∗ 𝑡
𝑚 g/s → Q(cc/s)
𝑉 𝑡 = 𝑉0 + 𝑄 ∗ 𝑡
∙ By measuring the weight of water (in grams) for different valve opening
times, we use the density relation to find the volume of the water.
∙ Using the V = a + Qt relationship derived from linear regression, we can
determine the theoretical run time to deliver any desired volume.
𝑉 𝑡 − 𝑉0
𝑡=
𝑄
Experimental Setup & Procedure
Setup
1.) Place the submersible pump in the bucket as close to the nozzle
assembly as possible, submersed in at least 6 in. of water.
2.) Plug the electronic relay into the breadboard, noting the location of each
pin.
3.) Plug the power supply and pump into the nearest power source, and
connect the black/white wire with the red wire of the solenoid to establish a
positive connection. Connect the black wire to the breadboard.
4.) Connect the DAQ Unit to the Breadboard in the ports corresponding to
the middle pins of the relay, then to the Laptop PC via USB.
5.) Connect the pump with the solenoid valve/nozzle assembly via
polyethylene tubing and fittings.
Experimental Setup & Procedure
Experimental Procedure
1.) Open the LabVIEW program
2.) Place beaker underneath the solenoid valve nozzle output, and use the
timer in the LabVIEW Program and allow the water to flow into the beaker.
3.) When the valve closes, measure the weight of the water (in grams) using
the scale.
4.) Empty the measure water back into the bucket, and use paper towels to
carefully dry any water left in or on the beaker
5.) Repeat 6,7, & 8 for various times.
LabVIEW Programming
Front Panel
•Sub-VI for calibration & Sub-VI for Volume Dispensing Combined
LabVIEW Programming
Block
Diagram
•Logic ensures no I/O errors if the user accidentally puts input for calibration & volume dispensing –
either the one intended occurs or the program stops.
•One branch for calibration, another for volume dispensing – argument passing, formula expression
from calibration, timing for self-check; both use flat structures enclosed in case structures.
LabVIEW Programming
Logic
•First boolean from each input
connected by ‘AND’, T/F trigger
top Volume Dispensing Branch
•Second boolean from each
input connected by ‘AND’ trigger
bottom Calibration Branch.
•Desired operation requires > 0
value in front panel for that
operation and <= 0 for the other
operation.
•If both >0, both branches false,
program ends.
LabVIEW Programming
Volume Dispensing & Calibration Branches
Volume Dispensing Sub-VI
Formula  “t” (output) = (Volume – 0.318)/(9.7745)
Calibration Sub-VI
Material Cost/Assembly Analysis
Description
Price
12V/500 mA Power Supply
$19.99
12V Solenoid Valve
$15.99
Electronic Relay
$2.00
Ecoplus 185 Submersible Pump
$15.50
Socket Breadboard
$9.99
(3) 1/4" NPT Polytube Fittings
$9.72
Lead Connector Accessory for Power Supply
$4.99
Wood Base Board
$4.31
2 Gallon Bucket
$3.58
1/4" Brass Female Pipe Coupling
$1.99
1/4" NPT Brass Hex Pipe Nipple
$1.19
1/4" OD Polyethylene Tubing
$0.28
Wood/Screws for Nozzle Holder Assembly
$0.00
TOTAL
$89.53
The Nozzle Holder Assembly was fabricated in the following Process:
∙Desired holes were marked for the screw locations on vertical/horizontal beams as well as the location for the
solenoid valve.
∙Holes were drilled using a vertical milling press in the Machine Shop
∙ Locations along width of baseboard for vertical supports of the nozzle holder assembly were marked using a
depth gage before fastening.
∙A Simple Project Contact Cement was applied to the regions making face contact with the baseboard
∙ The screws were drilled into the vertical supports/base board and horizontal beam/vertical beams to create
nozzle holder assembly.
∙ The output port of the solenoid valve was fitted with a ¼” Hex Pipe Nipple, which fits in the hole drilled in the
horizontal beam
∙ The length of the nipple extends through the beam, and is fastened along with the solenoid via a ¼” Brass
Female Pipe Coupling
∙ Finally, a spout was created with a small length of ¼” OD Polyethylene tubing and fittings.
Results
mass (grams)
4
9
14
19
24
28
38
48
52
57
67
97
117
147
166
196
215
245
274
294
313
342
362
392
421
440
489
539
587
636
685
732
782
830
879
927
976
1024
Mass vs. Time
1200
m = 9.7745t - 0.318
1000
Mass (grams)
t (s)
0.5
1.0
1.5
2.0
2.5
3.0
4.0
5.0
5.5
6.0
7.0
10.0
12.0
15.0
17.0
20.0
22.0
25.0
28.0
30.0
32.0
35.0
37.0
40.0
43.0
45.0
50
55
60
65
70
75
80
85
90
95
100
105
800
600
Mass vs. Time
9.7745t-0.318
400
200
0
0.0
20.0
40.0
60.0
80.0
100.0
120.0
Time (seconds)
Graph plotting the dispensed mass of water for allotted trial time (the time in seconds the solenoid valve was
opened for). As expected, a linear relationship was found between the mass dispensed and the trial time. Linear
Regression rendered the equation y = 9.7745x – 0.3198. Using known dimensions for the variables involved, m
= (9.7745grams/second)t – 0.3198 grams. The slope of this line is the mass flow rate of the system, 9.7745
grams/second. Considering the relationship between mass, density, and volume as well as a density of 1.00g/cc,
we find the desired volume flow of 9.7756 cc/sec.
Linear Regression
mass (grams)
4
9
14
19
24
28
38
48
52
57
67
97
117
147
166
196
215
245
274
294
313
342
362
392
421
440
489
539
587
636
685
732
782
830
879
927
976
1024
xixi
0.25
1
2.25
4
6.25
9
16
25
30.25
36
49
100
144
225
289
400
484
625
784
900
1024
1225
1369
1600
1849
2025
2500
3025
3600
4225
4900
5625
6400
7225
8100
9025
10000
11025
xiyi
2
9
21
38
60
84
152
240
286
342
469
970
1404
2205
2822
3920
4730
6125
7672
8820
10016
11970
13394
15680
18103
19800
24450
29645
35220
41340
47950
54900
62560
70550
79110
88065
97600
107520
y = a + bxi
4.569238
9.456506
14.34377
19.23104
24.11831
29.00558
38.78011
48.55465
53.44192
58.32919
68.10372
97.42733
116.9764
146.3
165.8491
195.1727
214.7218
244.0454
273.369
292.918
312.4671
341.7907
361.3398
390.6634
419.987
439.5361
488.4088
537.2814
586.1541
635.0268
683.8995
732.7722
781.6449
830.5175
879.3902
928.2629
977.1356
1026.008
[y 0.324031652
0.20839753
0.118180415
0.053380307
0.013997206
1.01118669
0.608577529
0.307636396
2.079126934
1.766734887
1.218201816
0.182610768
0.000556874
0.489986242
0.022776293
0.684442096
0.077416468
0.911318706
0.398188931
1.170616073
0.28395909
0.043793979
0.435861535
1.786473078
1.026132702
0.21521256
0.349552986
2.95341426
0.715496108
0.947098804
1.211122256
0.596246536
0.126131499
0.267837352
0.152263895
1.594891357
1.289519445
4.033068515
k
38
Sx
1379.0
Sy
13467.0
Sxx
88872
Sxy
868244
a
-0.31803
b
9.774536
theta
29.67544
ua
0.2228235
ub
0.0046076
𝑏=
𝑘𝑆𝑥𝑦 − 𝑆𝑥𝑆𝑦
𝑘𝑆𝑥𝑥 − 𝑆𝑥 𝑆𝑥
1/2
𝑆𝑥𝑆𝑥
θ
𝑢𝑎 = [
(1 +
)]
𝑘 𝑘−2
𝑘𝑆𝑥𝑥 − 𝑆𝑥 𝑆𝑥
1/2
𝑘
𝜃
𝑢𝑏 = [
(1 +
)]
𝑘−2
𝑘𝑆𝑥𝑥 − 𝑆𝑥 𝑆𝑥
Mass vs. Time
1200
1000
Mass (grams)
t (s)
0.5
1.0
1.5
2.0
2.5
3.0
4.0
5.0
5.5
6.0
7.0
10.0
12.0
15.0
17.0
20.0
22.0
25.0
28.0
30.0
32.0
35.0
37.0
40.0
43.0
45.0
50
55
60
65
70
75
80
85
90
95
100
105
(a+bxi)]2
𝑆𝑦 − 𝑏𝑆𝑥
𝑎=
𝑘
m = 9.7745t - 0.318
800
Mass vs. Time
600
9.7745t-0.318
400
200
0
0.0
20.0
40.0
60.0
Time (seconds)
80.0
100.0
120.0
Discussion
An expected linear relationship between delivered mass/volume and time elapsed
Effect of Initial Height of Water in Reservoir
∙ The height of the surface of the water does affect the velocity of the flow
∙ We noticed through various observations that increasing the height of water in the tank/above the pump resulted in an increase
in dispensed mass I.E. the volume/mass flow rate increased
∙ To maintain a constant flow rate throughout the course of the experiment an initial height of water was chosen, and any water
dispensed by the system was poured back into the reservoir.
Length of Tubing delivering water
∙ A specific length of tubing was used, such that a direct connection between the solenoid input and pump output was established
with minimal transfer height and kinks.
∙ As the length of the tubing through which the water was delivered was increased, there was an increased tendency for formation
of air bubbles.
∙ When the valve was closed these bubbles would be forced through the system from the pressure provided by the pump, eventually
leaking through valve ports.
∙ This effect was eliminated by a direct line with as little lift as possible.
Accuracy of Final Results
∙ Using relationships between mass, time, and volume we developed the relationship for time as a function of volume
∙ Using this function to calculate the required valve open time for a user specific value, we were able to achieve results within the
2cc accuracy limit
for volumes of 10, 50, 100, 500, 750, and 1000cc.
Conclusion
Using a constant flow rate water pump greatly simplified the problem
The height of the water in the reservoir was an important factor
∙ The pump requires at least 6 inches of water to operate
∙ The greater the height of water, the greater the volume flow rate through the system
Effects of Reservoir Geometry
∙ The larger the overall volume of the reservoir, the greater the accuracy of the calibration
Effects of Tubing Length/Diameter
∙ Minimizing kink and overall tubing length ensured constant flow and minimized air bubbles/pressure bursts
∙ A relatively small tubing diameter was chosen and maintained throughout the system to ensure flow consistency and
considerable rate for timing considerations
PC-DAQ-Valve Response Lag?
∙ While seemingly insignificant, a slight lag was present in timing
∙ Of fractional order, these effects can be neglected when considering accuracy of final results
Successful Problem Solving Approach
∙ Calibration Technique rendered extremely accurate results
Thank You