Liquid Metering System

Submitted November 21st, 2013 byKanchan 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.

Using a budget of 100 develop a simple system capable of delivering 1000cc of water.

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.

Objective

Motivations

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

∙Utilizing a pump greatly simplifies the problem; as we know the Volume Flow Rate is given by

𝑄=𝑉𝑜𝑙𝑢𝑚𝑒𝑡𝑖𝑚𝑒

∙ 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.

t

ρ𝐻20=

𝑚𝑎𝑠𝑠𝑉𝑜𝑙𝑢𝑚𝑒

=1.0gcc

mass (g )→Volume (cc )

∙ 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.

∙ 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. �̇� (g/ s )→Q (cc / s)

Theoretical Perspective and Design Considerations

𝑚𝑎𝑠𝑠 (𝑔)=𝑣𝑜𝑙𝑢𝑚𝑒(𝑐𝑐)=𝑄∗𝑡∙ 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.

∙ 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.

𝑚 (𝑡 )=𝑚0+�̇�∗𝑡

𝑡=𝑉 (𝑡 )−𝑉 0

𝑄

𝑉 (𝑡 )=𝑉 0+𝑄∗𝑡

�̇� (g/ s )→Q (cc / s)

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.

Experimental Setup & Procedure

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

Calibration Sub-VI

Formula “t” (output) = (Volume – 0.318)/(9.7745)

LabVIEW Programming

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.

Material Cost/Assembly Analysis

t (s) mass (grams)0.5 41.0 91.5 142.0 192.5 243.0 284.0 385.0 485.5 526.0 577.0 67

10.0 9712.0 11715.0 14717.0 16620.0 19622.0 21525.0 24528.0 27430.0 29432.0 31335.0 34237.0 36240.0 39243.0 42145.0 44050 48955 53960 58765 63670 68575 73280 78285 83090 87995 927

100 976105 1024

0.0 20.0 40.0 60.0 80.0 100.0 120.00

200

400

600

800

1000

1200

f(x) = 9.77453600317182 x − 0.318030220366779

Mass vs. Time

Mass vs. Time9.7745t-0.318

Time (seconds)

Mass (

gra

ms)

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.

Results

t (s) mass (grams) xixi xiyi y = a + bxi [y - (a+bxi)]2

0.5 4 0.25 2 4.569238 0.3240316521.0 9 1 9 9.456506 0.208397531.5 14 2.25 21 14.34377 0.1181804152.0 19 4 38 19.23104 0.0533803072.5 24 6.25 60 24.11831 0.0139972063.0 28 9 84 29.00558 1.011186694.0 38 16 152 38.78011 0.6085775295.0 48 25 240 48.55465 0.3076363965.5 52 30.25 286 53.44192 2.0791269346.0 57 36 342 58.32919 1.7667348877.0 67 49 469 68.10372 1.218201816

10.0 97 100 970 97.42733 0.18261076812.0 117 144 1404 116.9764 0.00055687415.0 147 225 2205 146.3 0.48998624217.0 166 289 2822 165.8491 0.02277629320.0 196 400 3920 195.1727 0.68444209622.0 215 484 4730 214.7218 0.07741646825.0 245 625 6125 244.0454 0.91131870628.0 274 784 7672 273.369 0.39818893130.0 294 900 8820 292.918 1.17061607332.0 313 1024 10016 312.4671 0.2839590935.0 342 1225 11970 341.7907 0.04379397937.0 362 1369 13394 361.3398 0.43586153540.0 392 1600 15680 390.6634 1.78647307843.0 421 1849 18103 419.987 1.02613270245.0 440 2025 19800 439.5361 0.2152125650 489 2500 24450 488.4088 0.34955298655 539 3025 29645 537.2814 2.9534142660 587 3600 35220 586.1541 0.71549610865 636 4225 41340 635.0268 0.94709880470 685 4900 47950 683.8995 1.21112225675 732 5625 54900 732.7722 0.59624653680 782 6400 62560 781.6449 0.12613149985 830 7225 70550 830.5175 0.26783735290 879 8100 79110 879.3902 0.15226389595 927 9025 88065 928.2629 1.594891357

100 976 10000 97600 977.1356 1.289519445105 1024 11025 107520 1026.008 4.033068515

𝑎=𝑆𝑦−𝑏𝑆𝑥

𝑘 𝑏=𝑘𝑆𝑥𝑦−𝑆𝑥𝑆 𝑦

𝑘𝑆𝑥𝑥−𝑆𝑥𝑆𝑥

𝑢𝑎=¿¿

𝑢𝑏=¿¿

0.0 20.0 40.0 60.0 80.0 100.0 120.00

200

400

600

800

1000

1200

f(x) = 9.77453600317182 x − 0.318030220366779

Mass vs. Time

Mass vs. Time9.7745t-0.318

Time (seconds)

Mass (

gra

ms)

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

Linear Regression

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.

Discussion

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

Conclusion

Thank You