Comparison of Different Flow Measurement

DevicesCHEG 2810 - Experiment 1

Danielle Valdivia, Travis Garlock, and Alex MaldonadoOctober 22th, 2015

ABSTRACT

Rotameter in lab

Example Rotameter

The purpose of this experiment was to calculate volumetric flow rates using various flow measurement devices and compare their accuracy and precision. The three flow measurement devices were: rotameter, orifice plate, and magnetic flow meter. As it turns out the most accurate and precise flow meter was the magnetic flow meter. The magnetic flow meter had an average of 2.1% error while the orifice plate and rotameter had a 16.9% and 2.6% error respectively. The magnetic flow meter and rotameter were both accurate and precise, but the orifice plate was neither. This error was more than likely to be caused by inefficiency in the water collected from the output and for the orifice plate the constant jumping of pressures did not allow accurate readings. These results show that when precision is essential the rotameter or magnetic flow meter should be used. Of these two when the flowrate needs to be immediately known and easy to see changes the rotameter is the best choice.INTRODUCTION and BACKGROUND INFORMATION

The rotameter is a versatile process control device that can demonstrate changes in flow of various materials; in both gas and liquid phases. The design of the rotameter is designed to exploit the opposition between the downward force of gravity and the opposing force of the flowing fluid. This force of the flowing fluid mainly comes from the pressure difference the bottom of the rotameter and the sides of the rotameter (Basics of Rotameters, 2002). When the fluid approaches the bottom of the bob, the velocity increases due to the contraction of the jet streams. When there is a volumetric flow passing through the meter, the velocity of the jet is

given by the equation u= qC c ax

where q is the

flow rate, Cc is the ratio of the narrowest part of the jet to the area of bob, and ax as the area of the tube. If we substitute this in to Bernoulli’s law we get

P1−P2=ρ2 ( q

C c ax )2

which demonstrates that the pressure difference

caused by the jet stream contraction causes the buoyant force. When the flow rate is increased (and the fluid and rotameter stay the same) the pressure difference becomes greater thus increasing the buoyant force (Dijstelbergen, 1964). When the buoyant force is the same as the gravitational force of the bob (neglecting the gravitational force of the fluid) the bob reaches equilibrium. This equilibrium stabilizes the height of the bob relative to the tube and the velocity of the fluid can be calculated using the equation

u=√ 2gV b

C Ab

∗( ρb−ρf

ρf)

Where,

u = flow velocity Vb = volume of the bob g = gravitational acceleration constant C = drag coefficient Ab = frontal area of the bob ρb = density of the bob ρf = density of the fluid

This equation can calculate the velocity in any rotameter with any incompressible fluid. When using the same rotameter and fluid, most of the variables remain constant. When using a rotameter, the selection of design can simplify the equation further and linearize it (Springstead, 2015).

Q=Cm∗y∗√ ρb−ρ f

ρf

=Cm'∗y

Where,

Q = volumetric flow rate Cm = variable that contains constants from previous equation

These equations and theory show the useful and versatile the rotameter is to measure flow rate. Rotameters are still very popular among industrial applications because of cost effectiveness. They are relatively inexpensive and provide a simple way to control flow for a wide variety of substances. With more complex flowmeters the accuracy and precision is greatly increased but comes with a hefty price tag. Overall rotameters are viable options when simplicity and cost effectiveness are priorities, and when precision is top priority different flow meters are better options.

Another widely used flow meter is called the orifice meter and measures the flow of a liquid similar to that of a venturi meter, by restriction.  The fixed-area flow is due to a finely machined concentric hole within a plate mounted perpendicularly between two flanges. Pressure taps

are placed before and after the machined plate and connected to a manometer and/or a differential pressure transmitter.  The cross sectional area of the pipe diameter is reduced, increasing the velocity head while decreasing the pressure head (McCabe, 227).

This reduction in pressure head is what the connected device measures and is correlated to the liquid flow rate. 

As the liquid approaches the orifice plate, a vena contracta forms.  This is where the fluid stream separates itself from the downstream side of the orifice plate and forms a jet in the downstream liquid and where the liquid is as its minimum cross section.  This is a good location for the tap to be placed so that the meter may measure the downstream velocity. This style of tap is called the vena contracta tap and will have a static hole one-half to two pipe diameters from the orifice plate and the other located at the vena contracta (Perry, 8-48).  These type of taps give the largest differential head for a given flow rate.  The flow rate equation is given below. 

Q=Cd A2

√1−( A2

A1)

2 √ 2 ( p1−p2 )ρ

Where

(p1-p2) = the pressure drop ρ = the density A1 = the pipe cross-sectional area A2 = the orifice cross-sectional area Cd = the discharge coefficient

The discharge coefficient changes with Reynold’s Number at the orifice, based on the orifice diameter and velocity (Perry, 10-16). This number will increase with edge-roundness of the machined hole in the plate. Near the orifice plate on the downstream side of liquid, eddies form in the liquid due to large friction losses. These friction losses account for the poor pressure recovery of an orifice meter and its largest disadvantage. Power losses need to be supplemented with pumping equipment.

The magnetic flow meter is a more advanced device used to measure the flow rate of a fluid. When using this device, a magnetic field is spread throughout the measuring tube; the ions flowing within the fluid create a potential difference to be measured by the flow meter. This potential difference is proportional to the flow velocity of the fluid. In order to use a magnetic flow meter to measure a flow-rate, the fluid must be conducting, and the pipe must be insulating. Magnetic flow meters are most useful in that they are a non-contact, non-moving flow meter, which is very useful when measuring the flow rate of a dirty liquid or wastewater material that is water-based.

The magnetic flow meter is based on the principle of Faraday’s Law. This states that the voltage across a conductor as it moves perpendicular to the magnetic field lines is proportional to the Theoretical Magnetic Flow

Meter (Cadillac Meters, 2013)

velocity of that conductor (Magnetic Flow Meters, 2015). Faraday’s Law is represented by the equation:

E=V∗B∗D

Where,

E = voltage generated in a conductor, V = velocity of that conductor, B = magnetic field strength, D = length of the conductor being measured.

Each magnetic flow meter is fitted to a maximum flow that can be measured by that particular flow meter. The induced potential and the measured flow are compared to the maximum permitted potential and maximum measurable flow, respectively (Springstead, 2015). The displayed value on the magnetic flow meter can either be the direct flow measurement, or a percentage of the maximum measurable flow of the flow meter.

Magnetic flow meters are one of the most common types of flow meters used in industry. They are used for their relative ease and their known accuracy. Magnetic flow meters are much less cost effective than other flow meters but are much more exact in their measurement. Magnetic flow meters also come with the caveat that only conducting fluids may be measured, which proves them to be inadequate in many industrial situations. Generally, magnetic flow meters are used when precision is necessary, and when conductive fluids are involved.

METHODS/PROTOCOL

Rotameter

When there is not a flow through the rotameter, the bob is at the lowest point in the tube. Mark this point on a piece of tape on the side of the rotameter. This will be the initial point when taking height measurements. Open the valves and allowing a small flow through the pipes and observe the small increase in height of the bob. Allow the system to find equilibrium from turbulent flow to more of a laminar flow. Take a ruler and measure from the initial point to the point where the bob is when water is flowing through. While taking the bob height measurement, for five seconds fill a bucket with the output water. Then weigh the bucket and record the mass of the water.

Orifice Plate

Generally, a manometer will measure the pressure drop by correlating it to the height of fluid in the two legs of the manometer. However, the digital manometer used in this lab will correlate the difference between the mechanical pressures on two transducers located at the taps. This will give a similar reading to the differential pressure transducer which will display as mA. The lower the flow rate, the lower the mechanical pressure and therefore, the lower the reading on both meters. When the experiment is started, there is no flow through the orifice plate and both meters will roughly read close to zero. As the flow rate increases through the piping at each step interval, so too does the reading on each meter. Each time the flow rate is increased, the system is allowed to equilibrate before flow measurements are taken with a bucket and a stop watch. The amount of water in the given time is then measured for mass and recorded, resulting in a flow rate versus pressure drop graph.

Magnetic Flow Meter

First, ensure that the magnetic flow meter reads zero when there is no flow through the pipe. Then open the appropriate valves allowing a small flow through the pipe that the flow meter is attached to. Also make sure that after the water passes through the flow meter, the water continues through the pipes and into the output tank without flowing through the other two flow meters. Once the system has reached equilibrium, record the percentage displayed on the flow meter; this percentage represents a percent of the maximum measurable flow of the flow meter. As the measurement is recorded, for five seconds fill a bucket with output water from directly from the pipe. Then weigh the bucket and record the mass of the water collected. Be sure to tare the bucket before each water sample is collected. Increase the flow of the system, allow it to reach equilibrium, and perform another sample collection and measurement. Do this until there are between five and ten data points.

RESULTS

Average Mass of Output Water (kg)

Height of Bob (cm)

Actual Volumetric

Flow Rate (m3

s )Measured Rotameter

Flow Rate(m3

s )Percent Error

0.72 1.3 0.000144 0.000132 9.6%1.56 3.2 0.000312 0.000319 1.9%2.04 4.1 0.000409 0.000407 0.3%2.54 5.3 0.000509 0.000525 3.1%3.12 6.4 0.000625 0.000634 1.4%3.86 7.7 0.000773 0.000761 1.5%4.42 8.9 0.000885 0.000880 0.6%

Rotameter

In theory the rotameter should be the least accurate of three tested flow measurement devices. However it finished as the second most accurate device in this experiment. There are several reasons for this specific apparatus which will be covered in the orifice plate section of the results. In the chart to the right, the actual volumetric flow rate is the calculated flow rate from the water output. This is calculated by using the mass of water and density of the water which is affected

by the temperature which was 18 ⁰C for all rotameter trials. V (m3 )= M (Kg)

ρ( Kgm3 ) This is the total

volume of the output water which when divided by the time the water was collected gives us the flow rate. For this experiment each sample was collected for five seconds. An example calculation would be as follows,

Q=

Mρt

=

2.04 kg

998.6kg

m3

5 s=0.002043 m3

5 s=0.000407

m3

s

Using the height of the bob when collecting the output water we can graph how the volumetric flow rate affects the height of the bob. Finding the linear relationship of the data set provides an equation to calculate the flow rate that height represents in the rotameter. For this data set, the linear regression equation with a R2 value of 0.998 is,

Q=9.841∙ 10−5∗h+3.698 ∙10−6

This can be used to calculate the flow rate reported from the rotameter. This is measured flowrate in the above table and the percent error is the difference in the actual and experimental data. Overall the rotameter was accurate and precise with exception to the first trial which proves the reliability of the rotameter.

Orifice Plate

The orifice plate meter was actually the least accurate of the meters tested partly due to the eddies forming where the downstream pressure sensor was located, causing constant fluctuation in the manometer and differential pressure gauge. In order to quantify the accuracy of this meter, the actual flow rate and the theoretical flow rates needed to be compared and analyzed for percentage error. To do this, the actual flow rate was measured by the amount of water exiting the apparatus in a given amount of time.

Mass Output of Water (Kg)

√(Pressure) (√(mmHg))

Theoretical Volumetric Flowrate (m3/s)

Actual Volumetric Flowrate (m3/s)

% Error

2.26 2.95 0.000453 0.000444712 62.18 3.406 0.000437 0.000560897 15.92.88 3.821 0.000577 0.000689103 18.92.72 4.382 0.000545 0.000751202 25.63.36 4.701 0.000673 0.000777244 17.9

By taking the mass of the water coming out of the system and dividing it by the density of water, the volume of water can be calculated. This can then be divided by the amount of time taken to gain that volume of water to arrive at the volumetric flowrate. This volumetric flowrate will be the actual flowrate used to determine the accuracy of the flow meter when compared to the theoretical data. The theoretical data is gained from the equation:

0 1 2 3 4 5 6 7 8 9 100

0.00010.00020.00030.00040.00050.00060.00070.00080.0009

0.001

f(x) = 9.84073825371799E-05 x + 3.69822176188577E-06R² = 0.99823659823377

The Relationship Between the Height of bob and Volumetric Flow Rate

Height of Bobber (cm)

Volu

met

ric F

low

Rat

e (m

3/s)

where Cd is assumed to be a constant. This would be done with all remaining samples and the error calculated. The table below depicts the calibration curve for the measured data gained from the experiment and shows the trendline and R2 value for that trendline.

Magnetic Flow Meter

Mass of Output Water (kg)

Percent of Maximum Flow

Actual Volumetric Flow-rate (m3/s)

Measured Volumetric Flow-rate (m3/s)

Percent Error

0.64 6.7 0.000128205 0.000128936 0.57%0.7 6.9 0.000140224 0.000132784 5.31%2.21 23.7 0.000442708 0.000456086 3.02%2.74 28.4 0.000548878 0.000546533 0.43%3.07 32.5 0.000614984 0.000625434 1.70%4.17 42.7 0.000835337 0.000821724 1.63%

Based on research and on theory, the results of the magnetic flow meter were as we would expect, in that it was the most accurate of the three flow meters used in this experiment. The display on the magnetic flow meter reads out the percent of the maximum flow rate that is being measured. From this we need to calculate the maximum flow rate of our specific flow meter. In order to do this, we use the equation:

Flow rate=Percent flow∗Max . flow rate

We do this my solving for the maximum flow rate using our recorded percent flows and the flow rate that is obtained by dividing the volume of water collected by the time it was collected in. A

sample calculation is as follows:

Max . flow rate= flow ratepercent flow

=

vol. of watertime

percent flow=

0.0007 m3

5 sec0.069

=0.00203327m3

sec

After performing all of the individual calculations, we take an average to determine the most approximate maximum flow rate. Our average value was 0.001924412 m^3/s. We then use this equation again only this time we solve for the flow rate using the percent flow observed and the maximum flow rate we just calculated. A sample calculation is shown below:

Flow rate=percent flow∗Max . flow rate=0.069∗0.0019244m3

sec=0.000132784

m3

sec

This calculation was done on all measured percent flows. Then they were compared to the flow rates from the first equation and a percent error was found. In all of our sample observations, we can see that the magnetic flow meter was a very accurate flow measurement device.

DISCUSSION

Rotameter

The theoretical or actual data would be the volumetric flow rate of the water output. As shown in the graph below the experimental data is accurate and precise. However, there is some discrepancy in the data and when there is need for extremely precise measurement a rotameter should suffice. When simplicity is of importance and quick compairson of the change in flow rate the rotameter is the best option.

0 1 2 3 4 5 6 7 8 9 100

0.0001

0.0002

0.0003

0.0004

0.0005

0.0006

0.0007

0.0008

0.0009

0.001Experimantal Data Compared to Theoretical Data

Theory

Experimental

Height of Bob (cm)

Vol

umet

ric F

low

Rat

e (m

3/s)

Orifice Plate

The orifice plate flow meter had a great amount of error when it came to theoretical and actual flow rate comparison; the graph on the next page depicts this discrepancy. From the results section concerning the orifice meter, the calibration curve showed a trendline with the R2 value being 0.946 which, while close to 1, is much smaller a number than should be for an accurate reading. This is most likely due to the eddies forming in the downstream piping as these can cause a large differentiation of manometer readouts. The manometer used would fluctuate consistently, making readout values more randomized than accurate. The four to five values that the manometer would read were averaged to make a more realistic and more accurate assumption of the values.

Magnetic Flow Meter

As we can depict from the graph below, our experimental data fits the theoretical data closely. There is very little error between the measured volumetric flow rates and the theoretical volumetric flow rates. This proves that our experiment follows the research in that the magnetic flow meter is the most accurate of the three flow meters in this experiment. If the precision of flow measurement is of utmost importance, then the magnetic flow meter should be the instrument used.

0 5 10 15 20 25 30 35 40 450

0.0001

0.0002

0.0003

0.0004

0.0005

0.0006

0.0007

0.0008

0.0009

Experimental Data vs. Theoretical Data

Experimental

Theory

Percent of Maximum Flow

Vol

umet

ric F

low

Rat

e

CONCLUSION

Out of the three flow meters tested throughout this experiment, the magnetic flow meter was found to be the most accurate while the orifice plate meter was the least accurate; the rotameter was found to be somewhere in between but on the higher accuracy side of the spectrum. Each of these were not exact forms of measurement as they each had error when comparing theoretical to actual flow rates, which is to be expected. The greatest source of error came from the orifice plate meter with over 16% error and the smallest from the magnetic flow meter at 2% error. Since the purpose of the experiment was to calculate volumetric flow rates and compare accuracies of the three meters, it would behoove a process plant to utilize a magnetic meter or rotameter in the field rather than an orifice meter, strictly on an accuracy standpoint. If a flowrate was of immediate importance, a rotameter should be used.

RECOMMENDATIONS

If we were to repeat this experiment, there would be a couple of things that we would do differently to make sure our experiment had smaller error. The first thing we would do is to fix all the piping; the pipe that the orifice plate was attached to had a leak in it. This leak could throw off our measurements for flow and increase our percent error. Another adjustment we would make to this lab would be to use a more precise collection method. Although the method we used was very accurate, using an automated collection tool would allow us to collect output water for exactly five seconds. With our manual collection, there is always room for some error when timing and holding the bucket. A third change we would make to this lab would be to increase the flow rate by smaller increments. This would allow us to take more data points, which would yield a more reliable data trend.

REFERENCES

Dijstelbergen, H. (1964). Rotameter dynamics. Chemical Engineering Science, 19, 853-865.

Magnetic Flow Meters. (2015). Omega Engineering. Retrieved October 20, 2015, from http://www.omega.com/prodinfo/magmeter.html

Mechanical Flow Meters vs Magnetic Flow Meters. (2013, February 4). Retrieved October 20, 2015, from http://cadillacmeter.com/2013/02/04/mechanical-flow-meters-vs-magnetic-flow-meters/

Springstead, J. (2015). Data Acquisition and Handling Laboratory Manual.

The Basics of Rotameters. (2002, October 1). Retrieved October 16, 2015, fromhttp://www.sensorsmag.com/sensors/flow/the-basics-rotameters-1068

McCabe, Warren L., Julian C. Smith, and Peter Harriott. (2005). Unit of Operations of Chemical Engineering. 7th. New York: McGraw-Hill, pg 227Perry, Robert H. and Green, Don W. (1997). Perry’s Chemical Engineers’ Handbook. 7th. New York: McGraw-Hill. pg 8-48, 10-16

APPENDICES

Appendix A: Data collection of rotameter.

Height of Rotameter (cm)

Mass of Water Output (Kg)

Temperature of Water Output (⁰C)

Time of collected Water Output (s)

Density of Water (kg/m3)

1.3 0.72 18 5 998.63.2 1.56 18 5 998.64.1 2.04 18 5 998.65.3 2.54 18 5 998.66.4 3.12 18 5 998.67.7 3.86 18 5 998.68.9 4.42 18 5 998.6

Appendix B: Calculations for theoretical rotameter data

Volume of Water Output (m3)

Volumetric Flow Rate of Water Output (m3/s)

0.72kg

998.6kg

m3

=0.000721 0.000721 m3

5 s=0.000144

1.56kg

998.6kg

m3

=0.001562 0.001562 m3

5 s=0.000312

2.04kg

998.6kg

m3

=0.002043 0.002043 m3

5 s=0.000409

2.54kg

998.6kg

m3

=0.002544 0.002544 m3

5 s=0.000509

3.12kg

998.6kg

m3

=0.003124 0.003124 m3

5 s=0.000625

3.86kg

998.6kg

m3

=0.003865 0.003865 m3

5 s=0.000773

4.42kg

998.6kg

m3

=0.004426 0.004426 m3

5 s=0.000885

Appendix C: Calculation of experimental flow rate of rotameter compared to actual flow rate of rotameter

When plotting the experimental volumetric flow rate in respect to the measured height of the bobber, we can use a linear regression trend line to find an equation that calculates the volumetric flow rate from the height. This equation is

Q=9.841∙ 10−5∗h+3.698 ∙10−6

Where,

Q - Volumetric Flow Rate (m3/s) H - Change in vertical height of bob from reference point (cm)

An example calculation for 4.1 cm would be

Q=9.841∙ 10−5∗(4.1 )+3.698 ∙ 10−6=0.000407m3

s

The percent error is calculated using

Percent Error=|Experimental−TheoreticalTheoretical |∗100

Measured Flow Rate (m3/s)

PercentError

0.000132 |0.000132−0.0001440.000144 |∗100=9.6 %

0.000319 |0.000319−0.0003120.000312 |∗100=1.9 %

0.000407 |0.000407−0.0004090.000409 |∗100=0.3 %

0.000525 |0.000525−0.0005090.000509 |∗100=3.1 %

0.000634 |0.000634−0.0006250.000625 |∗100=1.4 %

0.000761 |0.000761−0.0007730.000773 |∗100=1.5 %

0.000880 |0.000880−0.0008850.000885 |∗100=0.6 %

Appendix D:

Appendix G: Data Collection of Magnetic Flow Meter

Percent Maximum Flow

Mass of Water Output (kg)

Temperature of Water Output (C)

Time of Collected Water Output (s)

Density of Water (kg/m^3)

6.7 0.64 19 5 998.46.9 0.7 19 5 998.423.7 2.21 19 5 998.428.4 2.74 19 5 998.432.5 3.07 19 5 998.442.7 4.17 19 5 998.4

Appendix H: Calculations for Theoretical Magnetic Flow Meter Data

Volume of Water Output (m3)

Volumetric Flow Rate of Water Output (m3/s)

0.64kg

998.4kg

m3

=0.000641 0.000641 m3

5 s=0.0001282

0.70kg

998.4kg

m3

=0.0007011 0.0007011m3

5 s=0.000140

2.21kg

998.4kg

m3

=0.002214 0.002214 m3

5 s=0.0004427

2.74kg

998.4kg

m3

=0.002744 0.002744 m3

5 s=0.0005489

3.07kg

998.4kg

m3

=0.003075 0.003075 m3

5 s=0.000615

4.17 kg

998.4kg

m3

=0.004177 0.004177 m3

5 s=0.0008353

Appendix I: Calculations for comparing experimental flow rate of the magnetic flow meter to theoretical flow rate of the magnetic flow meter.

The percent error is calculated using the same equation used previously in this lab.

Percent Error=|Experimental−TheoreticalTheoretical |∗100

Measured Flow Rate

(m3/s)

PercentError

0.000128936 |0.000129−0.0001280.000128 |∗100=¿

0.000132784 |0.000133−0.0001400.000140 |∗100=1.9 %

0.000456086 |0.000456−0.0004430.000443 |∗100=0.3 %

0.000546533 |0.000546−0.0005490.000549 |∗100=3.1 %

0.000625434 |0.000625−0.0006150.000615 |∗100=1.4 %

0.000821724 |0.000822−0.0008350.000835 |∗100=1.5 %

Appendix J: Orifice Data from experimentation

Pressure (mmHg) Mass of Water (Kg) Temperature of Water (C)

Time (s)

5.1 2.26 19 54.8 2.18 19 58.3 2.88 19 57.4 2.72 19 511.3 3.36 19 5

Appendix K: Calculated Orifice Data

√(Pressure) (√(mmHg))

Denisty of Water

Volume of Water (m3)

Volumetric Flow Rate

Measured Flow Rate

Percent Error

(m3/s) (m/s)2.95 998.4 0.002263622 0.000453 0.000444712 63.406 998.4 0.002183494 0.000437 0.000560897 15.93.821 998.4 0.002884615 0.000577 0.000689103 18.94.382 998.4 0.002724359 0.000545 0.000751202 25.64.701 998.4 0.003365385 0.000673 0.000777244 17.9