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Gas Flow Meters

CHEN 3401W

Unit Operations Laboratory

Section 16, Group 2

Section Instructor: Aditya Bhan

March 29th, 2013

Planner: Alvaro de la Garza Musi

Experimenter: Reese Weber

Analyzer: Lia Palmore

Consultant: Laurel Dresel

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Abstract

A client contacted Uni-Minn to design a gas flow meter for a particle removal system

in one of their air filtration operations. The system has an air flow rate of 5,000 lbs/hr

through a 500ft pipe which enters the particle removal system at the specified inlet

conditions of 30 psig and 120F. The client requested a design for the optimal pipe

diameter, pressure drop across the system, compressor size, and type of meter.

Experimental data was gathered in the University of Minnesota pilot plant to perform the

scale up design for the client. Coefficients for the orifice, flow nozzle, and venturi meters

were calculated using the pitot tube as standard. The pressure drop across each meter

was found as a function of the Reynolds number. In the experiment, the meter type and

damper settings were considered to be the independent variables, while the manometer

height, air flow rate, pressure drops, and meter coefficients were taken as dependent.

Different flow rates were attained by changing the blower damper settings. This

resulted in a range of Reynolds numbers from 5,000 to 20,000 creating turbulent flow for

all damper settings. Air was approximated to be incompressible for the experiment, as

the blower did not compress the air by more than 10%.

The experiment was conducted by first centering the pitot tube. This was done by

measuring the fluid velocity at damper settings of 4, 6,7,10, and 12 and representative

points in the airflow of different cross-sectional areas. A maximum pitot velocity was

attained at the center of the pipe when the ruler on the pitot marked 2.70.1in. Centering

the pitot allowed us to calibrate the meters. The hot wire anemometer was the first

device to be calibrated. A calibration curve of the anemometer velocities versus the pitot

velocities yielded a slope of 1.100.06 and an R2 of .99. The slope of the curve validates

the pitot measurement as it is 0.1% away from the theoretical value of 1. Each gas flow

meter pressure drop was then measured. The venturi and flow nozzle meters at the

highest damper setting used, presented a head loss of 10,500300ft and 22,800300ft,

respectively. The circular meter presented a higher head loss of 51,000 300ft. The

head loss was larger than the theoretical value due to leaks and frictional losses in the

system. This behavior was consistent at all damper settings.

The meter coefficients were found by measuring the pressure drop over the meter

and calculating the velocity through the meter. The ratio of this and the velocity from the

continuity equation defined the coefficient. Venturi and circular orifice meter coefficients

were determined to be 0.940.04 and 0.590.02, respectively. The flow nozzle meter

presented a higher than unity coefficient of 1.040.04 which was attributed to air leaks.

After analysis, the venturi meter was recommended for scale up because of its

precision at high Reynolds numbers and low permanent pressure drop. A nominal 8

ANSI 40 schedule pipe was recommended for the design. The total pressure drop

across the system was 30.38psi. To overcome this pressure, a144 hp compressor is

necessary, so a rotary screw 150hp compressor is suggested. The residence time of the

fluid in the compressor is small enough that adiabatic compression can be

approximated, implicating a temperature rise. Air exits the compressor with a

temperature of 280F, which is higher than the one specified by the client. A finned shell-

and tube heat exchanger with an area of 49ft2 is suggested to lower the temperature.

Initial capital investment for the system was determined to be $43,000.

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TABLE OF CONTENTS

I. Introduction 4

II. Theory and Technical Background 4

i. Meter Types 5

ii. Design Problem Theory 7

III. Description of Apparatus/Experimental Procedure 10

i. Description of apparatus 10

ii. Experimental Procedure 12

iii. Shut-down Procedure 14

iv. Safety and Precautions 14

v. Process Flow Diagram 14

IV. Calculated Data Tables 16

i. Pitot Tube Data 16

ii. TSI Meter Data 17

iii. Orifice Meter Data 18

iv. Venturi Meter Data 19

v. Flow Nozzle Data 20

vi. Sound Data 21

V. Final Results 22

i. Pitot Tube Traverse 22

ii. Hot Wire Anemometer Calibration 22

iii. Meter Coefficients and Reynolds Numbers 23

iv. Permanent Pressure Loss and Head Loss 24

v. Sound Data Contour Plot 25

VI. Discussion of Results 26

i. Hot Wire Anemometer Calibration 26

ii. Meter Coefficients 26

iii. Permanent Pressure Loss and Head Loss 27

iv. Sound Data 27

VII. Conclusion and Recommendation 27

VIII. Design Problem 28

IX. Nomenclature 30

X. References 31

XI. Appendices

A. Original Data Sheets 32

B. Sample Calculations 55

C. Design Problem Calculations 68

D. Error (Uncertainty) Analysis 78

E. Consultants Special Topics Report 95

F. Data Transfer Sheet 103

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I. Introduction

The Gas Flow Meters Calibration experiment had the purpose of developing a feasible

scale up of an energy-efficient gas flow meter to satisfy the clients needs. The Special

Task Group asked for a gas flow meter designed to accurately measure air flow rate in a

particle removal process. This process will compress 5,000lbs/hr from ambient

conditions to a required inlet temperature and pressure of 120F and 30psig for an

installation located 500ft from the compressor. Three different types of gas flow meters

were calibrated in the laboratory: the orifice meter, the venturi meter, and the flow

nozzle meter. Calibrations were done in a fixed 6in. diameter pipe and different flow

rates were attained by changing the damper settings in a 5hp blower. Independent

variables were the meter type and damper settings, responses were the manometer

height, air flow rate, permanent pressure drops, and meter coefficients. For purposes of

this experiment air was approximated to be incompressible as the blower did not induce

a pressure ratio larger than 10%. Results from the experiment included the

dimensionless coefficient of each gas flow meter calibrated along with the different

pressure drops across the system. It is important to note the behavior of the

dimensionless coefficient with changing Reynolds numbers, as it is different for every

gas flow meter. The results of the experiment were sufficient to effectively design a gas

flow meter system fulfilling the requirements asked.

II. Theory and Technical Background

Quantification of gas flow is important in residential, commercial and industrial

facilities.(1) The most inexpensive way to do this is using a gas flow meter. A gas flow

meter consists of a device with a sudden diameter change in the pipe. The meter is

directly inserted in the pipe and contracts the gas flow to produce a pressure drop

across two points one before and one after the gas flow meter. Two pressure tabs and a

manometer are used to measure this pressure drop. The high pressure tab displaces the

fluid in the manometer inducing a measurable change in height which is translated to

pressure drop using equation 1-1.(2)

( ) ( ) (1-1)

Where P2 and P1 are the pressures across the gas flow meter, h is the change in

height, m is the manometer fluid density, and is the density of the working fluid.

The pressure drop measured with the manometer, along with a mechanical energy

balance across the system and the continuity equation, were used to determine the

velocity of the gas across the meter.

Mechanical energy balance:(2)

( )

(1-2)

Where V1 and V2 are velocities at point 1 and 2, and P1 and P2 are the pressures at the

same points as velocity.

Continuity Equation:(2)

(1-3)

Where D1 and D2 are the pipe diameters at the point where velocity was recorded.

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The velocity of the constricted flow was then obtained,(2)

( )

(1-4)

Where Ax is a generic cross-sectional area, Cx is a generic dimensionless coefficient

specific for each one of the gas flow meters used, and is defined as D2/D1. It is

important to mention that the equation used for the experimental data analysis

approximates air as an incompressible liquid because the pressure the fluid is submitted

is relatively low.

A detailed description of each one of the meters used, along with the theory applied to

analyze the experiment results is presented below.

i. Meter Types

Pitot Tube

The Pitot tube is used to measure local velocity in a particular conduit. It consists of a

tube pointing directly towards the fluid flow and a manometer connected to measure

pressure drop. At point 2, the air flow creates a pressure build up which results in a

velocity of approximately zero; this point is called the stagnation point. Figure 2-1 is a

schematic diagram of the pitot tube.

Since the velocity at the stagnation point is zero equation 1-2 can be rearranged to solve

for velocity at point 1,(2)

( )

(1-5)

Deviations from the mechanical energy balance occur due to friction losses in the pitot

tube, therefore a dimensionless coefficient Cp is added to the equation to take in account

this change. Literature values of Cp range from 0.98 to 1 (1) suggesting minimal friction

losses. For the purposes of this experiment the Cp value was determined to be 0.99.

Accuracy in the measurements was improved using the simple traverse method with the

pitot tube. This method consists of dividing the duct into a number of equidistant cross-

sectional areas according to equation 1-5. A mean velocity for the fluid is attained by the

simple traverse method.(1)

( )

(1-6)

Where L is the spacing between each measurement, r is the radius of the pipe, and N is

the total number of measurements.

Figure 2-1. A simplified

diagram of the pitot tube

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Hot Wire Anemometer

When a pitot tube is not available, or it is impractical to install, a hot wire anemometer

can be used. The anemometer, just as the pitot tube, provides a measurement of the

local velocity of a flow. Measurements from the hot wire anemometer are to be plotted

against the pitot tube velocities to validate the use of the pitot as a standard.(3)

[

]

(1-7)

2.5 Orifice Meter

A 2.5 orifice meter provides an inexpensive and simple way of measuring flow at a price

of a very high permanent pressure loss. It consists of a drilled plate with a 2.5 diameter

hole, the orifice meter is mounted between two flanges in the pipe as shown below.

The fluid is constricted suddenly when flowing through the orifice plate, and it then goes

through a sudden expansion right after the plate. These diameter changes create eddies

in the flow which translate to a permanent loss in fluid velocity and therefore pressure.

Equation 1-4 was used to find the mass flow rate using the specific value of the

dimensionless coefficient for the orifice meter C0, which according to Geankoplis was

0.61 (1). As stated above, the fluid does experience a permanent pressure drop after

crossing the orifice meter. The equation used is,(1)

( ) ( )( ) (1-8.a)

Where p1 and p2, are the pressures measured, p4 is the pressure several diameters from

the orifice, and is the diameter ratio.

Venturi Meter

The venturi meter is inserted directly into the pipeline and introduces a gradual

constriction to the flow, then the fluid tapers back slowly to the original pipe diameter. A

pressure drop is experienced across the flow constriction which is measured using

pressure taps. The mass flow rate is found with equation 1-4. The values of the

dimensionless coefficient in the venturi meter Cv are around 0.98.

Figure 2-2. A schematic

diagram of the orifice meter.

Figure 2-3. A

schematic diagram of

the venutri meter.

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Due to the gradual contraction and expansion of the flow in the venturi meter the

permanent pressure loss experienced is rather small. Literature values suggest a

permanent pressure loss of 15% of the measured pressure, therefore,(1)

( ) ( ) (1-8.b)

Flow-Nozzle Meter

A typical flow-nozzle meter has characteristics similar to those of the venturi meter but is

shorter and much less expensive. (1) The flow is constricted by a short cylinder of about

one-half the diameter of the pipe, with an elliptical approach. The mass flow rate is again

determined with equation 1-4 using dimensionless coefficient values of 0.98.

The permanent pressure loss is as follows,(1)

( ) ( )

( )( ) (1-8.c)

This head loss is expected to be much larger than the one incurred by the venturi meter,

but still smaller than the permanent pressure loss in the orifice meter.

Dimensionless Coefficient Determination

Even though literature values for the each meters dimensionless coefficient was found,

these need to be verified experimentally for the meters used in the pilot plant. The first

step for the coefficient calculation is solving for V2 the velocity at the point where the fluid

is at maximum constriction. V1, the initial flow velocity, measured with the pitot tube and

the continuity equation yield to equation 1-10.(1)

(1-9)

Equation (1-4) is rearranged and using the V2 value obtained the dimensionless

coefficient is determined.

ii. Design Problem Theory

After the experiments data analysis was done, dimensionless coefficients and

permanent pressure losses were calculated for each gas flow meter; a scale-up design

to industrial settings was possible. The client required a gas flow meter that will measure

a 5,000lbs/hr flow which after passing through a 500ft pipe is fed to an air filtration

system. Inlet conditions to the air filtration system were 30psig and 120F as specified by

the client. A cost-effective pipe diameter was determined to meet flow rate

specifications, and a meter type which maximized accuracy in the readings while

Figure 2-4. A simplified

diagram of the flow nozzle

meter.

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keeping a low pressure drop was chosen. To meet inlet conditions a compressor was

sized, as well as a heat exchanger.

The theory behind the design problem calculations is presented below,

Fluid Compressibility

The experiment done in lab used a blower which created a low pressure drop. For cases

where the outlet pressure is more than 10% higher than that of the inlet, compressibility

of the fluid has to be accounted for. Adding an expansion factor Y to equation (1-4) takes

in account compression of the fluid. Figure 2.5 below shows the relation of the

expansion factor with the pressure ratio for the different meters used.

( )

(1-10)

Optimal Pipe Diameter

The optimal pipe diameter was determined using equation 1-11 from Timmerhous (4),

where Di,opt is the optimal pipe inner diameter in inches, Qd is the desired volumetric flow

rate in ft3/s, and is the fluid density in lb/ft3.

(1-11)

It is important to remark that this function is obtained by taking the derivative of a

complex cost function with several other parameters; this is the reason for the

inconsistency in the units.

Optimal gas flow meter type

The determination of the optimal gas flow meter was done by plotting the Reynolds

number, given by equation 1-12, against the dimensionless coefficient and the

permanent pressure drop.(1)

(1-12)

Where D is the pipe diameter in ft, v is the fluid velocity in ft/s, is the density in lb/ft3,

is the fluid viscosity.

Figure 2-5. Graph of

Expansion factor vs.

p2/p1

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Pressure Losses

The pressure losses across the system were added to the required inlet pressure, so

that the required compressor horse power calculation is possible. The power loss across

the meter is measured during the experiment. Pressure loss of turbulent flow across a

pipe of length L is represented by equation (1-14), where is the dimensionless friction

factor, M is the fluids molar mass, and G is the mass flow rate over the pipes cross-

sectional area.(1)

(

)

(1-14)

Compressor

The short residence time of the air in the compressor allows very little heat dissipation

from the fluid to the environment therefore adiabatic compression was approximated.

The equation for shaft work used for adiabatic compression is presented below,(1)

[( )( )

] (1-15)

Where is the ratio of specific heat capacities Cp/Cv, and T1 is the inlet temperature. The

compressor shaft work is then turned into brake horsepower using the following

equation,(1)

(1-15.a)

Where m is the mass flow rate and is the compressor efficiency.

The gas is adiabatically compressed; therefore the relationship between the inlet and

outlet conditions can be equated according to the following,(1)

( ) (

)

(1-16)

Heat Exchanger

The gas compression causes a temperature rise, therefore a heat exchanger needs to

be sized to meet the inlet temperature of 120F. The heat exchangers area required is

given by equation 1-17,(1)

(1-17)

Where U is the overall heat transfer coefficient, Q is the total heat loss or gained during

the transfer, and(1)

( ) ( )

(( )

( ))

(1-18)

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III. Description of Apparatus/Experimental Procedure

i. Description of Apparatus In this particular experiment, Uni-Minn was asked to investigate five gas flow meters at various air flow rates to determine which meter to scale-up for the design problem. The orifice plate meter, venturi meter, flow nozzle meter, triangle orifice plate meter, and square orifice plate meter were calibrated against the pitot tube to determine pressure drop across the meter and permanent pressure drop. Analysis of the square and triangle meters is included in Appendix F, Consultants Special Topics Report (page #95). The apparatus consisted of an insulated blower connected to an insulated air intake filter through several feet of piping. This pipe had an inner diameter of 6.00 0.06 inches, and the intake side could be horizontally adjusted to accommodate meters of different lengths. Between the blower and intake filter were: a pitot tube, a temperature gauge, a TSI meter port, several pressure ports, and a space for a gas flow meter, as illustrated in Figure 3-1. The pressure ports were connected through two pressure taps that led to a manometer board which read the resulting pressure drops. Blower The blower, manufactured by N. American MFG, Co., was of size 320-D2-7-2, and had a volume cfm of 825. As the blower was insulated, a cooling fan was used to dissipate the heat generated from the blower. The cooling fan was required to be on for the duration of the blower use so the blower motor did not overheat. The blower also had a pipe that extended through the window for extra ventilation. Connected to the blower was a damper. Specific air flow rates could be sent through the pipe by selecting preset damper settings between 1 and 14. Pitot Tube The primary standard of the experiment was the pitot tube, attached just downstream of the insulated filter. Its height in the tube could be varied. Two pressure ports were attached to the pitot tube, one horizontal and one vertical. The stagnant flow of the pitot tube corresponded to the horizontal pressure port. Therefore, the higher pressure in the vertical port could be measured with respect to the stagnant flow. In order to find the average fluid velocity, the pressure drop across the pitot tube was measured at four separate traverse points and at the center of the pipe. The four separate traverse points split the tube into four equal cross-sectional areas. Attached to the outside of the pitot tube was a ruler, which was used to position the height of the pitot tube for each measurement. See appendix C for calculation of the traverse points. Meters Each gas flow meter was attached to the detachable portion of pipe upstream of the blower. All orifice meters and the flow nozzle meter were attached between two rubber gaskets placed between the movable portion of pipe and a section of straight pipe. Both sides were attached with 4 steel carriage bolts, 4 washers, and 4 wing nuts, tightened as securely as possible.

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Orifice Plate Meter The orifice plate meter had an orifice diameter of 2.50 0.06 inches, and was attached to the more upstream side of the straight pipe insert. The high pressure reading was taken one pipe diameter upstream of the meter, at pressure port 6. Low pressure was taken one pipe diameter downstream of the meter. Permanent pressure drop was taken four pipe diameters downstream of the meter, at pressure port 11. See figure 3-2 for a pictorial representation of the flow meter and the location of the pressure tap placement. Venturi Meter The venturi meter converged at a diameter of 3.00 0.06 inches at the vena contracta, and then expanded back to pipe diameter. High pressure was taken one pipe diameter upstream of the meter, at pressure port 6. Low pressure was taken at the vena contracta. However, the vena contracta had two pressure ports, so pressure measurements were taken at both ports. See figure 3-3 for a pictorial representation of the venturi meter and location of the pressure tap placements. Flow Nozzle Meter The flow nozzle meter had an air flow entrance at 6.00 0.06 inches, which then tapered off (over 4.50 0.06 inches) to decrease the diameter to 3.00 0.06 inches at the outlet of the nozzle. High pressure was again taken one pipe diameter upstream of the meter, at pressure port 6. Low pressure was read one half diameter downstream of the air flow entrance. See figure 3-4 for a pictorial representation of the flow nozzle meter and location of the pressure tap placement. Manometers Experimental pressure drop measurements were read from a manometer board, which contained four manometers of varying precision. 0-40 in. water and 0-200 in. water digital manometers (manufactured by Dwyer Instruments) measured the higher pressure drops, while lower pressure drops were measured by 0-1 in. water and 0-3 in. water inclined tube manometers (manufactured by the Meriam Instruments Co.). One side of each manometer was connected to a high pressure tap, while the other side was connected to a low pressure tap. The entrance to each manometer was sealed by a valve, so the manometers would only take measurements if the valve was opened, allowing the air to flow from high to low pressure. TSI Hot Wire Anemometer A port for the Model 8330 Velocicheck Air Velocity Meter was located three inches downstream of the pitot tube.(4) The meter was a hot wire anemometer that functioned by running a current through the wire. Water flowing across the velocity sensor cooled the sensor, which decreased the resistance. In order to maintain a constant voltage across the wire, more power was supplied. The amount of power supplied was proportional to velocity of the air. The velocity returned to the anemometers display was based off of a standard reference. Therefore, the velocity given needed to be related to the standard temperature and pressure of 70 oF and 14.7 psia.

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Sound Meter In order to comply with OSHA standards, sound levels were to be obtained and analyzed. To ensure sound levels did not rise above the OSHA limits, a Sper Scientific Sound Meter 840005 was used. A microphone inside the meter measured the sound (in decibels) and displayed the reading at either a low or high setting.

ii. Experimental Procedure To begin both labs, all manometers were leveled and zeroed. Then, the straight pipe was attached so the ruler on the pitot tube could be calibrated for accurate centering. Pressure drop across the pitot tube was measured for damper settings 4, 6, 8, 10, and 12 at different heights between 1.7 and 3.3 inches read on the ruler. The center of the pipe was determined to be where the pressure drop was highest, as maximum velocity occurs at the center of a pipe. As the air flow was turbulent (as shown in later calculations), the velocity profile was relatively flat. Therefore, only damper settings 10 and 12 showed a significant difference in pressure drop at small increments. From the data, it was determined that the pitot tube was at the center of the pipe when the ruler was positioned at 2.7 0.1 inches. As data were taken at 2.6, 2.7, and 2.8 inches for each of the five damper settings, pitot tube error could be determined. The largest fluctuation of pressure drop between the three points was 0.04 in. water. As this was 0.1 inch in each direction from the calibrated center, the error for each pressure drop reading thereafter was estimated as 0.02 in. water. The gas flow system reached steady state relatively quickly. In order to make sure the air flow was as steady as possible, each manometer valve was opened at least ten seconds after the velocity was changed. The pressure reading was then only taken when the measurement was steady for five seconds. This was not always possible for the digital manometers, as they had some fluctuation. In that case, the reading was taken when the fluctuation was at a minimum. Pressure was zeroed after every reading by removing the pressure taps from the ports and opening the manometer valve while the taps were exposed to atmospheric pressure. Each pressure drop measurement read from the inclined tube manometers was read at the tip of the meniscus of the manometer fluid. Note: Each time the blower was turned on, it was made sure that the damper setting was at the start position. The cooling fan was run for the duration of both labs. Pitot Tube Five pitot tube data points were taken per damper setting per meter. The pressure drop readings were taken in order, from 5.3 inches, to 4.2 inches, 2.7 inches, 1.2 inches, and 0.1 inches. Pressure was zeroed in between each reading. TSI Hot Wire Anemometer The pitot tube was used as the primary standard for the calibration of the anemometer. Pressure drop measurements were taken while the pitot tube was centered for damper settings 3 through 12. Then the pitot tube was moved to the top of the pipe so it would not hinder the anemometer measurement. The hot wire was placed into the anemometer

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port and centered best as possible, making sure the wire was not obstructed and completely parallel to air flow. As the anemometer could only take accurate data measurements up to 20 m/s (65.6 ft/s), there were only a limited number of damper settings that could be used to calibrate the TSI meter. Velocity data were recorded for damper settings 2 through 6, so the only damper settings where accurate measurements of velocity could be taken for both meters were damper setting 3 through 6. In order to minimize error, the velocity was taken when the reading had been steady for ten seconds. Meters Pressure drops for all five gas flow meters was taken at damper settings 4, 5, 7, 10, and 12. During the first week of lab, damper settings of 4, 7, 10, and 12 were chosen as to measure a wide variety of air flow velocity. When these data were analyzed to see the quality of data and meter coefficient, it could be seen that the air flow velocities of 7, 10, and 12 were very close together. Therefore, it was decided that another damper setting between 4 and 7 needed to be measured for all subsequent meters. At the end of the second lab period, the meters measured in the first week of lab were re-installed and damper setting 5 was measured so all meters had similar runs. Orifice Plate Meter and Flow Nozzle Meter The 2.5 inch orifice meter was placed between two rubber gaskets and put between the pipe and the piece of detachable straight pipe. Pressure drop across the meter was taken using the pressure tap placements mentioned above. Permanent pressure loss was then recorded. Then all five pressure drops from the pitot tube were recorded, followed by replicated measurements of pressure drop across the meter and permanent pressure loss. The same procedure was followed for the flow nozzle meter, except with different pressure tap placement, as noted above. Venturi Meter The venturi meter was attached likewise to the straight pipe, with the half of the meter containing the vena contracta located further upstream. Pressure drop across the meter, permanent pressure loss, and the pitot traverse were measured the same way as the orifice plate and flow nozzle meters, except two pressure ports were located on the vena contracta. Therefore data were taken for both meters (as readings were significantly different), to be analyzed later which port was correct. Sound In order to make a contour plot of the sound levels around the blower, data needed to be taken at many different points around the blower. Sound levels of 90 db, 85 db, 82 db, 78 db, and 75 db were taken for 7 different radial positions from the blower and the distance away from the blower motor was recorded. These measurements were done at damper setting 12 because that was the maximum operating damper setting in use for the experiment and would produce the most noise. This data could then be put on a plot for a contour of the blowers sound effects.

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iii. Shut-down Procedure To shut down the gas flow system, the blower was first turned off, followed by the cooling fan. The damper setting was returned to the start position, and the detachable portion of the pipe was removed. All the bolts, nuts, and washers were put away in the container connected to the apparatus, and the pressure taps were hung on the manometer board.

iv. Safety and Precautions Although a relatively simple machine to run, the gas flow system still has opportunity for injury. At least two people must be used to attach each meter and section of piping to the system. The support for the detachable section of pipe is not reliable, and it is easy for fingers to get pinched in the attachment process. Minor injuries could also be obtained by connecting the pressure taps, as the pressure ports were spring-loaded. Mistakes can easily be made with the gas flow system. During the first week of lab there were only two rubber gaskets available for use. These needed to be used to secure the plate meters, leaving the downstream portion of the straight pipe attachment with a less than ideal seal. Each bolt must be tightened as much as possible in order to obtain the most accurate velocity and permanent pressure drop measurements, as a leak could affect calculations.

v. Process Flow Diagram Table 3-1 A table showing all symbols and conventions used in figures 3-1 through 3-4.

Symbol Meaning

T Temperature Gauge

P1 First Pressure Port

Pn Final Pressure Port (along with Permanent)

TSI TSI Meter

Meter X Orifice, Venturi, or Flow Nozzle Meter

D One Pipe Diameter

Pressure Port

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Pitot

TSI

Meter X

T P1 Pn

Blower Intake

Damper

Fan

Air Flow

D D

D D D

Air Flow

D D

Air Flow

D/2

Figure 3-4: Flow Nozzle Meter

Figure 3-1: A process flow diagram of the gas flow system.

Figure 3-2: Orifice Plate Meter

Figure 3-3:Venturi Meter

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IV. Calculated Data Tables

i. Table 4-1: Calibrating/Centering the Pitot Tube

Damper Height of Pitot

Tube (in) Pitot Pressure Drop (lbf/ft

2) Manometer Used

4 2.3 0.1 1.4 0.1 0-3

4 2.5 0.1 1.4 0.1 0-3

4 2.6 0.1 1.4 0.1 0-3

4 2.7 0.1 1.5 0.1 0-3

4 2.8 0.1 1.4 0.1 0-3

4 3.0 0.1 1.3 0.1 0-3

6 2.3 0.1 3.7 0.1 0-3

6 2.5 0.1 3.6 0.1 0-3

6 2.6 0.1 3.7 0.1 0-3

6 2.7 0.1 3.6 0.1 0-3

6 2.8 0.1 3.6 0.1 0-3

6 3.0 0.1 3.5 0.1 0-3

8 1.7 0.1 8.3 0.1 0-3

8 2.0 0.1 8.2 0.1 0-3

8 2.3 0.1 8.1 0.1 0-3

8 2.5 0.1 8.2 0.1 0-3

8 2.6 0.1 8.1 0.1 0-3

8 2.7 0.1 8.1 0.1 0-3

8 2.8 0.1 8.2 0.1 0-3

8 3.0 0.1 8.1 0.1 0-3

8 3.3 0.1 7.9 0.1 0-3

10 2.0 0.1 10.3 0.1 0-3

10 2.3 0.1 10.2 0.1 0-3

10 2.5 0.1 10.2 0.1 0-3

10 2.6 0.1 10.2 0.1 0-3

10 2.7 0.1 10.3 0.1 0-3

10 2.8 0.1 10.4 0.1 0-3

10 3.0 0.1 10.3 0.1 0-3

10 3.3 0.1 9.9 0.5 0-40

12 2.6 0.1 10.9 0.5 0-40

12 2.6 0.1 11.0 0.1 0-3

12 2.7 0.1 11.0 0.1 0-3

12 2.8 0.1 10.8 0.1 0-3

12 3.0 0.1 10.8 0.1 0-3

A table presenting pressure drops at pitot tube heights near 3 inches. The 2.7-inch mark corresponded to the greatest pressure drop most consistently.

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For all pressure measurements, the manometer used is listed. Each manometer had a different amount of error, as an instrument is only as accurate as the smallest unit to which it can measure. Both digital manometers had fluctuation in their output.

The 0 to 1 inclined tube manometer had an error of 0.01 in. water

The 0 to 3 inclined tube manometer had an error of 0.02 in. water

The 0 to 40 digital manometer had an error of 0.1 in. water

The 0 to 200 digital manometer had an error 0.1 in. water

Table 4-1: Experimental Conditions

Ambient

Temperature (oF)

Ambient Pressure

(lbf/ft2)

Dryness Density (lbm/ft

3) Viscosity (lbm/fts)

x 10-4

Week 1 75.2 2040 19% 0.074 1.61

Week 2 75.2 2070 19% 0.074 1.61

Experimental conditions were approximated to be constants throughout the experiment, with no error.

Table 4-2: TSI Velocity Meter Calibration vs. Pitot Standard

Damper Manometer

Used

Pressure Drop across Pitot Tube

(lbf/ft2)

TSI Anemometer Velocity (ft/s)

Temperature (oF)

2 0-3 - 7.9 0.2 25 1

3 0-3 0.4 0.1 18.4 0.2 25 1

4 0-3 1.5 0.1 34.1 0.2 25 1

5 0-3 2.3 0.1 44.9 0.2 25 1

6 0-3 3.7 0.1 58.7 0.2 25 1

7 0-3 5.9 0.1 >65.6 25 1

8 0-3 8.2 0.1 >65.6 25 1

9 0-3 9.4 0.1 >65.6 25 1

10 0-40 9.35 0.05 >65.6 25 1

11 0-40 9.77 0.05 >65.6 25 1

12 0-40 10.03 0.05 >65.6 25 1

The TSI meter had an error of 0.05 m/s per reading, which was propagated to ft/s. All damper settings above 6 could not be measured by the TSI meter. Tables 4-3 through 4-5 below contain data for the orifice plate, venturi, and flow nozzle meters. In the run column, the first digit corresponds to the run number, which was changed for each damper setting. A change in letter corresponds to a change in height of the pitot tube, and the digit after the hyphen corresponds to which week the data was taken. For the venturi meter, pressure drop across the meter was taken at a left and right pressure port on the vena contracta. In Table 4-5, the error for each measurement was put in the column title, as the error was the same for all readings down each column.

Signature: 18

Table 4-3: 2.5-inch Orifice Plate Meter Calibration vs. Pitot Standard

Run Damper

Ruler Height of

Pitot Tube (in)

Pitot Pressure

Drop (lbf/ft

2)

Meter Pressure

Drop (lbf/ft2)

Permanent Pressure

Loss (lbf/ft2)

Manometer Used

1a - 1 4 5.3 0.1 0.40.1 0-3

1b - 1 4 4.2 0.1 0.60.1 0-3

1c - 1 4 2.7 0.1 0.70.1 0-3

1d - 1 4 1.2 0.1 0.80.1 0-3

1e - 1 4 0.1 0.1 0.50.1 0-3

1f - 1 4 - 56.40.5 47.10.5 0-40

1g - 1 4 - 58.10.5 46.50.5 0-40

2a - 2 5 5.3 0.1 0.60.5 0-40

2b - 2 5 4.2 0.1 1.10.5 0-40

2c - 2 5 2.7 0.1 1.30.5 0-40

2d - 2 5 1.2 0.1 1.10.5 0-40

2e - 2 5 0.1 0.1 0.80.5 0-40

2f - 2 5 - 84.00.5 67.20.5 0-40

2g - 2 5 - 84.00.5 66.90.5 0-40

3a - 1 7 5.3 0.1 0.60.1 0-3

3b - 1 7 4.2 0.1 1.50.1 0-3

3c - 1 7 2.7 0.1 1.70.1 0-3

3d - 1 7 1.2 0.1 1.70.1 0-3

3e - 1 7 0.1 0.1 1.10.1 0-3

3f - 1 7 - 129.20.5 103.50.5 0-40

3g - 1 7 - 128.70.5 103.40.5 0-40

4a - 1 10 5.3 0.1 1.10.1 0-3

4b - 1 10 4.2 0.1 1.90.1 0-3

4c - 1 10 2.7 0.1 1.90.1 0-3

4d - 1 10 1.2 0.1 1.90.1 0-3

4e - 1 10 0.1 0.1 1.40.1 0-3

4f - 1 10 - 145.30.5 116.50.5 0-40

4g - 1 10 - 146.20.5 116.80.5 0-40

5a - 1 12 5.3 0.1 1.30.5 0-40

5b - 1 12 4.2 0.1 1.80.5 0-40

5c - 1 12 2.7 0.1 2.00.1 0-3

5d - 1 12 1.2 0.1 2.00.1 0-3

5e - 1 12 0.1 0.1 1.50.1 0-3

5f - 1 12 - 147.50.5 118.10.5 0-40

5g - 1 12 - 147.80.5 118.60.5 0-40

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ii. Table 4-4: Venturi Meter Calibration vs. Pitot Standard

Run Damper

Ruler Height of Pitot Tube ( 0.1 in)

Pitot Pressure

Drop ( 0.1

lbf/ft2)

L. Meter Pressure

Drop (0.5

lbf/ft2)

R. Meter Pressure

Drop (0.5

lbf/ft2)

Permanent Pressure

Loss (0.5

lbf/ft2)

Manometer Used

1a - 2 4 5.3 0.7 0-3

1b - 2 4 4.2 1.0 0-3

1c - 2 4 2.7 1.0 0-3

1d - 2 4 1.2 1.0 0-3

1e - 2 4 0.1 0.8 0-3

1f - 2 4 - 22.4 15.5 2.9 0-40

1g - 2 4 - 22.3 15.5 2.9 0-40

2a - 2 5 5.3 1.1 0-3

2b - 2 5 4.2 1.7 0-3

2c - 2 5 2.7 2.3 0-3

2d - 2 5 1.2 2.3 0-3

2e - 2 5 0.1 1.7 0-3

2f - 2 5 - 40.8 28.8 4.8 0-40

2g - 2 5 - 40.8 29.1 5.1 0-40

3a - 2 7 5.3 3.7 0-3

3b - 2 7 4.2 4.8 0-3

3c - 2 7 2.7 5.9 0-3

3d - 2 7 1.2 5.6 0-3

3e - 2 7 0.1 3.9 0-3

3f - 2 7 - 107.5 77.3 12.8 0-40

3g - 2 7 - 107.0 77.2 12.8 0-40

4a - 2 10 5.3 6.1 0-3

4b - 2 10 4.2 8.0 0-3

4c - 2 10 2.7 8.8 0-3

4d - 2 10 1.2 8.6 0-3

4e - 2 10 0.1 6.8 0-3

4f - 2 10 - 177.0 127.4 20.7 0-40

4g - 2 10 - 178.6 128.6 22.5 0-40

5a - 2 12 5.3 5.0 0-3

5b - 2 12 4.2 7.9 0-3

5c - 2 12 2.7 9.0 0-3

5d - 2 12 1.2 8.8 0-3

5e - 2 12 0.1 6.7 0-3

5f - 2 12 - 190.3 138.5 24.4 0-40

5g - 2 12 - 190.5 137.9 24.0 0-40

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iii. Table 4-5: Flow Nozzle Meter Calibration vs. Pitot Standard

Run Damper

Ruler Height of Pitot Tube

(in)

Pitot Pressure

Drop (lbf/ft

2)

Meter Pressure

Drop (lbf/ft2)

Permanent Pressure

Loss (lbf/ft2)

Manometer Used

1a - 2 4 5.3 0.1 0.90.1 0-3

1b - 2 4 4.2 0.1 1.10.1 0-3

1c - 2 4 2.7 0.1 1.20.1 0-3

1d - 2 4 1.2 0.1 1.00.1 0-3

1e - 2 4 0.1 0.1 0.70.1 0-3

1f - 2 4 - 13.60.5 8.30.5 0-40

1g - 2 4 - 13.50.5 8.30.5 0-40

2a - 2 5 5.3 0.1 1.80.1 0-3

2b - 2 5 4.2 0.1 2.00.1 0-3

2c - 2 5 2.7 0.1 2.10.1 0-3

2d - 2 5 1.2 0.1 1.80.1 0-3

2e - 2 5 0.1 0.1 1.50.1 0-3

2f - 2 5 - 23.60.5 14.60.5 0-40

2g - 2 5 - 23.40.5 14.50.5 0-40

3a - 2 7 5.3 0.1 3.90.1 0-3

3b - 2 7 4.2 0.1 4.60.1 0-3

3c - 2 7 2.7 0.1 4.60.1 0-3

3d - 2 7 1.2 0.1 4.40.1 0-3

3e - 2 7 0.1 0.1 3.30.1 0-3

3f - 2 7 - 55.30.5 34.20.5 0-40

3g - 2 7 - 55.40.5 34.30.5 0-40

4a - 2 10 5.3 0.1 5.30.1 0-3

4b - 2 10 4.2 0.1 5.80.1 0-3

4c - 2 10 2.7 0.1 6.40.1 0-3

4d - 2 10 1.2 0.1 6.10.1 0-3

4e - 2 10 0.1 0.1 4.70.1 0-3

4f - 2 10 - 81.40.5 50.20.5 0-40

4g - 2 10 - 81.10.5 50.10.5 0-40

5a - 2 12 5.3 0.1 5.80.1 0-3

5b - 2 12 4.2 0.1 6.70.1 0-3

5c - 2 12 2.7 0.1 6.90.1 0-3

5d - 2 12 1.2 0.1 6.50.1 0-3

5e - 2 12 0.1 0.1 4.90.1 0-3

5f - 2 12 - 84.90.5 52.60.5 0-40

5g - 2 12 - 84.80.5 52.80.5 0-40

5h - 2 12 - 85.00.5 53.00.5 0-40

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iv. Table 4-6: Sound Data

Position

1 2 3 4 5 6 7

Decibel

(db) in. from blower

in. from blower

in. from blower

in. from blower

in. from blower

in. from blower

in. from blower

Hi

90 3 4 1 6 1 2 1 4 1

85 3 12 1 13 1 9 1 13 1

82 3 25 1 17 1 12 1 18 1

Lo 78 3 28 1 18 1 26 1 32 1 20 1

75 3 28 1 18 1 48 1 46 1 40 1 45 1 60 1

A table showing sound levels taken at varying radial positions and lengths from the blower. Seven radial positions and five sound levels were chosen. Then each sound level was found at a certain length away from the blower at each radial position, and that distance was recorded. A contour plot of the sound data can be found in figure 5-5. According to OSHA standards, the noise levels could not exceed 95 dB for a span of four hours. The sound level did not go above 90 dB, so hearing protection was not necessary.

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V. FINAL RESULTS

i. Pitot Tube Traverse

As stated in the procedure, a Pitot tube traverse was performed at each of the chosen damper settings using equation (1-6) for n = 1,2 and N = 4.

The table below demonstrates the calculated results of this traverse. Table 5-1: Pitot Tube Traverse Results

Position Inches Diameter Pitot Ruler Height

2.6 in above center 5.6 0.1 in 5.3 0.1 in

1.5 in above center 4.5 0.1 in 4.2 0.1 in

Center at 3.0 in 3.0 0.1 in 2.7 0.1 in

1.5 in below center 1.5 0.1 in 1.2 0.1 in

2.6 in below center 0.4 0.1 in 0.1 0.1 in

The values reported as the Pitot Ruler Height in Table 5-1 were used as the traverse points to take all measurements of the pressure drop at the various damper settings.

ii. Hot Wire Anemometer Calibration

Standard velocities were measured from damper settings 3 to12 using the hot wire anemometer. A correction using equation (1-7) to calculate the actual velocities measured at each damper setting by the meter.

[

]

Table 5-2 below reports the actual velocity measured at the damper settings in ft/s using the correction. The velocity measurements were calculated using the Pitot readings as a standard at each damper setting as well and are reported alongside the anemometer readings in ft/s. The velocity of the Pitot tube was calculated using equation (1-5).

Table 5-2: Anemometer and Pitot Tube Velocities at Varying Damper Settings

Damper Setting Anemometer Actual Velocity (ft/s)

Average Pitot Tube Velocity (ft/s)

3 19.3 0.3 18 4

4 35.8 0.5 35 2

5 47.1 0.6 44 2

6 61.6 0.8 56 2

7 >65.6 0.9 70.7 0.9

8 >65.62 0.9 83.2 0.8

9 >65.62 0.9 89.0 0.7

10 >65.62 0.9 88.8 0.7

11 >65.62 0.9 90.8 0.7

12 >65.62 0.9 92.0 0.7

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In Table 5-2 the anemometer velocities are reported at values >65.6 0.9 ft/s from damper settings 7 to 12 because the instrument does not measure velocities greater than this value. Figure 5-2 is a plot of the anemometer velocities versus the velocities of the Pitot tube in ft/s at damper settings 3, 4, 5, and 6. A best fit line is shown on the plot below and is represented by the equation TSI Velocity = (1.10 0.06)v1 - (1 3) where v1 is the velocity through the Pitot tube. (See error propagation appendix for the treadline equation derivation).

Figure 5-2: Calibration plot of the anemometer (TSI) velocity in ft/s versus the calculated

standard Pitot velocity in ft/s at damper settings 3, 4, 5, and 6.

iii. Meter Coefficients and Reynolds Numbers

The calculations of the meter coefficients involved the manipulation of equations (1-2), (1-4) and (1-9). The velocities through the Pitot tube were used to find the Reynolds Number of the fluid using equation (1-12). Next, the velocity through each meter was calculated separately by manipulation of the mechanical energy balance, resulting in equation (1-4).

This velocity was used to find the meter coefficient by using the ratio between the meter velocity and the velocity from the continuity equation, (1-3), as shown in equation (1-9)

The Pitot velocities, corresponding Reynolds number, calculated meter velocity, and meter coefficients are presented in Tables 5-2a,b,c at damper settings 4, 5, 7, 10, 12.

Table 5-3a: 2.5 Orifice Velocities and Pitot Velocities at Various Damper Settings along with Corresponding Reynolds Numbers and Calculated Coefficients Damper Setting Average Pitot

Velocity (ft/s) Reynolds Number

2.5 Orifice Velocity (ft/s)

2.5 Orifice Coefficient

4 23 3 5300 700 226 9 0.59 0.08

5 29 2 6600 500 270 20 0.61 0.06

7 33 2 7700 500 340 20 0.57 0.05

10 37 2 8500 400 360 20 0.59 0.05

12 38 2 8700 400 360 20 0.60 0.05

0

10

20

30

40

50

60

70

0 10 20 30 40 50 60 70

TS

I M

ete

r V

elo

city

(ft/s)

Pitot Meter Velocity (ft/s)

Calibration Plot of TSI Meter vs Pitot Meter Velocity (ft/s)

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Table 5-3b: Flow Nozzle Velocities and Pitot Velocities at Various Damper Settings along with Corresponding Reynolds Numbers and Calculated Coefficients Damper Setting Average Pitot

Velocity (ft/s) Reynolds Number

Flow Nozzle Velocity (ft/s)

Flow Nozzle Coefficient

4 29 3 6800 500 112 5 1.0 0.1

5 39 2 9000 400 148 6 1.06 0.07

7 59 2 13700 300 226 8 1.05 0.06

10 69 1 16000 300 274 9 1.01 0.05

12 72 1 16700 300 280 9 1.03 0.05

Table 5-3c: Venturi Meter Velocities and Pitot Velocities at Various Damper Settings along with Corresponding Reynolds Numbers and Calculated Coefficients

Damper Average Pitot Velocity (ft/s)

Reynolds Number

Venturi Meter Velocity (ft/s)

Venturi Meter Coefficient

4 28 3 6500 500 120. 5 0.94 0.09

5 39 2 9000 400 164 6 0.96 0.06

7 64 1 14700 300 267 9 0.96 0.05

10 80. 1 18600 300 340 20 0.94 0.05

12 80. 1 18400 300 360 20 0.89 0.05

The meter coefficients were then plotted against Reynolds number for the three different gas flow meters and are displayed in Figure 5-3 below.

Figure 5-3: Plot of the experimentally calculated meter coefficients versus the Reynolds number at damper settings 4,5, 7, 10, and 12 for the 2.5 Orifice, Flow Nozzle, and the Venturi Meters

iv. Permanent Pressure Loss and Head Loss

The next part of the analysis will be used to evaluate the effect that the flow meter has on permanent pressure loss and head loss. Head loss was derived from the mechanical energy balance and was calculated using equation (1-1).

Theoretical values of this pressure lost were estimated using equations (1-8.a-c) for each respective meter. The table below reports both the experimental and theoretical head losses for each meter at the recorded damper settings.

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

0 5000 10000 15000 20000

Mete

r C

oeff

icie

nt, C

Reynold's Number

Gas Flow Meter Coefficient vs Reynold's Number

2.5" Orifice

Flow Nozzle

Venturi

Signature: 25

Table 5-4: Experimental and Theoretical Head Loss Damper Setting

2.5 Orifice Head Loss (ft)

Flow Nozzle Head Loss (ft)

Venturi Meter Head Loss (ft)

Experiment Theory Experiment Theory Experiment Theory

4 20200 300 20400 800 3600 300 3500 200 1200 300 1010 50

5 28900 300 30000 2000 6300 300 6100 300 2100 300 1880 70

7 44600 300 46000 2000 14800 300 14400 500 5500 300 5000 200

10 50300 300 52000 2000 12700 300 21000 700 9300 300 8300 300

12 51000 300 53000 2000 22800 300 22000 800 10500 300 9000 300

The experimental values in Table 5-4 are presented below in Figure 5-4 for the plot of experimental head loss versus Reynolds number for the meters.

Figure 5-4: Plot of the experimentally calculated head loss versus the Reynolds number at damper settings 4,5, 7, 10, and 12 for the Flow Nozzle, 2.5 Orifice, and the Venturi Meters

v. Sound Data Contour

The sound data from damper setting 12 was plotted on a contour of 90, 85, 82, and 78 decibels versus distance away the blower below in Figure 5-5.

0

10000

20000

30000

40000

50000

60000

0 5000 10000 15000 20000

Head L

oss (

ft)

Reynold's Number

Experimental Head Loss vs Reynold's Number

2.5" Orifice

Flow Nozzle

Venturi

6" 4"

2" 4" 13"

12" 9" 13"

17"

25" 12" 18"

18"

28"

26" 32"

20"

Decibels versus Distance from Blower (in.)

90 dB

85 dB

82 dB

78 dB

Figure 5-5: Sound data contour plot of decibels versus measured distance away from the blower. The origin is the blower motor, the source of the sound. Note that all distances further away than the points at 78 dB were recorded at 75 dB and that there were no sound data recorded above 90 dB.

Signature: 26

VI. DISCUSSION OF RESULTS

i. Hot Wire Anemometer Calibration

A linear regression of the plot in Figure 5-2 of the anemometer velocity versus the Pitot meter velocity was essential for the calibration of the meter. This regression produced a calibration curve TSI Velocity = (1.10 0.06)v1 - (1 3). The theoretical value of the slope of the calibration curve is 1.0 (1) so the percent error of the calibration curve from the theoretical value produced by the experiment is 10%. This error can be attributed to the experimental error in the measurements taken for both the anemometer and the Pitot tube readings.

ii. Meter Coefficients

Using the Pitot tube velocities as standards and the incompressibility approximations, the meter coefficients were calculated at different flow rates. The plot in Figure 5-3 displays a similar, linear trend for the different meters versus Reynolds number. The coefficients were plotted against Reynolds number to produce a trend that is not only dependent on the velocity of the fluid, but also the conditions of the fluid that would affect its density and viscosity at turbulent flow. The calculated Reynolds numbers are indicative of turbulent flow and underline the validity of the equations used in the analysis.

The literature values of the meter coefficients for the 2.5 orifice, flow nozzle, and venturi meters are 0.61, 0.98, and 0.98 respectively. These literature values are reflective of an average of many different meters used, and are a good representation of what to expect from the experiment. To determine the precision of the meters, an average was taken along with a 95% confidence interval. The confidence interval of the averages addresses the change in the coefficient at different flow rates and is preferred to be kept to a minimum because the accuracy and precision of the meter is the most important factor at many different flow rates. The average coefficient of the 2.5 orifice was 0.59 with a 95% confidence interval of 0.02. The literature value of 0.61 falls within this confidence interval. The average venturi meter coefficient was 0.94 with a 95% confidence interval of 0.04, also including the literature value of 0.98. The small intervals demonstrate the precision of the orifice and venturi measurements, and its inclusion of literature values demonstrates their accuracy. The average coefficient of the flow nozzle was found to be 1.03 with a 95% confidence interval of 0.04. In this case, the flow nozzles precision is not enough to account for its lack in accuracy where the literature value does not even fall within the standard deviation. Additionally, a meter coefficient greater than unity is not a valid meter coefficient and must be addressed. The coefficient calculations are related to the inverse of calculated velocity across the meter. Leaks through the seal of the flow nozzle would explain the coefficient calculations, because if the air was leaking, the pressure readings across the meter would be recorded lower than the actual pressure loss by the meter. Thus, the corresponding velocities calculated using those pressure differences would be lower. Therefore, the coefficient was increased to larger than unity due to the decrease in velocity through the flow nozzle while maintaining accurate Pitot tube velocity calculations.

iii. Permanent Pressure Loss and Head Loss

The mechanical energy losses of the gas flow meters were compared and summarized in the plot of Figure 5-4 versus Reynolds number. As expected from the theoretical data results, the 2.5 orifice meter had the largest increase in head loss as the Reynolds number increased. The permanent pressure loss can be attributed to the geometry of

Signature: 27

the orifice meter that has an immediate change in cross sectional area in place of a more gradual change as seen in the flow nozzle and venturi meters. The gradual change in cross sectional area in the latter two justifies the much smoother slope of the plot of head loss versus Reynolds number. The meter which had the least effect on head from increasing the Reynolds number was the venturi meter.

iv. Sound Data

The contour plot of the sound data in Figure 5-5 at operating conditions on damper setting 12 displays the drop in decibel readings as you move further away from the blower at several different positions. This effect of distance away from the blower coincides with expected results. Additionally, it was recommended that the sound be recorded for safety reasons. The values remained under the OSHA limit of 95 decibels so hearing protection was not required at any location in the room of the blower.

VII. CONCLUSIONS AND RECOMMENDATIONS

This study was conducted to evaluate several different gas flow meters for the scale up feasibility problem. The results provided an effective calibration of the hot wire anemometer with an accurate and precise calibration curve with a slope of 1.10, 0.1 away from the theoretical value of 1.0. Additionally, the calibration of the 2.5 orifice meter and the venturi meter produced significant results for the meter coefficient dependency on Reynolds with average values of 0.59 0.02 and 0.94 0.04 respectively. Notably, the size of the 95% confidence interval was minimal and included the theoretical values of 0.61 and 0.98 respectively, providing precise and accurate results for the scale up. These averages can be considered a reliable representation of the meters used in the experiment. Furthermore, the accuracy justified the approximations made for the calculations including incompressibility of the fluid. Interestingly, the flow nozzle meter produced precise coefficients, however at an average of 1.04 0.04 the correctness of this value was addressed, as the true coefficient of gas meters should not exceed unity. Therefore the flow nozzle coefficient was determined to be an inaccurate representation of the meter, and an inaccurate result entirely because of leaks in the system when measurements were taken. The accuracy of the meters at increasing Reynolds numbers was quantified by the standard 95% confidence interval between the different coefficients. The orifice meter coefficient had a confidence interval of 0.02 while the venturi meter had a slightly larger confidence interval of 0.04. Although the orifice meter produced slightly more precise results according to this interval, the venturi meter had a significantly smaller effect on head loss at increasing Reynolds number and proved to be dependable at higher flow rates. Conclusively, this study produced meaningful coefficients for the 2.5 circular orifice and the venturi meter. However, the venturi meter would be a preferred manner of measuring flow rates due to its minimal effects on changing the head loss, or energy loss of the system, even at large Reynolds numbers.

The recommendation of this study is to reevaluate the flow nozzle coefficient and head loss. The study determined leaks to be the main issue analytically; however this should be verified with a study on the flow nozzle to obtain more reliable results. Additionally, more data points for the sound contour would be useful in developing a more accurate portrayal of the decibel dependency on distance away from the blower. The experiment should include noting the radial angle that the position is at for taking measurements.

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VIII. Design Problem

The Uni-Minn Corporation was contacted by a client to choose a gas flow meter which

would most accurately measure an air flow of 5,000lbs/hr through a 500ft pipe.

Additional specifications from the client include inlet conditions of 120F and 30psig for a

particle removal process. The client required design specifications for optimal pipe

diameter, compressor size, and type of meter. Data obtained from the University of

Minnesota pilot plant was used to create a scale up design which met the clients needs.

Compressibility of the fluid was a primary concern of the scale up design. Calculations

were done using the mechanical energy balance around the whole pipe along the

continuity equation to find the individual pressures before and after the venturi meter.

The ratio of these pressures along with figure 2-5 was translated into a compression

factor of 0.99. Air at the design conditions can therefore be treated as incompressible.

Compression is also adiabatic, which creates an increase in temperature. This change in

temperature further supports the fluids incompressibility following the ideal gas law.

The gas flow meter experiment suggested for the scale up was the venturi meter.

Although data analysis suggested a lower variation in the dimensionless coefficient of

the orifice meter, its R2 value was insignificant, which suggested an unreliable behavior

of the fit line at high Reynolds numbers. On the other hand, the venturi meter presented

the least tradeoff between variation and R2 value. The chosen gas flow meter provides

the most reliable measurement with an average Cv value of 0.94 with a 95% confidence

interval of 0.04 and a cost of $1,065. Figure 9-1 shows a simplified diagram of the

suggested scale-up design.

The optimal pipe diameter which met the required mass flow rate specification was

determined to be 7.5 inches (2). This value is not available commercially; but local

provider Discount Steel sells both 8 and 10 ANSI schedule 40 pipes. The 8 inner

diameter pipe was chosen for design scale up due to its proximity to the optimal

diameter value and its lesser price. Five hundred feet of the 8 pipe is offered for

$18,000. (6) Insulation in the pipe is recommended to prevent heat loss.

With this specified pipe diameter, the linear flow rate was calculated to be 19.3ft/sec.

The linear flow rate, along with the airs properties at the specified conditions obtained

from the Engineering Toolbox was used to calculate a Reynolds number of

approximately 208,000. The flow in the scale up design is therefore turbulent. (7)

Suction Vent Venturi Meter Compressor Heat Exchanger

Figure 8.1 General Schematic for scale up design

Air flow

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To accurately size the compressor for the design, the pressure change across the

system needs to be calculated. Three different pressure drops were determined: the

pressure of 30psig required by the client, the pressure drop across the venturi meter,

and the pressure drop through the 500ft pipe. The pressure drop through the meter was

determined by plotting the permanent pressure loss found experimentally against the

Reynolds number, which resulted in a 0.2psia drop. To calculate the pressure loss

across a pipe with turbulent flow, equation 1-14 was used. The permanent pressure loss

was calculated to be 0.18psia. Adding these three individual pressures gives the final

pressure of 30.38psia or 44.7psig which has to be provided by the compressor.

The residence time of the air in the compressor was very short due to the high fluid

velocity of 19.3ft/sec. Therefore compression was approximated to be adiabatic, and

equation 1-15 was used to obtain a 43,098 ft lbf/lbm shaft work. Literature values suggest

typical compressor efficiencies are around 75% resulting in a brake horsepower of

144hp. Amongst Minnesotan providers of commercial compressors, SULLAIR TS20 Air

Compressor is the final suggestion for the scale up design. The compressor chosen

provides a 150hp and has the retail price of $22,000.(8)

Adiabatic compression induces a temperature increase in the air flow. The compressor

outlet temperature was determined to be 280F which was higher than the outlet

temperature specified by the client. To decrease the air temperature to the specified

value of 120F, a heat exchanger was added to the suggested scale up design. A simple

finned shell-and-tube countercurrent heat exchanger was chosen because of its low cost

and high availability. Following an experiment done previously in the University of

Minnesota pilot plant, the coolant in the heat exchanger was chosen to be the cooling

water flow rate used in a double effect evaporator experiment. The cooling water had a

temperature of 36F and a flow rate of 3.73lbs/sec. Geankopolis estimates overall heat

transfer coefficients for this type of heat exchanger to be around 20 to 40 btu/h ft2 F(1),

which results in a heat exchanger area of 49ft2. Bell and Gossett, a Minneapolis

provider, offers a Shell and Tube 5TNV3 Heat Exchanger for $585.(9)

The venturi meter, compressor, heat exchanger and piping needed for the design

problem add up to an initial capital investment of $43,000. Approximating the particle

removal system will be used at all times in the plant, the plant works for two complete

shifts, and water and energy prices of $0.003/gal and $0.12/kW respectively; the annual

cost of the scale up design is $107,747.

It is important to note that the results presented above were done with a D1/D2 value of

0.5, which represents the value obtained in the pilot plant.

Refer to Appendix C for design sample calculations.

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IX. NOMENCLATURE Symbols listed in the order in which they appear. : Pressure before fluid enters gas flow meter : Pressure at outlet of gas flow meter Manometer reading Density of the manometer fluid Density of the air Gravity SI units Velocity before gas flow meter Velocity after gas flow meter Pipe Diameter Vena Contracta Diameter Pi Generic dimensionless coefficient Diameter one and two ratio Gravity English units Pitot tube coefficient

Spacing between each measurement Radius of the pipe Total number of measurements Temperature Pressure : Pressure several diameter away from the meter Expansion Factor Optimal pipe diameter

Volumetric flow rate Reynolds number Dynamic viscosity of air Friction factor Pipe Length Mass flow rate over cross sectional area Ideal gas constant Molar mass Shaft work Specific heat capacities ratio Mass flow rate Compressor efficiency Heat exchanger area Total heat Overall heat transfer coefficient Logmean temperature Orifice meter coefficient Venturi meter coefficient

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X. References

1. Green, Don W.; Perry, Robert H.. Perrys Chemical Engineers Handbook (8th Edition). Blacklick, OH, USA; McGraw-Hill Professional Publishing, 2007. p 1037.

2. Geankoplis, Christie, Transport Processes and Speration Process Principles, 4th ed., Prentice Hall, Upper Saddle River, NJ (2003).

3. University Of Minnesota, CHEN 3401W TSI Velocity Instruction Manual

4. Peters, M.S. and Timmerhous, K., Plant Design and Economics for Chemical Engineers, 3rd ed. McGraw-Hill Companies, NY.

5. Discount Steel Steel Pipes http://www.discountsteel.com/ items/Electric_Welded_ERW_Round_Steel_Tube.cfm (accessed Mar. 23 2013)

6. The Engineering Toolbox. Air Properties http://www.engineeringtoolbox.com/air-properties-d_156.html (accessed Mar. 25 2013)

7. Sullair Compressors, TS20 rotary screw compressor, http://www.sullair.com/Americas/en/Products/Stationary+Air+Power/Compressors/60+-+100+hp/TS-20+Two-Stage+Variable+Capacity+Rotary+Screw+Air+Compressor (accessed Mar. 23 2013)

8. Grainger, Bell and Gossett Heat Exchangers http://www.grainger.com/Grainger/BELL-GOSSETT-Heat-Exchanger-5TNV3?gclid=CKie3sCUjLYCFY-iPAodEGsAJg&cm_mmc=PPC%3AGooglePLA-_-HVAC+and+Refrigeration-_-HVAC+Controls- (accessed Mar. 23 2013)

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APPENDIX A: Week One Original Data Sheets

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APPENDIX A: Week Two Original Data Sheets

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APPENDIX B: SAMPLE CALCULATIONS

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APPENDIX C: DESIGN PROBLEM CALCULATIONS

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APPENDIX D: ERROR ANALYSIS

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APPENDIX E: ANALYSIS OF SQUARE AND TRIANGLE ORIFICE METERS

Orifice meters are a common choice of meter, especially in gas metering applications. They are generally consistent, relatively easy to install, can be less expensive than venturi or flow nozzles, and can be replaced more efficiently. When manufactured under the correct specifications, orifice flow meters are a simple and reliable way of measuring flow. For the sake of practicality, circular orifices are logical as they are a more simple design to manufacture. See section (V-iii) for analysis of a 2.5 orifice meter.

For this experiment, however, two orifice meters with irregular openings were analyzed. The same apparatus used to calibrate the venturi meter, flow nozzle, hot wire anemometer, and 2.5 circular orifice meter was used. The hydraulic radii were calculated and used for analysis, rather than a traditional diameter. Sample calculations of the orifice meters are shown in Appendix B. The first analyzed orifice meter had an equilateral triangle opening with 3 0.1 in. sides. This orifice had an area of 3.9 0.2 in2. The value was calculated to be 0.29 0.01. The second had a square opening with 3 0.1 in. sides as well. This orifice had an area of 9 0.4 in2, and a value of 0.50 0.01. These meters were placed on the left flange of an opening in the 6 ID pipe downstream of the pitot tube. At five damper settings (4, 5, 7, 10, and 12), two pressure difference readings were taken (in inches water). The first was taken directly over the orifice meters, at a distance of one pipe diameter on each side. This pressure difference was recorded to determine the meter coefficient. The second was taken one pipe diameter upstream of the meter and four pipe diameters downstream of the meter. This pressure difference was essentially a representation of the permanent pressure loss due to the orifice meters being placed in the way of the airflow. For this experiment, these data were taken to analyze the meter coefficients of these irregular orifice meters as well as the effect these meters had on the overall flow of air through the pipe. See Tables E-4 and E-5 at the end of Appendix E for a summary of the raw data obtained during lab. The triangle orifice meter was analyzed with Reynolds numbers between 2900 200 and 7300 700, and had meter coefficients that increased from 0.37 0.03 to 0.64 0.03. Permanent pressure losses in the pipe due to the installation of the triangle orifice meter were between 61.34 0.04 and 129.62 0.04 lbf/ft

2. The square orifice meter had coefficients ranging from 0.61 0.03 to 0.66 0.03 with Reynolds numbers of 6000 100 to 14,000 200. The permanent pressure losses due to the installation of the square orifice meter were between 12.65 0.04 and 68.43 0.04 lbf/ft

2. The damper settings used in the collection of these data were the same for both

meters. The pitot tube was used to determine an average velocity of the air flow through the pipe. Note that the type of meter installed did affect the respective velocity determined upstream of the meter. With the same damper settings, the triangle orifice meter had lower Reynolds numbers than those of the square orifice meter.

Table E-1 illustrates the volumetric flow rates calculated at each damper setting. The maximum volumetric flow rate allowed with the blower used in this experiment was 824 cfm. All volumetric flow rates calculated from the air velocities determined from the pitot tube and the pipe diameter were below this maximum. It should also be observed that the volumetric flow rates follow the same trend as the Reynolds number, with respect to the meters. The triangle meter had less of a volumetric flow rate at each damper setting than the square meter.

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Table E-1: Volumetric flow rates of the triangle and orifice meter at varying damper settings, in cfm

Damper Setting

4 5 7 10 12

Triangle 160 10 214 8 288 8 369 8 396 9

Square 329 8 398 9 640 10 580 10 760 20

The average pipe velocity, Reynolds number, meter coefficient, and permanent pressure losses at the respective damper settings for the triangle and square orifice meters are summarized in Tables E-2 and 3, respectively. The average pipe velocities were calculated from the pressure differences over the pitot tube, as it was used as the standard. With the calculated pipe velocities and measured pipe diameter, the Reynolds numbers were determined. The coefficient associated with each individual meter was calculated using equation (1-4) and the pressure drop over the respective meter. The experimental pressure drop was calculated from equation (1-1) and a pressure difference between the meter and four pipe diameters downstream of the meter. These theoretical values of the permanent pressure drop were calculated from the experimental values of and pressure drops over the meter. That is, the theoretical values arent general values for any meter, but specific to the meters used in this experiment.

Table E-2: Results of the triangle orifice meter

Damper Setting

4 5 7 10 12

Pipe velocity ft/sec 13.4 0.8 18.2 0.6 24.4 0.4 31 3 33 3

Reynolds # 2900 200 3900 100 5300 100 6800 600 7300 700

Meter coefficient 0.37 0.03 0.43 0.02 0.49 0.02 0.60 0.06 0.64 0.07

Experimental

permanent P lbf/ft2 61.3 0.0.4 84.1 0.4 117.3 0.4 128.5 0.4 129.6 0.4

Theoretical permanent P - lbf/ft

2 68.01 0.3 93.0 0.3 129.6 0.3 142.1 0.3 143.8 0.3

Table E-3: Results of the square orifice meter

Damper Setting

4 5 7 10 12

Pipe velocity ft/sec

28 4 34 3 55 2 49 2 65 2

Reynolds # 6000 800 7300 700 11900 400 10600 500 14000 300

Meter coefficient 0.65 0.09 0.61 0.06 0.66 0.04 0.50 0.03 0.65 0.03

Experimental

permanent P

lbf/ft2

12.6 0.4 21.3 0.4 47.9 0.4 66.0 0.4 68.4 0.4

Theoretical permanent P -

lbf/ft2

14.1 0.4 23.4 0.4 52.3 0.8 72 1 75 1

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The meter coefficients are a function of the Reynolds number (5). In the case of circular orifice meters, the meter coefficients tend to rise sharply with increasing Reynolds numbers. With values greater than about 0.6, the coefficients then decrease rather sharply. With values less than that, they decrease less dramatically and level off. This change from a positive to negative slope occurs around a Reynolds number of 1,000. The coefficients and Reynolds numbers associated with the square orifice meter were comparable to those of circular orifice meters. This was not the case with the triangle orifice meter, however. Figure E-1 illustrates these results.

Figure E-1: Meter coefficients as a function of Reynolds number for ideal circular square-edged orifice (5). The markers denoted with triangles correspond to the data associated with the triangle orifice meter. The square orifice meter data are represented by the square markers.

Disregarding the data point associated with the square orifice meter with a coefficient of 0.50 0.03 and a Reynolds number of 10,600 500, the square orifice meter has coefficients that align with circular orifice meters. That is, it had coefficients of 0.61 0.06 to 0.66 0.04 at Reynolds numbers between 6000 800 and 14,000 400. There wasnt a clear positive or negative slope, indicating a relatively constant coefficient within this range of Reynolds numbers, as opposed to the coefficients of the triangle orifice meter. The triangle orifice meter was observed to have a very different trend than circular orifice meters at the same Reynolds numbers. At Reynolds numbers where circular orifice meters were observed to have decreasing or constant coefficients, the triangle orifice meter had the opposite trend. With the data collected from this experiment, the coefficients showed a sharp increase from 0.37 0.03 to 0.64 0.07 in the range of Reynolds numbers from 2900 200 to 7300 700. A more detailed depiction of the coefficients for the triangle and square orifice meters are shown in Figures E-2 and 3, respectively. Note that the error associated with the meter

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coefficients at the two highest Reynolds numbers for the triangle orifice meter are larger because the 0-40 inch manometer was used to collect the pressure drop over the pitot tube instead of the 0-1 inch manometer. The pressure drop over the pitot tube were small compared to the permanent pressure drop and pressure change over the meter, and the 0.1 in. water error was more obvious.

Figure E-2: Meter coefficient as a function of Reynolds number for the triangle orifice meter

Figure E-3: Meter coefficient as a function of Reynolds number for the square orifice meter

0

0.1

0.2

0.3

0.4

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0.6

0.7

0.8

0 2000 4000 6000 8000 10000

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ter

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eff

icie

nt

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The square and triangle orifice meters differed in their effect on permanent

pressure loss, as well. The triangle orifice meter displayed a greater permanent

pressure loss, most likely because of the smaller orifice area available for air to flow

through. At Reynolds numbers between 2900 200 and 7300 700, the permanent

pressure losses were between 61.3 0.4 and 129.6 0.4 lbf/ft2 . These experimental

values were all just under 10% of the theoretical permanent pressure losses of 68.0 0.3

to 143.8 0.3 lbf/ft2 at the same Reynolds numbers. The theoretical values were

calculated using equation (1-8.a). See Figure E-4. The triangle orifice meter had an

overall pressure loss of 80%.

Figure E-4: Experimental and theoretical permanent pressure losses over the triangle orifice meter as a function of Reynolds number with 10% error bars associated with the theoretical values of permanent pressure loss

At greater Reynolds numbers of 6000 800 to 14000 400, the permanent pressure losses were between 12.6 0.4 and 68.4 0.4 lbf/ft

2 for the square orifice meter. These experimental values were also 10% less than those of the theoretical permanent pressure losses of 14.1 0.4 and 75 1 lbf/ft

2 at the same Reynolds numbers, with the exception of the data point associated with the lowest Reynolds number. This experimental pressure loss was 15% less than the theoretical pressure loss at that same Reynolds number. See Figure E-5.

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loss

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f/ft

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Experimental

Theoretical

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Figure E-5: Experimental and theoretical permanent pressure losses over the square orifice meter as a function of Reynolds number with 10% error bars associated with the theoretical values of permanent pressure loss

At less turbulent Reynolds numbers, the triangle orifice meter still had a greater effect on the reduction of the pressure through the pipe. More data at a wider variety of Reynolds numbers would need to be obtained to observe the effect of the triangle orifice meter at higher Reynolds numbers and the effect of the square meter at lower Reynolds numbers. The 1-2 term from equation (1-8.a) can be thought of as a representation of the theoretical energy associated with the air flow. As it is equal to the permanent pressure loss divided by the pressure drop over the orifice meter itself, this ratio was calculated to relate to this energy term. For both the square and triangl meters, this ratio was less than the 1-2 term, meaning energy was lost. This is