pump performance measurement

University of Arkansas Mechanical engineering department

MEEG 4202L Lab III: February 24, 2014

Thursday Section Group 3

Pump Performance Measurement Stacy Evans, Josh Parker, Nuwan Liyanage, Ford Lewallen

[email protected], [email protected], [email protected], [email protected]

ABSTRACT

The analysis performed was on the transient heat transfer on similarly shaped samples of different materials to determine the thermal conductivity for an unknown material. The four samples included two slabs and two spheres. One of each shape was made of Aluminum with known material properties, and one of each shape was made of an unknown material. To determine the thermal conductivity, the samples, which were initially at room temperature, were submerged into a temperature controlled water bath. The internal temperature change with respect to time of each sample was measured by a thermocouple placed within the sample. LogUD software was utilized to extract the transient temperature readings. The change in the temperature gradient with respect to time was used to curve fit the data. This data was then used to compare

the experimental values of * with the calculated values of *0. The value of k then adjusted to have a close match for the data curves, and determining the materials identity based on k value chosen. This is a cheap way to calculate the k value of an unknown material. The unknown slab was found to be Polycarbonate with k = 0.155 Btu/hr-ft2-F with an error of 41%. The unknown sphere was found to be PVC with k = 0.009 Btu/hr-ft2-F with an error of 85%.

NOMENCLATURE T Temperature oF Ti Initial Temperature oF T Infinite Temperature oF Bi Biot Number unit-less h Heat Transfer Coefficient Btu/hr-ft2-F k Thermal Conductivity Btu/hr-ft-F As Surface Area ft2

V Volume ft2

cp Specific Heat Btu/lbm-F Density lbm/ft3

tc Time Constant s L Thickness ft Thermal Diffusivity ft2/s Fo Fourier Number unit-less r0 Radius ft

0 Temperature Gradient unit-less

C Correlation Coefficient unit-less Position Within Body unit-less

INTRODCUTION

The concept of heat transfer as a result of a temperature difference between two objects is widely known throughout the science and engineering community; likewise, it is dominantly applied when analyzing heat transfer within a system.

Furthermore, comparing the different means of heat transfer, including heat transfer by conduction and convection, allows one to experimentally determine the material of an unknown sample. The thermal conductivity of a sample is determined by the material that the sample is composed of. The convection heat transfer coefficient, however, is determined by the geometry of the sample. If the convection heat transfer coefficient is known for a sample that is geometrically similar to a sample of an unknown material, the convection heat transfer coefficient will be constant; therefore, a mathematical solution can be applied to determine the thermal conductivity of the unknown material and thus the material itself. The ratio of the internal resistance of a body to heat conduction to its external resistance to heat convection is known as the Biot number. When the Biot number is less than 0.1, the object is approximated to have a uniform temperature distribution throughout the body and can be evaluated using lumped system analysis. As the Biot number increases, a temperature gradient begins to from within the object. If high accuracy is not relevant, lumped system analysis can still be used; however, one-term approximation results in more accurate results when the Biot number is outside of this criterion. If the heat transfer coefficient is high enough, the Biot number infinitely increases. From this, a third method of determining material properties is derived. Thus, the heat transfer properties of a material can be mathematically determined for a range of temperature differences as a function of time and location.

OBJECTIVE

The objective of this lab is to determine the thermal

conductivity and heat transfer coefficient for a slab and sphere

of both known and unknown materials by analyzing their

temperature changes over time when exposed to a constant

temperature environment.

THEORY When an object with a uniform initial temperature (Ti) is

placed within a medium with a uniform temperature (Tinf), heat will be transferred from the object with a higher temperature to the other object at an logarithmic rate until both are in thermal equilibrium. As the temperature of both objects reach equilibrium, the rate of heat transfer will exponentially decrease. This is shown in Figure 1 below.

2 Copyright 2013 by UARK MEEG

Figure 1: Temperature profiles of a wall when Tinf < Ti [2]

Using a thermocouple to measure the temperature change with respect to time of a sample placed in an environment at Tinf, a range of data points of temperature (T), and time (t) can be recorded. A ratio of these temperature values, known as the dimensionless temperature value, can be determined as shown in Equation 1.

inf

inf*

TT

TT

i

(Eq. 1)

The heat transferred during this experiment can be calculated using Equation 2.

TmCdtTThA pis )( inf (Eq. 2)

Integrating Equation 2 provides the following solutions

p

s

VC

hAb

(Eq. 3)

bt

i

AeTT

TT

inf

inf* (Eq. 4)

Where, A is a based on the Biot number. The thermal conductivity of a sample is the resistance of the material to conduct heat. This value can be experimentally determined using three different mathematical solutions. The Biot number determines the best approach and is calculated using Equation 5,

k

hLB ci (Eq. 5)

Where, Lc is the volume divided by the surface area. If the Biot number is less than 0.1, the system can be treated as a lumped mass. Lumped System Analysis assumes a uniform temperature distribution throughout the body. Using this method, the heat transfer coefficient of a sample with a known material composition can be determined at any given time using Equation 6.

VC

thA

TT

TT

p

s

i exp

inf

inf* (Eq. 6)

Once the heat transfer coefficient is known, the thermal conductivity of a sample with the same geometry but different material composition can be determined using one-term approximation for both slab and spherical geometries. Taking the experimental values found and solving Equation 1 results in a range of * that can be plotted verses time on a data analysis program such as Microsoft Excel. Once plotted, an exponential trend line can be added with the corresponding function in the form of A*exp(-bt) as shown in Equation 4. Equation 7 relates the one-term approximation of * with information found using lump system analysis

Fo

eC2

1

1

* (Eq. 7)

Where, Fo is the Fourier number, C1 is a function of , and is a function of the Biot number. These values are computed using Equations 8 through 11

2L

tFo

(Eq. 8)

pC

k

(Eq. 9)

Slab: )2sin(2

)sin(4

11

11

C (Eq. 10a)

Sphere: )2sin(2

)]cos()[sin(4

11

1111

C (Eq. 10b)

Bi

aa

Bi

aa 32

102

1

exp1

(Eq. 11)

Where, a0, a1, a2, and a3 are constants that are dependent on the geometry of the sample. Comparing Equation 7 and Equation 4, it can be concluded that C1=A, where A was graphically determined. Substituting A for C1 in Equation 10 yields one equation with one unknown

value, . Therefore, can be calculated. Next, Equation 1 and Equation 7 can be equated so that the only unknown value is the Fourier Number. Once the Fourier number is determined, can then be calculated by rearranging Equation 8. Finally, Equation 9 can be rearranged to solve for the thermal conductivity. An alternative method to using lumped system analysis to determine the heat transfer coefficient and thus the thermal conductivity is to assume that the heat transfer coefficient is infinity large. This causes the Biot number to become infinite, reducing Equation 11 as shown below.


202

1

1aa

(Eq. 12)

From Equation 12, can be calculated, and the same process as discussed can be followed.

EXPERIMENTAL SETUP

This experiment was performed in the Mechanical Engineering building at the University of Arkansas Fayetteville in the first lab experiment hub down the hall of room 109. The setup for the experiment is shown in Image 1 of App A. Fill the bath with water and heat with the heater/circulator. Attach the thermocouple to the LJTick-InAmp, the LJTick-InAmp to the LabJack, and the LabJack to the computer and open LabView software. Measure the time it

takes for the four sample specimens to reach by attaching the thermocouple to them and placing them (individually) in the circulation chamber of the bath.

PROCEDURE

1. Turn on pump/heater. 2. Turn thermostat to desired temperature and allow bath

to reach steady state.

3. Attach LJTick-InAmp to FI04, FI05 channels. 4. Connect k-type thermocouple to the corresponding

positive and negative screw terminals.

5. Connect the 10k resistor to the negative screw terminal and to the ground screw terminal.

6. Make sure all LJTick-InAmp switches are off. 7. Set the gain to 201 by turning switch 10 on. Set the

voltage offset to +0.4V by turning switch 5 on. See

Appendix B

8. Open the LogUD software. 9. Convert the voltage difference in the thermocouple to

oC by inputting the scaling equation

y=TCVoltsToTemp[thermocouple

type:tcVolts:cjTemp]-273.15 into the first scaling

equation where = is entered. 10. Enter k for thermocouple type. 11. Enter (b offsetVoltage)/gain for tcVolts. Refer to

step 7.

12. To calibrate the thermocouple, adjust the cold junction temperature value (cjTemp) to equal the room

temperature measured with a thermometer by adding

or subtracting a few degrees.

13. Set the Resolution to 1, the interval to .5s, and the number of channels to 2.

14. Put the metal slab into the tub and click write to file to begin recording temperature. Record until

-ln(T-T)/(Ti-T) > 4.

15. Put the plastic slab into the tub. Begin recording temperature at the time when Fo = 0.2.

16. Repeat Step 15 for the metal sphere and the plastic sphere, recording data once Fo = 0.2.

Note: Attach thermocouple to sample specimens before putting them in the bath.

= [:( 0.4)

201: 295.37 2] 273.15

(Eq. 13)

ln (

) > 4

(Eq. 14)

EQUIPMENT

2 type-k thermocouples o Omega Stamford CT

2 Resistors 10k

Heater/Circulator o Cole Parmer o Model No. 1252-00 circulator o Type: 1252-0012, 115V, 60Hz

Engineering Laboratory Design Inc. o Model No. 204 o Box 276

LabJack o Model U3-HV version 1.3 o SN: 320050659

LJTick-InAmp o Rev. 2.0

Metal Slab Sample Specimen o 4in. x 6in. x0.5in.

Metal Sphere Sample Specimen o 2.5in. diameter

Plastic Slab Sample Specimen o 4in. x 6in. x0.5in.

Plastic Sphere Sample Specimen o 2.5in. diameter

DATA AND RESULTS

The dimensions of each sample were measured using a dial caliper. The dimensions for the slab are shown in Table 1. All other dimensions can be found in Appendix F.

Table 1: Slab Sample Dimensions.

Slab Sample Units

Height-H 0.5 ft

Width - W 0.333 ft

Thickness - 2L .042 ft

Volume 0.000198749 ft^3

Surface Area-As 0.037673675 ft^2

T-initial 69.44 F

T-inf 118.49 F

Max-T 116.82 F

The material properties of the Aluminum samples are shown in Table 2. PVC and Polycarbonate properties can be found in Appendix F.


Table 2: Material Properties

Aluminum 2024T351

Density - 172 lbm/ft^3

Thermal Conductivity -k 70 Btu/hr-ft-F

Specific Heat - Cp 0.214 Btu/lbm-F

Alpha - 1.902

The temperature of the bath was measured by an analog thermometer. This value was entered in the LogUD to calibrate and match thermocouple temperature to bath temperature. Then the temperatures of the ambient bath and test specimen were recorded in LogUD using the initial software formula settings as explained in experimental setup. A snapshot of the experimental setup in LogUD is shown below.

Figure 3: Log UD Screenshot

A correction factor is considered to offset the lack of calibration in the internal temperature thermocouple. This was accounted for in LogUD program to provide accurate temperature readings. To find the heat transfer coefficient for the Aluminum slab, the temperature vs. time was plotted to ensure that an accurate logarithmic curve was generated as shown below.

Figure 4: Temperature Curve for Aluminum Slab

A line equation was found for the plot of * vs. Time for both the slab and the sphere samples in the form of A*EXP(-bt) using an exponential curve fit as shown in the Figures below.

Figure 6: Theta vs. Time for Aluminum Slab

The values A and b were used to calculate h for the aluminum samples. The h value was found to be 93.24 Btu/hr-ft2-F. Theoretically, the convection coefficient, h, should be the same for geometrically similar samples. The k value for each sample was evaluated using both one-term approximation method, and the method assuming an infinite heat transfer coefficient. This done by initially assuming k and comparing

the experimental values of * with the calculated values of *0. To get the approximation k was adjusted to get the experimental and calculated lines matching as close as possible. Figure 7 and 8 show these curve fits.

Figure 7: Theta vs. Time for PVC Slab

0.00

50.00

100.00

150.00

0.0 20.0 40.0 60.0 80.0

Temperature verses Time

Al Slab

y = 0.94268e-0.04083x

R = 0.99050

0.000

0.200

0.400

0.600

0.800

1.000

0.0 20.0 40.0 60.0 80.0

* verses Time

y = 1.4774e-0.009x

R = 1

0.00

0.20

0.40

0.60

0.80

1.00

0 100 200 300 400 500 600

* verses Time, PVC

*, PVC *


Figure 8: Theta vs. Time for PC Slab

Tables 4 and 5 show the calculated k values for both unknown samples. The error for k values were also recorded in the table below. Sample calculations can be found in appendix C.

Table 4: Thermal Conductivity of Slab Samples

Slab h k Error

Btu/hr-ft2-F Btu/hr-ft-F %

PVC 0.0259 0.125 116%

Infinite 0.100 72%

PC 0.0259 0.155 41%

Infinite 0.012 9%

Table 5: Thermal Conductivity of Sphere Samples

Sphere h k Error

Btu/hr-ft2-F Btu/hr-ft-F %

PVC 0.0302 0.009 85%

Infinite 0.0085 85%

PC 0.0302 0.011 90%

Infinite 0.010 91%

DISCUSSION

Initially all the samples were supposed to be at room

temperature. After the samples were placed in the bath, a

transfer in heat from the water occurred. Each sample had

different rates of heating but overall the Aluminum samples

heated much faster than the plastic samples. Also it should be

noted that the slabs heated faster than the spheres. This showed

that the Thermal Conductivity of Aluminum was much higher

than the Plastic. These observations are confirmed by looking

at the Biot number of each material and shape. Higher Biot

numbers directly correlated to longer heating times.

In order to calculate the thermal conductivity, the data

needed to be plotted and curve fit. The curve fit used was an

exponential which provided the proper form to use the one term

approximation calculations. Thermal conductivity values were

found for both sets of material properties. The slab was found

to be polycarbonate; it had a lower percentage of error than the

value found for PVC. The sphere was found to be PVC, but its

error percentage was very close to that of PC.

The slab was found to have a much lower percentage of error

than the sphere. The plastic sphere was not properly sealed

around the thermocouple and could possibly be a source of

error. Also, the sphere had significant cracking inside the seal

and could have added complexity to the setup. When assuming

the Bi number was infinite, the slab had a higher percentage of

error. Coincidentally the error for the sphere stayed roughly the

same and still pointed to PVC. This was most likely directly

related to the geometry and the characteristic length.

A large portion of blame for the error in this report may be

due the data recording or experimental setups. The heat transfer

coefficient was found using lump mass, but when initially used

for the unknown material calculations errors immediately

happened. Other sources of error identified in the experiment

included small thermocouple calibration issues, inaccuracies in

the heating methods of the thermal bath, data fluctuations

attributed to thermocouple movement, and inconsistent

material properties of the test specimens.

CONCLUSION

Our slab was determined to be made of

Polycarbonate with an error percentage of 41%.

Our sphere was determined to be made of

Polyvinylchloride with an error percentage of 85%.

Samples with high thermal conductivities can be used

to find convection coefficients via observing changes

in a temperature gradient with time.

The lower the Biot number the faster a sample can be

heated, with respect to geometry

Lumped analysis is valid to use for objects with a Bi

< 0.1.

Thermal conductivity can be approximated for

objects with a high Bi number without knowing the

overall heat transfer coefficient by approximating

that the Bi ~ with limited success, mainly due to

geometry.

The maximum error was found when assuming Bi ~

for the slab when assuming the material was PVC,

with an error percentage of 116%.

The minimum error was found when assuming Bi ~

for the slab when assuming the material was PC,

with an error percentage of 9%.

ACKNOWLEDMENTS

The members of this team would like to thank Monty Roberts and Jason Bailey for their instruction and guidance, and the

y = 1.5273e-0.009x

R = 1

0.00

0.20

0.40

0.60

0.80

1.00

0 100 200 300 400 500 600

* verses Time, PVC

*, PC *


University of Arkansas Mechanical Engineering Department for supplying the necessary equipment.

REFERENCES [1] Audon Electronics, LabJack U3-LV USB Multifunction Data Acquisition Unit 2.4V Input Range, http://www.audon.co.uk/usb_multi/u3.html, Feb. 14.

[2] Cengel, Yunus, and Afshin, Ghajar. Heat and Mass Transfer, Fundamentals & Applications. New York: McGraw-Hill, 2007. Print

[3] LabJack, Appendix C Thermocouples, http://labjack.com/support/ljtickinamp/datasheet/appendix-c, Feb. 2014.

[4] LabJack, LJTick-InAmp Data Sheet, http://labjack.com/support/ljtick-inamp/datasheet, Feb. 2014.

[5] Sensors, 5-in-1 Digital Multimeter from Omega Engineering,http://www.sensorsmag.com/product/5-1-digital-multimeter-omega-engineering, Feb. 2014.


APPENDIX A

Experimental Equipment and Setup

Image A1: Bath with heater/circulator next to thermocouple, LabJack, and LJTick-InAmp

Image A2: View of circulation chamber, bath filled with water

Image A3: LJTick-InAmp Image A4: Side view of heater/circulator

Image A5: Heater/circulator Image A6: LabJack U3-HV

Image A7: Model No. of bath and table of physical properties of material specimens Image A8: Type-k thermocouple


Image A9: Metal and plastic slabs Image A10: Metal and plastic spheres

Image A11: Example image of LabView software


APPENDIX B

LJTick-InAmp Data Sheet

Switch

# Name Description

1 BxR32 Custom gain determined

by R32

Applies to channel B only. All off equals a gain of 1.

2 Bx11 Gain of 11

3 Bx52 Gain of 51

4 Bx201 Gain of 201

5 0.4V Output offset of +0.4

volts.

Voffset applies to both channels. Switch # 5 or 6 should

always be on, but not both.

6 1.25V Output offset of +1.25

volts.

7 AxR17 Custom gain determined

by R17

Applies to channel A only. All off equals a gain of 1.

8 Ax11 Gain of 11


9 Ax51 Gain of 51

10 Ax201 Gain of 201

APPENDIX C Sample Calculations

Sample Calculation for *

=

=

67.96 118.49

69.44 118.49= 1.030

Sample Calculation for h, given the b value found by curve * vs time.

=

=

0.0408 172 0.214 0.00694

0.403= 0.0259

Sample Calculation for for slab

=

=

0.155

74.90 0.201= 1.91 06

Sample Calculation for Bi of a slab

=

=

0.0259 0.017

0.155= 10.376

Sample Calculation for 1/2 for Slab. 1

2= 0 +

1

+ 2

3 = .3552 +

. 9935

10.376+ .0504

3.55010.376 = 0.4708

Sample Calculation for C1

1 =4 sin 1

21 + sin 21=

4 sin 1.4574

2 1.4574 + sin 2 1.4574= 1.4774

Sample error calculation of error calculation for k

= |

| 100 = |

0.155 0.11

0.11| 100 = 41%


APPENDIX D

Graphs

Figure D1: Temperature vs. Time for Aluminum Sphere

y = -0.0044x2 + 1.0013x + 58.183R = 0.9846

0.00

20.00

40.00

60.00

80.00

100.00

120.00

140.00

0.0 20.0 40.0 60.0 80.0 100.0 120.0 140.0 160.0

Temperature verses Time

Al Sphere


Figure D1: Theta vs. Time for Aluminum Sphere

Figure D1: Theta vs. Time for PVC Sphere

y = 1.3214e-0.0236x

R = 0.9892

0.000

0.100

0.200

0.300

0.400

0.500

0.600

0.700

0.800

0.900

1.000

0.0 20.0 40.0 60.0 80.0 100.0 120.0 140.0 160.0

* verses Time

y = 0.5024e-0.001x

R = 1

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

0 200 400 600 800 1000 1200 1400 1600 1800

* verses Time, PVC

*, PVC *


Figure D4: Theta vs. Time For PC Sphere

Figure D5: Theta vs. Time for PVC Slab, h~infinity

y = 0.4978e-0.001x

R = 1

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

0 200 400 600 800 1000 1200 1400 1600 1800

* verses Time, PVC

*, PC *

y = 1.2742e-0.009x

R = 1

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

0 100 200 300 400 500 600

* verses Time, PVC

*, PVC *


Figure D6: Theta vs. Time For PC Slab, h~infinity

Figure D7: Theta vs. Time for PVC Sphere, h~infinity

y = 1.2742e-0.008x

R = 1

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

0 100 200 300 400 500 600

* verses Time, PVC

*, PC *

y = 0.4989e-0.001x

R = 1

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

0 200 400 600 800 1000 1200 1400 1600 1800

* verses Time, PVC

*, PVC *


Figure D8: Theta vs. Time For PC Sphere, h~infinity

Appendix E

Observation Notes

Ford Lewallen Experimental Setup, Procedure, Equipment, Nomenclature, References, Appendices A & B

Stacy Evans Abstract, Introduction, Objective, Theory, Formatting and Editing

Josh Parker Data and Analysis, Discussion, Conclusions

Nuwan Liyanage Appendix C, Data and Results

y = 0.4938e-0.001x

R = 1

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

0 200 400 600 800 1000 1200 1400 1600 1800

* verses Time, PVC

*, PC *


APPENDIX F

Material Properties and Raw Data

Table F1: Material Properties

Material Density-lbm/ft3

Thermal Conductivity-Btu/hr-ft-F

Specifc Heat-Btu/lbm-F

Aluminum 2024T351 172 70 0.214

PVC 91.8 0.058 0.201

Polycarbonate 74.8 0.11 0.301

Table F2: Sample Dimensions

L, plate 0.021 ft r0, sphere 0.104 ft

W, plate 0.333 ft As, sphere 0.136 ft^2

H, plate 0.500 ft V, sphere 0.005 ft^3

As, plate 0.403 ft^2 Lc, sphere 0.035 ft

V, plate 0.007 ft^3 , Al 172 lbm/ft^3


Lc, plate 0.017 ft k, Al 70 Btu/hr-ft-F

, Al 172 lbm/ft^3 c, Al 0.214 Btu/lbm-F

k, Al 70 Btu/hr-ft-F , PVC 91.8 lbm/ft^3

c, Al 0.214 Btu/lbm-F k, PVC 0.058 Btu/hr-ft-F

, PVC 91.8 lbm/ft^3 c, PVC 0.201 Btu/lbm-F

k, PVC 0.058 Btu/hr-ft-F , PC 74.9 lbm/ft^3

c, PVC 0.201 Btu/lbm-F k, PC 0.11 Btu/hr-ft-F

, PC 74.9 lbm/ft^3 c, PC 0.301 Btu/lbm-F

k, PC 0.11 Btu/hr-ft-F

c, PC 0.301 Btu/lbm-F

APPENDIX G

RAW DATA

Sample Slab values

t, s Ti * -ln(*) , PVC 91.80 lbm/ft^3 , PC 74.90 lbm/ft^3

0.0 67.96 1.030 -0.030 k, PVC 0.058 Btu/hr-ft-F k, PC 0.110 Btu/hr-ft-F

0.5 69.43 1.000 0.000 c, PVC 0.201 Btu/lbm-F c, PC 0.301 Btu/lbm-F

1.0 70.64 0.976 0.025 , PVC 1.88E-06 , PC 1.91E-06

1.5 71.71 0.954 0.047 Bi, PVC 12.866 Bi, PC 10.376

2.0 73.58 0.916 0.088 1/1^2 0.4708 1/1^2 0.4869

2.5 74.38 0.899 0.106 1 1.4574 1 1.4331

3.0 75.59 0.875 0.134 C1 1.4774 C1 1.5273

3.5 76.66 0.853 0.159 k, PVC 0.125 Btu/hr-ft-F k, PC 0.155 Btu/hr-ft-F

4.0 78.12 0.823 0.195 %ER, PVC 116% %ER, PC 41%

4.5 79.19 0.801 0.222

5.0 80.12 0.782 0.246

5.5 81.32 0.758 0.277


6.0 82.79 0.728 0.318

Sample Sphere values

t, s Ti * -ln(*)

0.0 69.97 0.997 0.003 , PVC 91.80 lbm/ft^3 , PC 74.90 lbm/ft^3


1.0 69.97 0.997 0.003 c, PVC 0.201 Btu/lbm-F c, PC 0.301 Btu/lbm-F

1.5 70.37 0.989 0.011 , PVC 1.28E-07 , PC 1.34E-07

2.0 69.97 0.997 0.003 Bi, PVC 443.560 Bi, PC 345.896

2.5 70.10 0.994 0.006 1/1^2 0.1016 1/1^2 0.1018

3.0 69.97 0.997 0.003 1 3.1366 1 3.1346

3.5 70.10 0.994 0.006 C1 0.5024 C1 0.5033


4.5 70.10 0.994 0.006 %ER, PVC 85% %ER, PC 90%