11:01 ☑ canvas.ucsd.edu -> ☐ ... : Page < 2 of 2 - ZOOM + Data Set 1 Data Set 2 Volumetric Suction, Suction, water W W k/ks content, 0 (kPa) (m³/m³) (kPa) 0.0 0.396 0.0 1.000 1.0 0.396 1.1 1.000 2.0 0.394 1.6 0.950 4.2 0.390 1.9 0.900 5.9 0.386 2.9 0.765 7.8 0.379 4.9 0.595 10.9 0.370 6.9 0.480 18.6 0.340 9.8 0.338 28.0 0.300 13.5 0.200 39.2 0.260 18.2 0.100 58.9 0.220 19.6 0.074 78.5 0.200 25.2 0.300 88.3 0.194 33.3 0.010 98.1 0.190 ... 11:01 ☑ canvas.ucsd.edu 口 : ... Page 1 > of 2 Q - ZOOM + 4. Consider the two separate sets of measured data for a silt-loam soil measured by Mualem (1976): (1) suction versus water content, and (2) suction versus relative permeability of unsaturated soil, k/ks. Assume that 0s 0.396, 0res = 0.131, and Ks=5.74×10-7 m/s. a. Using the method of least squares in Excel, compute the best-fit values for αNG (kPa¹) and nvg for the van Genuchten (1980) relationship for data set # 1 (assume m = 1-1/nvG). See the example spreadsheet in the homework folder under the files section of Canvas for help in performing this calculation. b. Repeat part (a) and estimate the λ and ac parameters for the Brooks and Corey (1964) SWRC for data set #1. Note that you may need to include an "if" statement at the air entry suction. c. Plot the data for the SWRC versus the fitted van Genuchten (1980) and Brooks and Corey (1964) curves. Which relationship matches the capillary pressure data better (BC or VG)? Explain why this may be the case based on the features of the two models. d. Write the equation for k in terms of suction that would be obtained using the vG-Mualem model (put Equation 2 for the van Genuchten SWRC into Equation 7 for k in the Handout). e. Write the equation for k in terms of suction that would be obtained using the Burdine-BC model (put Equation 1 for the Brooks-Corey SWRC into Equation 8 for k in the handout). f. Using the parameters from the suction vs. 0 model that provided the best match to data data set #1 (VG or BC), calculate the volumetric water content values for each pressure head value given in data set #2 (remember, the two data sets were obtained in different tests but on the same soil so this should be valid). g. Using the expressions for k obtained in parts d and e and the parameters from the fits in parts a and b, plot the predicted k vs. 0 curves against the measured k vs. 0 data from data set #2. Do the predictions look to be satisfactory? Give reasons for any discrepancies between the fitted and predicted curves. h. Using the method of least squares in Excel, compute a new set of best-fit values for ovG (kPa) and ng by fitting the vG-Mualem model to the K vs. 0 data from data set #2 (assume m 1-1/nvG). How do your best fit values of avG (kPa) and nvG compare with those from part a? ← Data Set 1 Data Set 2 Volumetric ...
11:01 ☑ canvas.ucsd.edu -> ☐ ... : Page < 2 of 2 - ZOOM + Data Set 1 Data Set 2 Volumetric Suction, Suction, water W W k/ks content, 0 (kPa) (m³/m³) (kPa) 0.0 0.396 0.0 1.000 1.0 0.396 1.1 1.000 2.0 0.394 1.6 0.950 4.2 0.390 1.9 0.900 5.9 0.386 2.9 0.765 7.8 0.379 4.9 0.595 10.9 0.370 6.9 0.480 18.6 0.340 9.8 0.338 28.0 0.300 13.5 0.200 39.2 0.260 18.2 0.100 58.9 0.220 19.6 0.074 78.5 0.200 25.2 0.300 88.3 0.194 33.3 0.010 98.1 0.190 ... 11:01 ☑ canvas.ucsd.edu 口 : ... Page 1 > of 2 Q - ZOOM + 4. Consider the two separate sets of measured data for a silt-loam soil measured by Mualem (1976): (1) suction versus water content, and (2) suction versus relative permeability of unsaturated soil, k/ks. Assume that 0s 0.396, 0res = 0.131, and Ks=5.74×10-7 m/s. a. Using the method of least squares in Excel, compute the best-fit values for αNG (kPa¹) and nvg for the van Genuchten (1980) relationship for data set # 1 (assume m = 1-1/nvG). See the example spreadsheet in the homework folder under the files section of Canvas for help in performing this calculation. b. Repeat part (a) and estimate the λ and ac parameters for the Brooks and Corey (1964) SWRC for data set #1. Note that you may need to include an "if" statement at the air entry suction. c. Plot the data for the SWRC versus the fitted van Genuchten (1980) and Brooks and Corey (1964) curves. Which relationship matches the capillary pressure data better (BC or VG)? Explain why this may be the case based on the features of the two models. d. Write the equation for k in terms of suction that would be obtained using the vG-Mualem model (put Equation 2 for the van Genuchten SWRC into Equation 7 for k in the Handout). e. Write the equation for k in terms of suction that would be obtained using the Burdine-BC model (put Equation 1 for the Brooks-Corey SWRC into Equation 8 for k in the handout). f. Using the parameters from the suction vs. 0 model that provided the best match to data data set #1 (VG or BC), calculate the volumetric water content values for each pressure head value given in data set #2 (remember, the two data sets were obtained in different tests but on the same soil so this should be valid). g. Using the expressions for k obtained in parts d and e and the parameters from the fits in parts a and b, plot the predicted k vs. 0 curves against the measured k vs. 0 data from data set #2. Do the predictions look to be satisfactory? Give reasons for any discrepancies between the fitted and predicted curves. h. Using the method of least squares in Excel, compute a new set of best-fit values for ovG (kPa) and ng by fitting the vG-Mualem model to the K vs. 0 data from data set #2 (assume m 1-1/nvG). How do your best fit values of avG (kPa) and nvG compare with those from part a? ← Data Set 1 Data Set 2 Volumetric ...
Introduction to Chemical Engineering Thermodynamics
8th Edition
ISBN:9781259696527
Author:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Publisher:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Chapter1: Introduction
Section: Chapter Questions
Problem 1.1P
Related questions
Question
Transcribed Image Text:11:01
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Page
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Data Set 1
Data Set 2
Volumetric
Suction,
Suction,
water
W
W
k/ks
content, 0
(kPa)
(m³/m³)
(kPa)
0.0
0.396
0.0
1.000
1.0
0.396
1.1
1.000
2.0
0.394
1.6
0.950
4.2
0.390
1.9
0.900
5.9
0.386
2.9
0.765
7.8
0.379
4.9
0.595
10.9
0.370
6.9
0.480
18.6
0.340
9.8
0.338
28.0
0.300
13.5
0.200
39.2
0.260
18.2
0.100
58.9
0.220
19.6
0.074
78.5
0.200
25.2
0.300
88.3
0.194
33.3
0.010
98.1
0.190
...
Transcribed Image Text:11:01
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1
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Q
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ZOOM
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4. Consider the two separate sets of measured data for a silt-loam soil measured by Mualem
(1976): (1) suction versus water content, and (2) suction versus relative permeability of
unsaturated soil, k/ks. Assume that 0s 0.396, 0res = 0.131, and Ks=5.74×10-7 m/s.
a. Using the method of least squares in Excel, compute the best-fit values for αNG (kPa¹)
and nvg for the van Genuchten (1980) relationship for data set # 1 (assume m = 1-1/nvG).
See the example spreadsheet in the homework folder under the files section of Canvas for
help in performing this calculation.
b. Repeat part (a) and estimate the λ and ac parameters for the Brooks and Corey (1964)
SWRC for data set #1. Note that you may need to include an "if" statement at the air
entry suction.
c. Plot the data for the SWRC versus the fitted van Genuchten (1980) and Brooks and
Corey (1964) curves. Which relationship matches the capillary pressure data better (BC
or VG)? Explain why this may be the case based on the features of the two models.
d. Write the equation for k in terms of suction that would be obtained using the vG-Mualem
model (put Equation 2 for the van Genuchten SWRC into Equation 7 for k in the
Handout).
e. Write the equation for k in terms of suction that would be obtained using the Burdine-BC
model (put Equation 1 for the Brooks-Corey SWRC into Equation 8 for k in the handout).
f. Using the parameters from the suction vs. 0 model that provided the best match to data
data set #1 (VG or BC), calculate the volumetric water content values for each pressure
head value given in data set #2 (remember, the two data sets were obtained in different
tests but on the same soil so this should be valid).
g. Using the expressions for k obtained in parts d and e and the parameters from the fits in
parts a and b, plot the predicted k vs. 0 curves against the measured k vs. 0 data from
data set #2. Do the predictions look to be satisfactory? Give reasons for any discrepancies
between the fitted and predicted curves.
h. Using the method of least squares in Excel, compute a new set of best-fit values for ovG
(kPa) and ng by fitting the vG-Mualem model to the K vs. 0 data from data set #2
(assume m 1-1/nvG). How do your best fit values of avG (kPa) and nvG compare with
those from part a?
←
Data Set 1
Data Set 2
Volumetric
...
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