MAE123, Assignment 4
Problem 1 (25 points)
The data below were obtained by gravimetric sampling just prior to and two days
following an irrigation.
Sampling time
Before irrigation
After irrigation
Sampling
number
1
2
3
4
Bulk density
(gm/cm3 )
1.2
1.5
1.2
MAE125b, Assignment 1
Problem 1 (30 points)
Consider a sample of a porous medium that is composed of nine solid cylinders
whose packing is shown below. The diameter of each cylinder is d = 10/3cm.
The length of each cylinder is l = 10cm. The size of the s
MAE125b, Assignment 2
Problem 1 (25 points)
An undisturbed cylindrical core sample of soil 10 cm high and 5 cm in diameter
weights 350gm. The density of solids is s = 2.65g/cm3 . Calculate the total
porosity.
Problem 2 (25 points)
Derive the solution for
MAE125b, Assignment 3
Problem 1
Given a piezometric surface with a regional slope of 7m/km, calculate the natural
rate of groundwater discharge (flux) through a confined aquifer with transmissivity
T = 0.002m2 /sec.
Problem 2
Three piezometers are located
MAE125b, Assignment 4
Problem 1 (25 points)
The data below were obtained by gravimetric sampling just prior to and two days
following an irrigation.
Sampling time
Before irrigation
After irrigation
Sampling
number
1
2
3
4
Bulk density
(gm/cm3 )
1.2
1.5
1.
Class notes for MAE 123:
Introduction to Transport in Porous Media
Instructor: Daniel M. Tartakovsky
January 7, 2014
Transport in Porous Media
Instructor: Daniel M. Tartakovsky
- ii -
Table of Contents
1
2
3
Basic Concepts
1
1.1
Microscopic and Macroscopi
MAE 123: Homework 3
Due: Wednesday, Feb 15, 2017
Problem 1 (30 points)
Three piezometers are located 1000 m apart in the same horizontal aquifer.
Piezometer A is directly south of Piezometer B and Piezometer C is directly
east of the midpoint of the line
MAE 123: Homework 2
Due: Monday, Jan 30, 2017
Problem 1 (20 points)
After completely saturating a soil sample with water, you measure the total
mass to be 30 g, and the volume is 18 cm3 . Following, you dried the sample
in an oven and measured the dry mas
MAE 123: Homework 4 Solutions
Due: Friday, Feb 24, 2017
Problem 1 (40 points)
1. You are notified of a leaking underground storage tank that contained
hydrocarbons. The spill is partially in the saturated zone and partially in
the vadose zone.
a) Followin
MAE 123: Homework 4
Due: Friday, Feb 24, 2017
Problem 1 (40 points)
1. You are notified of a leaking underground storage tank that contained
hydrocarbons. The spill is partially in the saturated zone and partially in
the vadose zone.
a) Following the exam
MAE 123: Homework 2
Due: Monday, Jan 30, 2017
Problem 1 (20 points)
After completely saturating a soil sample with water, you measure the total
mass to be 30 g, and the volume is 18 cm3 . Following, you dried the sample
in an oven and measured the dry mas
MAE 123: Homework 1 Solutions
Due: Friday, Jan 20, 2017
Problem 1 (40 points)
Consider the following idealized porous media consisting of solid cylinders
packed in the configurations shown below.
#2
#1
5 cm
5 cm
10 cm
10 cm
5 cm
5 cm
Medium #1 contains ni
MAE 123: Homework 3
Due: Wednesday, Feb 15, 2017
Problem 1 (30 points)
Three piezometers are located 1000 m apart in the same horizontal aquifer.
Piezometer A is directly south of Piezometer B and Piezometer C is directly
east of the midpoint of the line
Chapter 1
Basic Concepts
This course describes fundamentals of mathematical modeling of physical and bio-chemical processes in
subsurface environments. The importance of this subject is underscored by Figure 1.1. This figure also
explains the genesis of g
MAE 123: Homework 1
Due: Friday, Jan 20, 2017
Problem 1 (40 points)
Consider the following idealized porous media consisting of solid cylinders
packed in the configurations shown below.
#2
#1
5 cm
5 cm
10 cm
10 cm
5 cm
5 cm
Medium #1 contains nine solid c
MAE123, Assignment 4
Problem 1 (25 points)
The data below were obtained by gravimetric sampling just prior to and two days following an irrigation.
Sampling time
Before irrigation
After irrigation
Sampling
number
1
2
3
4
Bulk density
(gm/cm3 )
1.2
1.5
1.2
MAE 123, Midterm 1
Problem 1 (30 pts)
Consider two-dimensional groundwater ow in a homogeneous anisotropic aquifer with hydraulic conductivity tensor K given by
K=
Kxx Kxy
.
Kyx Kyy
(1)
The ow is driven by hydraulic head gradient
h=
1
.
0
(2)
Find Darcys
MAE123, Midterm 2
A homogeneous isotropic soil has porosity and saturated hydraulic conductivity Ks ,
and is characterized by the Gardner-Russo constitutive relations
K ( ) = Ks e ,
( ) = e/2 (1 + /2)
2/2.5
.
(1)
A precipitation event has lead to inltrati
MAE123, Assignment 3
Problem 1
Given a piezometric surface with a regional slope of 7m/km, calculate the natural
rate of groundwater discharge (ux) through a conned aquifer with transmissivity
T = 0.002m2 /sec.
Problem 2
Three piezometers are located 1000
MAE123, Assignment 1
Problem 1 (30 points)
Consider a sample of a porous medium that is composed of nine solid cylinders
whose packing is shown below. The diameter of each cylinder is d = 10/3cm.
The length of each cylinder is l = 10cm. The size of the sa
MAE123, Assignment 2
Problem 1 (25 points)
An undisturbed cylindrical core sample of soil 10 cm high and 5 cm in diameter
weights 350gm. The density of solids is s = 2.65g/cm3 . Calculate the total
porosity.
Problem 2 (25 points)
Derive the solution for K
Transport in Porous Media
Flow IN
Instructor: Daniel M. Tartakovsky
Flow OUT
Mass generated within
Change in mass stored within
Figure 2.1: Mass conservation.
2.3
Continuity Equations
Equations of groundwater flow are derived by combining Darcys law (2.26
Transport in Porous Media
Instructor: Daniel M. Tartakovsky
Figure 1.4: A schematic representation of Darcys experiment.
from a point where the fluid elevation is higher to a point where it is lower. The experimental relation (1.6)
can be written in diffe
MAE 123: Midterm 1
Due: Friday, Feb 3, 2017
Problem 1 (100 points)
Pond
hp
b
Aquifer
River
hr
L
Datum
You must show all your work for full credit.
Consider this one-dimensional aquifer. It is bounded above and below by
impermeable rock, and by a contamina