Part 4

1. 1
Advanced Soil and Water
Engineering #4
Masahiro Tasumi
Dept. Forest & Env. Sci.
Class schedule
No. Date Contents
1 4/11 Course outline for Advanced Soil and Water Engineering
2 4/18 Physical characteristics of soil I
3 4/25 Physical characteristics of soil II (NO CLASS)
4 5/9 Physical characteristics of soil III
5 5/16 Physical characteristics of soil IV
6 5/23 Micrometeorology I
7 5/30 Micrometeorology II
8 6/6 Micrometeorology III
9 6/13 Micrometeorology IV
10 6/20 Soil water and Evapotranspiration I
11 6/27 Soil water and Evapotranspiration II
12 7/4 Soil water and Evapotranspiration III
13 7/11 Soil and water engineering in operation I
14 7/18 Soil and water engineering in operation II
15 7/25 Discussions
Some evidences for
- Surface tension
- Capillary rise
- Potential

2. 2
Capillary rise
https://www.youtube.com/watch?v=yw3KsRRbIf4
Flow of water in saturated soil
Q = flow; ρw = water density;
a = radius of the tube
μ = viscosity of water
L = length of the tube
PA, PB pressure of inlet and
outlet of the tube
Hagen-Poiseuille flow
Slow water flow in a narrow tube
Flow of water in saturated soil
Darcy’s Law
=
∆
or
where K is Hydraulic
conductivity of soil
Darcy’s Law and Ohm’s Law
Ohm’s Law： I = V / R
（Current = Potential Diff. / Resistance）
Higher Potential Differences More Current
Higher Resistance Less current

3. 3
Darcy’s Law and equations for energy flux
Latent Heat (Evapotranspiration)
( )
av
21
air
r
q-q
ρ=E
ah
pair
r
dTCρ
=H
Sensible Heat
Flow of water in saturated soil
Darcy’s law is generally applied to determine
(or calibrate) hydraulic conductivity of soil.
(e.g. for dam constructions)
Flow of water in saturated soil
Constant head? Falling head?
https://bae.okstate.edu/faculty-
sites/Darcy/Conductivity/McWh
orter.htm
Equation for falling head method
kt = conductivity for water
temperature T (m/s)
h1 and h2 (cm) in the equation are;
h0 and h1 in the left picture,
respectively. Units for a and A are
cm2. Units for t1 and t2 are sec. Unit
for L is cm. The factor 1/100 is for
unit conversion from cm to m.

4. 4
Exercise
100cc Soil Sampler
Diameter 5.0cm; Height 5.1cm;
Volume 100cc
hA=3.0cm (fixed)
hB=1.0cm (fixed)
Q = 0.4cm3 /sec
What is the hydraulic
conductivity of the soil?
=
∆
Unsaturated
Soil particles are the
obstacles.
Matric Potential is not
considered.
Hydraulic constant is a
“constant” for the soil.
Soil particles provides
important route of water flow.
Matric potential is necessary to
be considered.
Hydraulic constant widely
changes by water availability.
Saturated
Flow of water in unsaturated soil
Buckingham-Darcy Law
K is not a constant but
function of matric
potential (or water
availability in soil)
Flow of water in saturated soil
Some typical assumptions for “K”.