Q = KiA
K=Q
iA
K=
⎡
⎢
⎢
⎢
⎣
⎡
1cm 3
⎢ Volume ml
1ml
⎢
⎢
time sec
⎢⎣
⎤
⎥
⎥
⎥
⎥⎦
⎤
⎥⎡
⎤
2 54cm) 2⎥
⎥ ⎢π ( radius in 2.54cm
in
⎦
⎥⎣
⎦
( h2 − h1 )in
distance in
=
XX cm
sec
Reasonable for sand?
yielded
145ml discharge in 13min48sec
Our error last class was that we used a tracer travel time of 7 min
for 30cm but it was the length of the tube which is 30 inches
SO calculation of K was fine BUT effective porosity was not
Q = KiA
K=Q
iA
K=
Q = 1.5cm3
sec
⎡
⎢
⎢
⎢
⎢⎣
1cm 3 ⎤
⎥
1ml ⎥
⎥
60 sec
⎥⎦
90
ml
=
0.2 cm
sec
⎡
⎤
⎢ ( 17.5 – 10.8 )in (2.54cm/in) ⎥ ⎡
2⎤
⎢
⎥ ⎢π ( 1 in 2.54cm ) ⎥
in
⎦
⎢
⎥⎣
(45cm)
⎣
⎦
yielded
= 0.37
A = 20cm2
Reasonable
for
sand?
145ml discharge in i13min48sec
Yes see:
http://en.wikipedia.org/wiki/Hydraulic_conductivity#Ranges_of_values_for_natural_materials
1
How will flow change if we rotate the sand column?
What if we bend the column?
Flow will not
change if we
rotate column
Average flow
will not
change if we
bend column
but will be
slower on
short side and
faster on long
side
Our error last class was that we used a tracer travel time of 7 min
for 30cm but it was the length of the tube which is 30 inches
Calculate
Effective
Porosity
SO the effective
porosity calculation
was
wrong, correcting that:
using data from
Darcy
Apparatus
Calculate
Effective
Porosity
using data from
What
Wh t measurements
Darcy
D
Apparatus
A t will
ill
t you need?
d?
What measurements will you need?
equation
will
Travel time What
of a tracer
through
theyou
sandsolve?
=
What equation will you solve?
Vdarcy
=
=
Q= 1.5cm3
sec
A= 20cm 2
0.075 cm/sec
=
= 0.41
Dye moves through the tube
Vtracer
30in 2.54cm/in
0.18 cm/sec
It moves
~30 cm in 7 min
7min 60sec/min
2
I got the column up and running again after class
and collected new data
Q = KiA
K=Q
iA
Q = 2.3cm3
sec
⎡
⎢
⎢
⎢
⎢⎣
3
140 ml 1cm
1ml
60 sec
⎤
⎥
⎥
⎥
⎥⎦
Recall the sand has
been removed and
replaced since the
prior
i measurements,
t
so we do not expect
the same value of K
=
K=
0.8 cm
sec
⎡
⎤
( 2.5
)in
⎢
⎥⎡
⎤
2 54cm ) 2⎥
⎢
⎥ ⎢π ( 1 in 2.54cm
in
⎦
⎢ (45cm) (1in/2.54cm) ⎥ ⎣
⎣
⎦
A = 20cm2
Reasonable for sand?
yieldedi = 0.14
Yes see:
145ml discharge in 13min48sec
http://en.wikipedia.org/wiki/Hydraulic_conductivity#Ranges_of_values_for_natural_materials
Calculate Effective Porosity
using data from
Darcy Apparatus
What
Wh t measurements
t will
ill you need?
d?
Travel time of a tracer through the 30 inch tube = 300 sec
What equation will you solve?
Vdarcy
=
Q= 2.3cm3
sec
A= 20cm 2
0.1 cm/sec
=
=
= 0.39
0 39
Dye
moves through
the tube
30in 2.54cm/in
0.254 cm/sec
It moves
~30 cm in 7 min
300 sec
Vtracer
3