Geoscience Reference
In-Depth Information
Fig. 3 General tank scheme and view of the flume from A-A (dimensions in centimeters)
2.2 Statistical Analysis
The influence of the seepage flow on the flow velocity components and velocity
fluctuations of the open-channel flow was analyzed by estimating the statistical
moments of the flow measurements; namely, the arithmetic mean, covariance,
skewness, and kurtosis. Other turbulence parameters that were compa
red
with
and without seepage are the
Reynolds stresses
in the
xy
-plane
u
0
v
0
r
and
TKE.
In statistics, any random variable can be characterized by statistical moments
of different orders. A statistical moment of
n
th order for data collected at one
point is defined according to the expectation theory (Czernuszenko and Holley
2007
):
1
n
n
p
E½x
¼
x
ðÞ
d
x
(5)
1
where
p
(
. For discrete
variables, the first statistical moment (expected value) is called the mean of the
random variable (Czernuszenko and Holley
2007
).
From this part of the chapter and to facilitate the identification of the flow
velocity measurements, the velocity components in the
x-
,
y-,
and
z-
directions are
denoted as
V
x
,
V
y,
and
V
z
, respectively. Hence, the first statistical moment of the
i-
velocity component (
V
i
) of an stationary ergodic event with an established time
period
T
is calculated with the formula:
x
) is the probability density function (PDF) of the variable
x
ð
t
o
þT
1
T
E
½
V
i
¼m ¼
lim
T!1
V
i
dt
(6)
t
o
