Hydraulic Efficiency of Grate and Curb Inlets - Urban Drainage and ...

The second Pi group is the square of the Froude number for a general channel cross
section, and the third Pi group is the Froude number for a rectangular channel. Both forms of the
Froude number were tested for statistical significance, and either form was used in the final
equations. Compiling the Pi groups into power-equation form resulted in Equation 5-6:
⎛
E = N⎜
⎝
h
L
a
b
2
⎞ ⎛V
T ⎞
⎟
⎜
gA
⎟
⎠ ⎝ ⎠
2
⎛V
⎞
⎜
gh
⎟
⎝ ⎠
c
2
⎛V
gL ⎟ ⎞
⎜
⎝ ⎠
d
e
( S ) ( S ) f
c
l
Equation 5-6
where:
N = coefficient of regression;
a,b,c,d,e,f = regression exponents to be determined by statistical analysis of the test data;
and
remaining parameters were defined previously.
The computer application Statistical Analysis Software (SAS) was used to efficiently
analyze the large amount of test data. Analysis was carried-out using the logarithms of each Pi
group so a multi-variable linear regression model could be fit to the data. Coefficients given by a
linear model for each independent variable are the exponents (a, b, c, d, e, and f) and the y-
intercept given is the logarithm of the coefficient N for the equivalent power-equation form, as
shown in Equation 5.7:
logΠ
Π
a b c d e f
6
= N Π1
Π2
Π3
Π
4
Π5
Π7
6
= log N + alogΠ1
+ blogΠ2
+ clogΠ3
+ d logΠ4
+ elogΠ5
+ f log
, or
Π
7
Equation 5-7
The Statistics Department at CSU was consulted to assist in examination of the
regression statistics from SAS. When a regression is performed using SAS, the significance of
each parameter is examined and the effect of each possible parameter combination on the
regression fit is tested. Significance of each parameter is evaluated by dividing the standard
error of the parameter estimate by the estimate itself. The result is called the “t” value and a
significant parameter has an absolute t value greater than 2 (i.e., the estimate itself is at least two
times larger than its error, and the 95% confidence interval for the estimate is two times the
standard error). The level of confidence that a parameter estimate has not arisen by chance
(called the significance level) is also evaluated by SAS and reported as the Pr value. A Pr value
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