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

the model was often either lower or higher than the exact point of splash-over velocity for a
given grate length. No efforts were made to directly measure splash-over velocity in this study.
It was possible, however, to determine a theoretical splash-over velocity from the efficiency,
velocity, and flow characteristics of each applicable test. The approach presented here is to
back-calculate V o from the equations given previously in Sections 2.2.1 and 2.2.2. A unique
value for V o can then be determined for a given inlet length from a regression of the results.
When Equation 2-7 is solved for V o , the following form presented as Equation 5-1 results:
( 1−
R )
⎡ f ⎤
Vo = V − ⎢ ⎥
Equation 5-1
⎣ 0.
09 ⎦
where:
V = velocity of flow at the inlet (ft/s) determined from Q/A;
V o = splash-over velocity (ft/s); and
R f = ratio of frontal flow captured by the inlet to the total frontal flow.
In Equation 5-1, the parameter R f must be less than or equal to one to determine a
physically-meaningful splash-over velocity. When R f is greater than or equal to one, flow
velocity is less than or equal to splash-over velocity and all frontal flow is captured by a grate.
When R f is less than one, flow velocity is greater than splash-over velocity and splashing of some
frontal flow over a grate occurs. As grate length increases, flow velocity must increase for water
to splash completely over a grate. When Equation 2-10 is solved for R f , the following form
presented as Equation 5-2 results:
R
f
⎡
E
⎣
⎛ Q
R ⎜
⎝
⎞⎤
⎟⎥ ⎠ ⎦
Q
s
= ⎢ −
s
Equation 5-2
Q Qw
where:
E = inlet capture efficiency;
R s = ratio of side flow captured to total side flow;
R f = ratio of frontal flow captured by the inlet to the total frontal flow;
Q = volumetric flow rate (cfs);
Q w = flow rate in the depressed section of the gutter (cfs); and
Q s = flow rate in the section above the depressed section (cfs).
Parameters Q w , Q s , and R s were calculated directly from the geometry of the street and
gutter sections using the applicable equations presented previously in Sections 2.2.1 and 2.2.2.
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