Rational method
Rational
method was first used in 1889 developed by Emil Kuichling. This Method is widely
used to estimate the peak surface runoff rate for design of a variety of
drainage structures, such as a length of storm sewer, a storm water inlet, or a
storm water detention pond. The Rational Method is most suitable for small
urban watersheds that don't have storage such as ponds or swamps. It is best
for areas less than 100 acres, but is sometimes used for up to 2 mi2 areas.
The Rational Method Equation
The
equation that is the centerpiece of the Rational Method is:
q = CiA,
Where q is the peak surface runoff
rate in Cubic feet/seconds, from a watershed of area, “A” acres, and runoff
coefficient, C, due to a storm of intensity, i in/hr. The units on peak runoff
rate, q, are actually acre-in/hr, but the conversion from acre-in/hr to is Cubic
feet/seconds very nearly one, so the more common unit, Cubic feet/seconds, is typically
used for q. In order to calculate a value for peak runoff rate for a given
drainage area, values are needed for the three parameters, A, C, and i.
Following is an example problem
that illustrates the application of the Rational method to estimate peak
discharges for the construction of Culvert.
Design
of Culverts
For the construction or design of
culverts we need the maximum rate of runoff at the inlet to a proposed culvert.
For this purpose we generally use the 25 to 50 years of return period. After
the estimation of the run off rate we construct the cross-section of the
culvert according to the runoff rate so that it can convey all the runoff and
no water remains there for long time.
As discussed earlier that through
Rational method we can find the maximum amount of runoff or discharge that will
pass through a point therefore we will use rational equation. For using rational
equation the following set of data is collected first.
Site
data:
Using a topographic map and a
field survey, the area of the drainage basin upstream from the point in
question is found. In addition, the following data were measured:
Average overland slope
Length of overland
Length of main basin channel
Slope of channel Roughness
coefficient (n)
Type of soil and land cover is
determined for the estimation of Runoff coefficient.
Runoff
coefficient (C):
The
runoff coefficient is the fraction of rainfall striking the drainage area that
becomes runoff from that drainage area. It is an empirically determined
constant, dependent on the nature of the drainage area surface.
From
the topographic survey conducted earlier the type of the cover is determined.
The land cover means the area consists of vegetation, forests, or it is
concrete/asphalt. Similarly the type of the soil is determined. Then using the
table the value of Runoff Coefficient i.e. C is determined.
For areas with a mixture of land uses, a
composite runoff coefficient is used. The composite runoff coefficient is
weighted based on the area of each respective land use and can be calculated
as:
Where:
Time of concentration
It is the time required for water to flow from the most remote
part of the area to the outlet. When the storm duration equals the time of
concentration all parts of the watershed are contributing simultaneously to the
discharge at the outlet.
It depends on the watershed factors i.e. Slope, length, type of
surface etc
In culvert design the length and slope of the watershed is
determined and is used to calculate the Time of Concentration (TOC).
The
equation of TOC is Tc = 0.0195 L0.77
S-0.385
The Rainfall Intensity (I):
Rainfall
intensity, i, is the average rate of rainfall in inches per hour. Intensity is
selected on the basis of design frequency of occurrence, a statistical
parameter established by design criteria, and rainfall duration. For the
Rational Method, the critical rainfall intensity is the rainfall having
duration equal to the time of concentration of the drainage basin.
Where:
After the Tc has been
determined, the rainfall intensity should be obtained. For the Rational method,
the design rainfall intensity averaging time (it) should be that
which occurs for the design year storm whose duration equals the time of
concentration. The rainfall amounts for various storm frequencies and duration
is obtained from the Meteorological Center.
The rainfall intensity is determined by
dividing the total rainfall by the duration (time of concentration) in hours.
Area
It
is the area (A) of the basin. A map showing the limits of the drainage basin
used in design is superimposed on the grading plan showing sub-basins. As
mentioned earlier, the configuration of the contributing area with respect to
pervious and impervious sub-areas and the flow path should be considered when
deciding whether to use all or a portion of the total area.
Peak runoff calculation:
Now the Rational equation is used to
calculate the Peak runoff rate.
In terms of British units the equation
is:
q= CiA
Where q = Runoff
(cubic feet per second)
C = Runoff
Coefficient (dimensionless)
A = Area of the
water shed (Acre)
Similarly in SI units the equation is:
q = 0.0028CiA
Where q = Runoff
(m3 per sec)
A = Area (ha)
After the determination of the peak
runoff rate the size of the culvert is determined and then it is checked
through other formula i.e. Manning’s equation etc. if the result is same then
the design is accurate and is approved.