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Drainage Design and Analysis
Using the Rational Method
Hands-On Training
9 February 2011
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The Rational Formula
The Rational Method was introduced in 1889
in England
Its genesis was based on pure reasoning, thusthe name
The Rational Method is used to compute the
peak runoff after a rainfall event
The Rational Method is applicable to small
drainage areas (2,000 hectares)
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The Rational Formula
The Rational Formula is given by:
Q = C*I*A/360
Where Q = Discharge (cubic meters per second) C = Coefficient of Runoff
I = Rainfall Intensity (millimeters per hour)
A = Drainage Area (hectares)
The Rainfall Intensity will depend on the Time ofConcentration and on the Rainfall IntensityFrequency Curve
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The Rational Formula
Time of Concentration
Tc = (L1.15)/(51*H0.385)
Where Tc = Time of Concentration (minutes)
L = Length of watershed along the mainstream(meters)
H = Difference in elevation between the mostdistant ridge in the watershed and point ofinterest under review (meters)
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Road Alignment
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Principal
Waterways
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Roadway
Crossings
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Direction
of
Waterflow
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Ridge
Lines
Point of Interest
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Point of InterestElev.
1180
Elev
1540
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Rational Formula
Time of Concentration
Tc = (L1.15)/(51*H0.385)
L = 2,572 meters H = 1540 - 1180 = 360 meters
Tc = 33.708 minutes
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Use 10 year frequency for pipe culvert
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Use C = 0.3 (gravel surface road and shoulder)
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Rational Formula
Discharge
Q = (A*C*I)/360
A = 134.73 hectares C = 0.3
I = 250 millimeters per hour
Q = 28.29 cubic meters per second
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Install:
4-1520 mm RCPC
Capacity = 4*8
= 32 m3/sec
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Exercise
Which of the following most nearly gives the DrainageArea, in hectaresa. 54 b. 41
Which of the following most nearly gives the length ofwatershed along the mainstream, in metersa. 750 b. 2,400 c.
Which of the following most nearly gives the highestelevation of the most distant ridge, in meters
a. 1,130 b. 1,020 c. 1,26 Which of the following most nearly gives the lowest
elevation at the point of interest, in metersa. 1,130 b. 1,020 c. 1,2
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Exercise
Which of the following most nearly gives theTime of concentration, in minutes
a. 7.5 b. 24.8
Which of the following most nearly gives theRainfall intensity (using frequency of 10 years), inmillimeters per hour
a. 250 b. 63
Which of the following most nearly gives theDischarge, in cubic meters per second
a. 2.8 b. 23.6