# Rational Area Method

Topics: Hydrology, Surface runoff, Soil Pages: 23 (1820 words) Published: December 18, 2012
General
• The Rational Formula is one of the most frequently used urban hydrology methods in Malaysia. It gives satisfactory results for small catchments only
• The formula is:
C . y It . A
Qy =
360

where,
Qy =

y year ARI peak flow (m3/s)

C=

dimensionless runoff coefficient

yI
t

=
y year ARI average rainfall intensity over time of concentration, tc , (mm/hr)
A=

drainage area (ha)

Or
Q=CiA
i = average rainfall intensity (in/hr)equals to tc
A = catchment area ( acre)
Q = Peak flow ( cusecs)

Rational Method

1

Qp

tc

tc +td

• Experience has shown that the Rational Method can provide satisfactory estimates of peak discharge on small catchments of up to 80 hectares. For larger catchments, storage and timing effects become significant, and a hydrograph method is needed.

• Assumptions used in the Rational Method are as follows:
1. The peak flow occurs when the entire catchment is contributing to the flow. 2. The rainfall intensity is the same over the entire catchment area. 3. The rainfall intensity is uniform over a time duration equal to the time of concentration, tc..

4. The ARI of the computed peak flow is the same as that of the rainfall intensity, i.e., a 5 year ARI rainfall intensity will produce a 5 year ARI peak flow.

• Experience has shown that when applied properly, the Rational Method can provide satisfactory estimates for peak discharges on small catchments where storage effects are insignificant. The Rational Method is not recommended for any catchment where:

1. the catchment area is greater than 80 hectares
2. ponding of stormwater in the catchment might affect peak discharge. 3. the design and operation of large (and hence more costly) drainage facilities is to be undertaken, particularly if they involve storage. Rational Method

2

Estimation of Time of Concentration
• Overland flow
to =

to
L
n
S

=
=
=
=

107. n . L 1 / 3
S 0.2

overland sheet flow travel time (minutes)
overland sheet flow path length (m)
Manning’s roughness value for the surface
slope of overland surface (%)
Values of Manning’s 'n' for Overland Flow
Manning n

Surface Type
Concrete/Asphalt
Bare Sand
Bare Clay-Loam
(eroded)
Gravelled Surface
Packed Clay
Short Grass
Light Turf
Lawns
Dense Turf
Pasture
Dense Shrubbery
and Forest Litter

Rational Method

Recommended
0.011
0.01
0.02

Range
0.01-0.013
0.01-0.06
0.012-0.033

0.02
0.03
0.15
0.20
0.25
0.35
0.35
0.40

0.012-0.03
0.02-0.04
0.10-0.20
0.15-0.25
0.20-0.30
0.30-0.40
0.30-0.40
0.35-0.50

3

• Time in drain
The Manning's Equation is recommended for this purpose:
V=

1 2 / 3 1/ 2
RS
n

From which,
t ch =

n .L
60 R 2 / 3 S 1 / 2

V
n
R
S
L
tch

=
=
=
=
=
=

average velocity (m/s)
Manning's roughness coefficient
friction slope (m/m)
length of reach (m)
travel time in the channel (minutes)

• Time of concentration, tc = to + td

Rainfall Intensity
• The rainfall intensity, I, in the Rational Formula represents the average rainfall intensity over a duration equal to the time of concentration for the catchment. Refer to Chapter 13 for details on IDF relationships for estimating design rainfall intensity.

ln( R I t ) = a + b ln(t ) + c(ln(t ))2 + d (ln(t ))3
RI =
t

the average rainfall intensity (mm/hr) for ARI and duration t R = average return interval (years)
t = duration (minutes)
a, b, c and d are fitting coefficients, which are dependent on ARI.

Rational Method

4

Example: Coefficients for the IDF Equations for Johor Bahru Johor Coefficients of the IDF Polynomial
Equations

ARI
(year)
a

b

c

d

2

3.8645

1.1150

-0.3272

0.0182

5

4.3251

1.0147

-0.3308

0.0205

10

4.4896

0.9971

-0.3279

0.0205

20

4.7656

0.8922

-0.3060

0.0192

50

4.5463

1.1612

-0.3758

0.0249

100

5.0532

0.8998

-0.3222

0.0215...