Question

Describe briefly the principle of the Rational method and the limitation of this method for runoff estimation. A sub-catchment of area 0.1km² is built on gently sloping land. The average slope of the land is 0.001. The length of the longest natural flow path L is 276.3m. The flow time t_f in the drainage system is 3min. Determine the 50yr design discharge for the subdivision using the rational method, given that the average runoff coefficient of the subdivision is C=0.7.

The above sub-catchment is drained by a pipe system which is also used to drain the second sub-catchment. The second sub-catchment is of area 0.2km², average slope 0.002, L=300m, and t_f=3min, C=0.5. If the pipe system is designed for the 50-yr rainfall event, what is the appropriate duration to be used? Explain briefly. Hence determine the 50yr design discharge of the drainage system.

The 50-yr rainfall intensity i can be calculated from i(mm/hr)=a/(td+b)^c, where a=687, b=4.2, c=0.42, t_d(min)=duration.

Answer 1

Ans) In rational method, it is assumed that rainfall duration is same as the time of concentration and return period of rainfall intensity is same as the peak runoff . The basic principle of rational method is that the time of concentration of drainage area should be less than peak rainfall intensity .This method is has the following limitations :

a) This method provides only peak discharge only and cannot produce hydrograph.

b) It is difficult to determine accurate Runoff coefficient, hence peak discharge can vary greatly with runoff coefficient

c) Not valid for catchment more than 200 acres

d) This method does not account for storage in drainage area

Now, for sub-catchment,

Determine time of concentration using Bransby William equation, Tc = 0.14465 L /

where, L = 276.3 m, S = 0.001 and A = 0.1 km2 or

=> Tc = 0.14465(276.3) / []  

=> Tc = 50.31 min

Total time of concentration = 50.31 min + 3 min= 53.31 min

=> Rainfall intensity (i) = 687 /

=> i = 125.3 mm/hr  

Determine peak flow rate (Qp) using Rational method :

Qp = C i A / 360

where, C = Runoff coefficient = 0.70 (given)

i = Rainfall intensity in mm/hr = 125.3 mm/hr

A = Area in hecatres = 0.1 km2 or or 10 hectares

=> Qp = 0.70 x 125.3 x 10/360

=> Qp = 2.436 /s

For second sub-catchment,

  Tc = 0.14465 L /

where, L = 300 m, S = 0.002 and A = 0.2 km2 or 2 x

=> Tc = 0.14465(300) / []  

=> Tc = 44.4 min

Total duration to be used concentration = 44.4 min + 3 min= 47.4 min

=> Rainfall intensity (i) = 687 /

=> i = 131.1 mm/hr  

Determine peak flow rate (Qp) using Rational method :

Qp = C i A / 360

where, C = Runoff coefficient = 0.50 (given)

i = Rainfall intensity in mm/hr = 131.1 mm/hr

A = Area in hecatres = 0.2 km2 or 2 x or 20 hectares

=> Qp = 0.50 x 131.1 x 20/360

=> Qp = 3.641 /s

Hence, total design drainage for the system = 2.436 + 3.641 = 6.08 /s