L6 - Time Area Method PDF

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Time Area Method Tutorial Solution...

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Tutorial question 5: Surface runoff Question 1: Time - area method The two branches of a stream have catchments A and B of 200 hectares each. Their time-area diagrams are as follows: 0-1

Time of travel (hours) Area between isochrones (hectares)

1-2

2-3

3-4

A

60

100

40

B

30

50

80

40

A storm lasting for 3 hours has rainfall depth of 50 mm for the whole storm. The temporal pattern and loss rates for the storm are as follows: Times (hours)

Temporal pattern (% of total rainfall)

Loss rate (mm/hour)

0-1

60

8

1-2

30

2

2-3

10

2

Calculate and plot the hydrograph of surface runoff downstream of the confluence of the two branches of the stream.

Solution 1. Calculate rainfall excess Times (hours)

Temporal pattern (% of total rainfall)

Loss rate (mm/hour)

Rainfall intensity (mm)

Rainfall excess (mm)

0-1

60

8

30

22

1-2

30

2

15

13

2-3

10

2

5

3

2. Calculate hydrograph ordinates at catchment A and B Catchment A: Example: Column (2) Ordinate t=1 is Q1 = 60*22=1320 t=2 Q2= 60*12=780 t=3 Q=60*3=180

Catchment A (1) Q0 Q1 Q2 Q3 Q4 Q4 Q6 Q7 Q8 Q9

A1*R

A2*R

(2) 0 1320 780 180 0

QA(m3/s) Total of ordinates =Total/360 (6) (5) 0 1320 3.67 2980 8.28 2360 6.56 820 2.28 120 0.33 0 0

A3*R (3) (4)

0 2200 1300 300 0

0 880 520 120 0

Catchment B: Catchment B Q1 Q2 Q3 Q4 Q4 Q6 Q7

B1*R

B2*R

0 660 390 90 0

0 1100 650 150 0

B3*R

0 1760 1040 240 0

B4*R

Total

0 880 520 120 0

0 660 1490 2500 2070 760 120 0

QB(m3/s) =Total/360 0.00 1.83 4.14 6.94 5.75 2.11 0.33 0.00

Surface runoff downstream of the confluence of the two branches of the stream equals to the total of hydrographs at each time step Q at Catchment outlet A m3/s 0.00 3.67 8.28 6.56 2.28 0.33 0.00 0.00

Q at Catchment outlet B m3/s 0.00 1.83 4.14 6.94 5.75 2.11 0.33 0.00

Q at the confluence m3/s 0.00 5.50 12.42 13.50 8.03 2.44 0.33 0.00...