CIVE 445 - ENGINEERING HYDROLOGY
SPRING 2009 - REVIEW SESSION

PROBLEM 1

Rain falls on a 150-ha composite catchment which drains two subareas, as follows: (1) subarea A, draining 30%, with time of concentration 20 min; and (2) subarea B, draining 70%, with time of concentration 60 min.

The φ-index is 25 mm/hr.

Calculate the peak flow corresponding to the 10-yr frequency.

Use the following IDF function:

I = 650 T^0.22 / (t_r + 18)^0.75

in which I = rainfall intensity (mm/hr), T = return period (yr), and t_r = rainfall duration (min).

Assume linear flow concentration at the catchment outlet.

Solution.-
Assume runoff concentration without diffusion, and use Eq. 4-12 in the rational formula:
Q_p = I_e ∑A = (I - φ) ∑A = (I - 25) ∑A
Several rainfall durations are tried, as shown in the following table:

t_r I I_e Subarea A Subarea B
contribution ∑ A Q_p
(min) (mm/hr) (mm/hr) (ha) (ha) ∑ A m³/s

20 70.48 45.48 45 35.0 80.0 10.11

30 59.15 34.15 45 52.5 97.5 9.25

40 51.33 26.33 45 70.0 115.0 8.41

50 45.55 20.55 45 87.5 132.5 7.56

60 41.10 16.10 45 105.0 150.0 6.71

Q_p = I_e ∑ A = 45.48 mm/hr × 80 ha × 10,000 m²/ha × 0.001 m/mm × (1 hr/3600 seconds) =
Q_p = 10.11 m³/s

The peak flow is 10.11 m³/s. ANSWER.

PROBLEM 2

An overland flow plane has the following characteristics:

plane length L = 50 m;

plane slope S_o = 0.007;

Manning's n = 0.06;

rainfall excess i = 45 mm/hr.

Determine if the kinematic wave approximation is applicable to this set of overland flow conditions.

Solution.-
Kinematic flow number K = (S_oL)/(F_o²h_o)
Calculate equilibrium outflow; establish rating; calculate h_o from rating; calculate mean velocity v_o, and Froude number.
Equilibrium outflow q_e = iL = (45 mm/hr × 50 m × 0.001 m/mm) / (3600 s/hr) = 0.000625 m³/s/m
Rating: q_e = b h_o^m
b = (1/n) S_o^1/2 = (1/0.06) (0.007)^1/2 = 1.394
Choose m = 5/3 [Manning friction in wide channels (overland flow)]; 1/m = 3/5 = 0.6
Calculate h_e = (q_e/b) ^1/m = (0.000625/1.394)^0.6 = 0.00979 m
h_o = h_e = 0.00979 m
Calculate v_o = q_e / h_e = (0.000625/0.00979) = 0.0638 m/s
Calculate F_o² = v_o² / (gh_o) = (0.0638)² / (9.81 × 0.00979) = 0.042
Calculate K = (S_oL)/(F_o²h_o) = (0.007 × 50) / (0. 042 × 0.00979) = 851 > 20.

The flow is kinematic. ANSWER.

PROBLEM 3

A certain basin has the following 2-hr unit hydrograph (1 cm of rainfall), defined at hourly ordinates:

Cumulative time (hr) 0 1 2 3 4 5 6
Flow (m³/s) 0 10 30 20 10 10 0

Calculate the flood hydrograph for the following effective storm pattern:

Time (hr) 0-3 3-6

Effective rainfall (cm/hr) 1 2

Effective rainfall (cm) 3 6

Solution.-

Time 2-hr UH 2-hr SH Lagged 3 hr 3-hr UH 3 cm × UH 6 cm × UH
(lagged 3 hr) Flood
hydrograph
(hr) (m³/s) (m³/s) (m³/s) (m³/s) (m³/s) (m³/s) (m³/s)

0 0 0 0 0 0 0 0

1 10 10 0 6.67 20 0 20

2 30 30 0 20 60 0 60

3 20 30 0 20 60 0 60

4 10 40 10 20 60 40 100

5 10 40 30 6.67 20 120 140

6 0 40 30 6.67 20 120 140

7 0 40 40 0 0 120 120

8 0 40 40 0 0 40 40

9 0 40 40 0 0 40 40

10 0 40 40 0 0 0 0

11 0 40 40 0 0 0 0

12 0 40 40 0 0 0 0

∑ 80 - - 80 240 480 720

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