CIV E 445 - APPLIED HYDROLOGY
SPRING 2011
SOLUTION TO HOMEWORK 5, CHAPTER 4

Problem 5-1

Since rainfall duration is greater than time of concentration, the flow is superconcentrated and the entire catchment is contributing. For subcatchments with different runoff coefficients, use a weighted formula for peak runoff (see Eq. 4-14):

Qp = I Σ(CA) =

Qp = 45 mm/h • [ (0.3 • 80 • 25/100) + (0.5 • 80 • 35/100) + (0.7 • 80 • 40/100) ] ha • (10,000 m2/ha • 0.001 m/mm) / (3600 s/h) = Qp = 5.3 m3/s.  ANSWER.


Problem 5-2

Several rainfall durations are tried, as shown in the following table.

tr
(min)
I
(mm/h)
Subarea A
(C = 0.7)
(ha)
Subarea B
(C = 0.3)
(ha)
Σ(CA)
(ha)
Qp
(m3/s)
10141.733011.6724.59.65
20120.353023.3328.09.36
30105.42303531.59.22
4094.313046.6735.09.17
5085.673058.3338.59.16
6078.74307042.09.19

The fraction of subarea B contributing to peak runoff increases linearly with rainfall duration.

Therefore: Qp = (10/3600) I Σ(CA) = 0.00278 I Σ(CA).

The 25-y peak runoff is the maximum value, corresponding to a 10-min duration: 9.65 m3/s.  ANSWER.


Problem 5-3

Using Eq. 4-19, the equilibrium outflow is:

qe = iL/3600 = 75 mm/h • 144 m / 3600 = 3 L/s/m

qe = 3 L/s/m = 3 • 10-3 m3/s/m = 0.003 m2/s.

For T = 20°C, ν = 1.0 • 10-6 m2/s (Table A-1).

Using Eq. 4-27: CL = (9.81 m/s2 • 0.01) / (3 • 1.0 • 10-6 m2/s) = 32,700 m-1s-1.

In Eq. 4-25, for laminar flow, b = CL, and m = 3. Therefore:

he = (qe / CL)1/3 = (0.003/32,700)1/3 = 0.00451 m = 4.51 mm  ANSWER.

For T = 25°C, ν = 0.893 • 10-6 m2/s.

Using Eq. 4-27: CL = 36,618 m-1s-1.

Therefore, with Eq. 4-25: he = (0.003/36,618)1/3 = 0.00434 m = 4.34 mm  ANSWER.


Problem 5-4

The rainfall excess in m/s is:

i = (25 mm/h • 0.001 m/mm) / (3600 s/h) = 6.94 •10-6 m/s.

qe = 6.94 •10-6 m/s • 80 m = 0.0005555 m3/s/m = 0.5555 L/s/m.

For 75% turbulent flow, m = 2. Therefore, in Eq. 4-29:

te = [ 2 • (0.05 • 80)1/2 ] / [(6.94 •10-6)1/2 • 0.011/4 ] = 4800 s.

Using Eq. 4-36, the rising limb of the overland flow hydrograph is calculated as shown in the following table.  ANSWER.