Example on Infiltration

Example on Infiltration
Example1: Find the Index of a certain catchment has the change of the rainfall intensity which given below. If the runoff=33mm, P=75mm



Example2: A tabulated below are data for a number of storms happened on a river. Compute the W-index for all storms, what would be the av. Error and av. Percentage error in estimated runoff .If the av. W-index was used to compute the runoff?
Error=Rcomp.-Rob. Rcomp.=P-W*t W-index
(cm/hr.) Rob.
(cm) P
(cm) Duration,t
(hr.) Storm no.
-0.12 1.2 0.125 1.32 2.82 12 1
-1.02 0 0.041 1.02 2.98 48 2
-1.15 1.31 0.087 2.46 4.55 24 3
-2.92 4.5 0.094 7.42 14.22 72 4
0.01 0.44 0.136 0.43 2.87 18 5
0.19 0.67 0.143 0.48 3.91 24 6
1.31 3.24 0.171 1.93 8.1 36 7
1.12 2.79 0.228 1.67 4.41 12 8
-0.72 1.26 0.111 1.98 5.31 30 9
1.4 4.55 0.213 3.15 6.98 18 10
?=-1.9 ?=19.96 ?=1.35 ?=21.86
Error=-0.19 (W) ave = 1.35/10 = 0.135
For check:
Av. Error= (?Rcomp.- ?Rob.)/10
= (19.96-21.86)/10
=-0.19 ok.
-------------------------------------------------------------------------------------Example3: A rain storm with intensity=10cm and direct runoff=5.8cm If the distribution of the storm as given in table below. Find the
?-Index for the storm
8 7 6 5 4 3 2 1 t(hr.)
0.5 1 1.6 1.4 2.3 1.5 0.1 0.4 Excess rainfall/hr.

Example4:The equation of the f(t) curve for a certain catchment is given by:
f(t) =1.2+4.2 e-0.33t
1-Compute the runoff volume for the following rain storm:
2- Compute ?-Index & W- index and choose the best from them and explain cause that
6 5 4 3 2 1 t(hr.)
3 6.5 12.2 12.8 8.5 6 Rainfall(mm)



Ic t(hr.)
5.4 0
4.2 1
3.4 2
2.8 3
2.3 4
2 5
1.8 6
Solution:

P=(6+8.5+12.8+12.2+6.5+3)
= 49 mm
Depth of the infiltration =?y dt
=(1.2+4.2 e-0.33t)dt
= 1.2t-(4.2/0.33)e-0.33t]
] *e-0.33*0 4.2/0.33) )- =[1.2*6-(4.2/0.33)*e-0.33*6]-[1.2*0
= 18.19mm
R=P-I
=49-18.19
=30.81mm
W-index=(P-R)/t
=18.19/6
=3.032 mm/hr.
To Find The ?-Index:
R=30.81 mm
30.81=(12.8-12.2)*1+(12.2-8.5)*2+(8.5-6.5)*3+(6.5-6)*4+(6- ?)
30.81=16+6*5-5* ?
?=3.038 mm/hr.
We choose the w-index because it gives larger surface runoff.
Example:
A catchment soil has the following Horton infiltration Parameters:
f0 = 100 mm/min, fc = 20 mm/min, and k = 2 min-1 the required.
1- Plot the infiltration capacity curve with time for this catchment
2- Plot the potential cumulative infiltration for this catchment





Solution:
f(t) =fc+(fo-fc) e-Kt (Horton equ.)
F (t) = f_c t + (( f_o - f_c )(1-e^(-Kt)))/K (cumulative infiltration rate)





Example:
?? Find out the sensitivity of the infiltration capacity curve to different decay coefficients (k) assuming that f0 = 2.9 in/h and fc = 0.5 in/h
?? Assume k values = 0.15, 0.30, and 0.45 hour -1


Solution:
f(t) =fc+(fo-fc) e-Kt (Horton equ.)
t (hr) fp(in/hr) fp(in/hr) fp(in/hr)
K= 0.15 K= 0.30 K= 0.45
0 2.9 2.9 2.9
1 2.6 2.3 2
2 2.3 1.8 1.5
3 2 1.5 1.1
4 1.8 1.2 0.9
5 1.6 1 0.8
6 1.5 0.9 0.7
7 1.3 0.8 0.6
8 1.2 0.7 0.6
9 1.1 0.7 0.5
10 1 0.6 0.5
11 1 0.6 0.5
12 0.9 0.6 0.5
13 0.8 0.5 0.5
14 0.8 0.5 0.5
15 0.8 0.5 0.5
16 0.7 0.5 0.5
17 0.7 0.5 0.5
18 0.7 0.5 0.5
19 0.6 0.5 0.5
20 0.6 0.5 0.5
21 0.6 0.5 0.5
22 0.6 0.5 0.5
23 0.6 0.5 0.5
24 0.6 0.5 0.5
25 0.6 0.5 0.5
26 0.5 0.5 0.5