Formula Sheets: Flood Estimation & Flood Routing | Engineering Hydrology - Civil Engineering (CE) PDF Download

 Page 1


Flood Estimation, Routing, and Surface
Run-off Models F ormula Sheet for GA TE Civil
Engineering
Hydrology: Flood Estimation and Routing, Surface
Run-off Models
1. Flood Estimation
• Rational Method for Peak Discharge :
Q
p
=
C·i·A
360
where Q
p
= peak discharge (m³/s), C = runoff coefficient, i = r ainfall intensity
(mm/hr),A = catchment ar ea (ha).
• Time of Concentr ation (T
c
) - Kirpich F ormula :
T
c
= 0.01947L
0.77
S
-0.385
whereL = length of flow path (m), S = aver age slope of catchment.
• Flood Frequency Analysis (Gumbel’ s Method) :
Q
T
=
¯
Q+K
T
·s
whereQ
T
= flood discharge for return period T ,
¯
Q = mean flood discharge, s =
standard deviation,K
T
= frequency factor .
K
T
=-
v
6/p
[
0.5772+ ln
(
ln
(
T
T -1
))]
• Return Period (T ) :
T =
1
P
whereP = probabil ity of exceedance.
1
Page 2


Flood Estimation, Routing, and Surface
Run-off Models F ormula Sheet for GA TE Civil
Engineering
Hydrology: Flood Estimation and Routing, Surface
Run-off Models
1. Flood Estimation
• Rational Method for Peak Discharge :
Q
p
=
C·i·A
360
where Q
p
= peak discharge (m³/s), C = runoff coefficient, i = r ainfall intensity
(mm/hr),A = catchment ar ea (ha).
• Time of Concentr ation (T
c
) - Kirpich F ormula :
T
c
= 0.01947L
0.77
S
-0.385
whereL = length of flow path (m), S = aver age slope of catchment.
• Flood Frequency Analysis (Gumbel’ s Method) :
Q
T
=
¯
Q+K
T
·s
whereQ
T
= flood discharge for return period T ,
¯
Q = mean flood discharge, s =
standard deviation,K
T
= frequency factor .
K
T
=-
v
6/p
[
0.5772+ ln
(
ln
(
T
T -1
))]
• Return Period (T ) :
T =
1
P
whereP = probabil ity of exceedance.
1
2. Flood Routing
• Hydrologic Routing (Stor age-Indication Method) :
2S
t+?t
?t
+O
t+?t
=
2S
t
?t
-O
t
+I
t
+I
t+?t
whereS
t
,S
t+?t
= stor age at timet andt+?t ,O
t
,O
t+?t
= outflow , I
t
,I
t+?t
= inflow ,
?t = time step.
• Muskingum Method :
O
t+?t
=C
0
I
t+?t
+C
1
I
t
+C
2
O
t
where:
C
0
=
-Kx+0.5?t
K(1-x)+0.5?t
, C
1
=
Kx+0.5?t
K(1-x)+0.5?t
, C
2
=
K(1-x)-0.5?t
K(1-x)+0.5?t
K = stor age time constant,x = weighting factor (0 to 0.5),
?
C
i
= 1 .
• Continuity Equation for Routing :
I-O =
dS
dt
whereI = inflow , O = outflow , S = stor age.
3. Surface Run-off Models
• Rational Method :
Q =C·i·A
where Q = runoff discharge (m³/s), C = runoff coefficient (0 to 1), i = r ainfall
intensity (m/s),A = area (m²).
• SCS Curve Number Method :
Q =
(P -0.2S)
2
P +0.8S
for P > 0.2S
S =
25400
CN
-254
whereQ = runoff depth (mm), P = r ainfall depth (mm),S = potential maximum
retention (mm), CN = curve number (depends on soil, land use, and antecedent
moisture condition).
• Initial Abstr action (I
a
) :
I
a
= 0.2S
• Effective Rainfall :
P
e
=P -I
a
-F
whereP
e
= effective r ainfall, F = infiltr ation losses.
2
Page 3


Flood Estimation, Routing, and Surface
Run-off Models F ormula Sheet for GA TE Civil
Engineering
Hydrology: Flood Estimation and Routing, Surface
Run-off Models
1. Flood Estimation
• Rational Method for Peak Discharge :
Q
p
=
C·i·A
360
where Q
p
= peak discharge (m³/s), C = runoff coefficient, i = r ainfall intensity
(mm/hr),A = catchment ar ea (ha).
• Time of Concentr ation (T
c
) - Kirpich F ormula :
T
c
= 0.01947L
0.77
S
-0.385
whereL = length of flow path (m), S = aver age slope of catchment.
• Flood Frequency Analysis (Gumbel’ s Method) :
Q
T
=
¯
Q+K
T
·s
whereQ
T
= flood discharge for return period T ,
¯
Q = mean flood discharge, s =
standard deviation,K
T
= frequency factor .
K
T
=-
v
6/p
[
0.5772+ ln
(
ln
(
T
T -1
))]
• Return Period (T ) :
T =
1
P
whereP = probabil ity of exceedance.
1
2. Flood Routing
• Hydrologic Routing (Stor age-Indication Method) :
2S
t+?t
?t
+O
t+?t
=
2S
t
?t
-O
t
+I
t
+I
t+?t
whereS
t
,S
t+?t
= stor age at timet andt+?t ,O
t
,O
t+?t
= outflow , I
t
,I
t+?t
= inflow ,
?t = time step.
• Muskingum Method :
O
t+?t
=C
0
I
t+?t
+C
1
I
t
+C
2
O
t
where:
C
0
=
-Kx+0.5?t
K(1-x)+0.5?t
, C
1
=
Kx+0.5?t
K(1-x)+0.5?t
, C
2
=
K(1-x)-0.5?t
K(1-x)+0.5?t
K = stor age time constant,x = weighting factor (0 to 0.5),
?
C
i
= 1 .
• Continuity Equation for Routing :
I-O =
dS
dt
whereI = inflow , O = outflow , S = stor age.
3. Surface Run-off Models
• Rational Method :
Q =C·i·A
where Q = runoff discharge (m³/s), C = runoff coefficient (0 to 1), i = r ainfall
intensity (m/s),A = area (m²).
• SCS Curve Number Method :
Q =
(P -0.2S)
2
P +0.8S
for P > 0.2S
S =
25400
CN
-254
whereQ = runoff depth (mm), P = r ainfall depth (mm),S = potential maximum
retention (mm), CN = curve number (depends on soil, land use, and antecedent
moisture condition).
• Initial Abstr action (I
a
) :
I
a
= 0.2S
• Effective Rainfall :
P
e
=P -I
a
-F
whereP
e
= effective r ainfall, F = infiltr ation losses.
2
4. Unit Hydrogr aph Application in Run-off
– Direct Runoff Hydrogr aph :
Q(t) =P
e
·U(t)
whereQ(t) = runoff h ydrogr aph ordinate, P
e
= effective r ainfall (cm), U(t) =
unit h ydrogr aph ordinate.
– Convolution for Multi-Period Rainfall :
Q
n
=
n
?
m=1
P
m
U
n-m+1
whereQ
n
= runoff at time step n ,P
m
= effective r ainfall at time step m ,U
n-m+1
= unit h ydrogr aph ordinate.
5. Infiltr ation Losses (Related to Run-off )
*
Horton’ s Infiltr ation Model :
f(t) =f
c
+(f
0
-f
c
)e
-kt
wheref(t) = infiltr ation r ate (mm/hr), f
c
= final infiltr ation r ate, f
0
= initial
infiltr ation r ate, k = deca y constant.
*
Phi-Index (? ) :
? =
P -Q
t
whereP = total r ainfall (mm),Q = runoff (mm), t = dur ation (hr).
6. Flood Hydrogr aph Components
· T otal Hydrogr aph :
Q
total
(t) =Q
direct
(t)+Q
base
(t)
whereQ
direct
= direct runoff, Q
base
= basefl ow .
· Peak Time and Discharge : Determined from h ydrogr aph analysis or
unit h ydrogr aph convolution.
3