Formula Sheets: Abstractions from Precipitation | Engineering Hydrology - Civil Engineering (CE) PDF Download

 Page 1


Hydrology F ormula Sheet for GA TE Civil
Engineering
Hydrology: Hydrologic Cycle, Precipitation, Evapo-
r ation, Evapo-tr anspir ation, W atershed
1. Hydrologic Cycle
• W ater Balance Equation :
P =Q+E +?S
whereP = precipitation,Q = runoff, E = evapor ation/evapotr anspir ation,?S =
change in stor age (soil moisture, groundwater , etc.).
2. Precipitation
• A ver age Rainfall (Arithmetic Mean) :
P
avg
=
P
1
+P
2
+···+P
n
n
whereP
i
= r ainfall at stationi ,n = number of stations.
• Thiessen Polygon Method :
P
avg
=
?
(P
i
·A
i
)
?
A
i
whereA
i
= area of Thiessen polygon for stationi .
• Isoh yetal Method :
P
avg
=
?
(P
i
·A
i
)
?
A
i
whereP
i
= aver age r ainfall between isoh yets,A
i
= area between isoh yets.
• Rainfall Intensity :
i =
P
t
wherei = intensity (mm/hr),P = r ainfall depth (mm),t = dur ation (hr).
1
Page 2


Hydrology F ormula Sheet for GA TE Civil
Engineering
Hydrology: Hydrologic Cycle, Precipitation, Evapo-
r ation, Evapo-tr anspir ation, W atershed
1. Hydrologic Cycle
• W ater Balance Equation :
P =Q+E +?S
whereP = precipitation,Q = runoff, E = evapor ation/evapotr anspir ation,?S =
change in stor age (soil moisture, groundwater , etc.).
2. Precipitation
• A ver age Rainfall (Arithmetic Mean) :
P
avg
=
P
1
+P
2
+···+P
n
n
whereP
i
= r ainfall at stationi ,n = number of stations.
• Thiessen Polygon Method :
P
avg
=
?
(P
i
·A
i
)
?
A
i
whereA
i
= area of Thiessen polygon for stationi .
• Isoh yetal Method :
P
avg
=
?
(P
i
·A
i
)
?
A
i
whereP
i
= aver age r ainfall between isoh yets,A
i
= area between isoh yets.
• Rainfall Intensity :
i =
P
t
wherei = intensity (mm/hr),P = r ainfall depth (mm),t = dur ation (hr).
1
3. Evapor ation
• Pan Evapor ation :
E =K
p
·E
pan
whereE = lak e evapor ation,K
p
= pan coefficient (typically 0.7–0.8), E
pan
= mea-
sured pan evapor ation.
• Dalton’ s Law of Evapor ation :
E =k(e
s
-e
a
)
wherek = constant,e
s
= satur ation vapor pressure,e
a
= actual vapor pressure.
4. Evapo-tr anspir ation
• Crop Evapotr anspir ation (ET
c
) :
ET
c
=K
c
· ET
o
whereK
c
= crop coefficient, ET
o
= reference evapotr anspir ation.
• Reference Evapotr anspir ation (ET
o
) : Estimated using Penman-Monteith or
Blaney-Criddle methods.
• Blaney-Criddle F ormula :
ET
o
=p(0.46T
mean
+8.13)
wherep = percentage of annual da ytime hours,T
mean
= mean temper ature (°C).
5. W atershed Char acteristics
• Runoff Coefficient ( C ) :
Q =C ·P ·A
whereQ = runoff volume, P = r ainfall depth,A = watershed area.
• Time of Concentr ation (T
c
) : Time for runoff to tr avel from the farthest point
to the outlet.
– Kirpich F ormula:
T
c
= 0.01947L
0.77
S
-0.385
whereL = length of flow path (m), S = slope of watershed.
• W atershed Area (A ) : Measured from topogr aphic maps or GIS.
• Shape F actor :
Shape F actor =
L
2
A
whereL = length of main stream.
2
Page 3


Hydrology F ormula Sheet for GA TE Civil
Engineering
Hydrology: Hydrologic Cycle, Precipitation, Evapo-
r ation, Evapo-tr anspir ation, W atershed
1. Hydrologic Cycle
• W ater Balance Equation :
P =Q+E +?S
whereP = precipitation,Q = runoff, E = evapor ation/evapotr anspir ation,?S =
change in stor age (soil moisture, groundwater , etc.).
2. Precipitation
• A ver age Rainfall (Arithmetic Mean) :
P
avg
=
P
1
+P
2
+···+P
n
n
whereP
i
= r ainfall at stationi ,n = number of stations.
• Thiessen Polygon Method :
P
avg
=
?
(P
i
·A
i
)
?
A
i
whereA
i
= area of Thiessen polygon for stationi .
• Isoh yetal Method :
P
avg
=
?
(P
i
·A
i
)
?
A
i
whereP
i
= aver age r ainfall between isoh yets,A
i
= area between isoh yets.
• Rainfall Intensity :
i =
P
t
wherei = intensity (mm/hr),P = r ainfall depth (mm),t = dur ation (hr).
1
3. Evapor ation
• Pan Evapor ation :
E =K
p
·E
pan
whereE = lak e evapor ation,K
p
= pan coefficient (typically 0.7–0.8), E
pan
= mea-
sured pan evapor ation.
• Dalton’ s Law of Evapor ation :
E =k(e
s
-e
a
)
wherek = constant,e
s
= satur ation vapor pressure,e
a
= actual vapor pressure.
4. Evapo-tr anspir ation
• Crop Evapotr anspir ation (ET
c
) :
ET
c
=K
c
· ET
o
whereK
c
= crop coefficient, ET
o
= reference evapotr anspir ation.
• Reference Evapotr anspir ation (ET
o
) : Estimated using Penman-Monteith or
Blaney-Criddle methods.
• Blaney-Criddle F ormula :
ET
o
=p(0.46T
mean
+8.13)
wherep = percentage of annual da ytime hours,T
mean
= mean temper ature (°C).
5. W atershed Char acteristics
• Runoff Coefficient ( C ) :
Q =C ·P ·A
whereQ = runoff volume, P = r ainfall depth,A = watershed area.
• Time of Concentr ation (T
c
) : Time for runoff to tr avel from the farthest point
to the outlet.
– Kirpich F ormula:
T
c
= 0.01947L
0.77
S
-0.385
whereL = length of flow path (m), S = slope of watershed.
• W atershed Area (A ) : Measured from topogr aphic maps or GIS.
• Shape F actor :
Shape F actor =
L
2
A
whereL = length of main stream.
2
6. Infiltr ation
• Horton’ s Infiltr ation Model :
f(t) =f
c
+(f
0
-f
c
)e
-kt
where f(t) = infiltr ation r ate at time t , 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 a infall,Q = runoff, t = dur ation of r ainfall.
7. Hydrogr aph Analysis
• Unit Hydrogr aph : Hydrogr aph for 1 cm of effective r ainfall over a specific
dur ation.
• Peak Discharge (Rational Method) :
Q
p
=
C ·i·A
360
where Q
p
= peak discharge (m³/s), C = runoff coefficient, i = r ainfall intensity
(mm/hr),A = area (ha).
8. Losses in W atershed
• T otal Losses :
L =P -Q
whereL = losses (infiltr ation, evapor ation, interception, etc.).
• Interception : Depends on vegetation type, typically 10–20% of r ainfall.
3