This document provides a solution to a hydrology problem using the Rational Method. The key details are: 1) The problem involves calculating the withdrawal rate from a reservoir given inflow, seepage loss, precipitation, evaporation, and change in storage over a period. 2) The calculations involve determining the inflow (Qin), outflow (Qout), and change in storage (ΔS) over the period using the provided data. 3) The withdrawal rate is then calculated as the difference between inflow, outflow, and change in storage. The final withdrawal rate is calculated to be 10.11 m3/s.

1. SOLUTION TO QUESTION
Data given:
Inflow = 0.5 Mm3/day
Seepage loss, G = 2.5 cm
Precipitation, P = 18.5 cm
Evaporation, E = 9.5 cm
ΔS = -0.75m
Qin = PA+inflow
= (18.5cm/100) m x 1375 x 104m2/106
+ 0.5 x 106 Mm3/day x 30day
= 17. 543 Mm3
Qout = (2.5 + 9.5)/100x1375 x 104m2/106
=1.65 Mm3
ΔS = -0.75m x 1375 104 /106 m2
= -10.31 Mm3
Withdrawal = Qin- Qout – ΔS = 26.203 Mm3
Withdrawal rate
= 26.203 x 106/(30x24x3600) = 10.11 m3/s
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2. CONCEPT AND MEASUREMENT OF
WATERSHED
ERT257 HYDROLOGY AND WATER RESOURCES ENGINEERING
Mrs Siti Kamariah Md Sa’at
FTKK
UniMAP

3. WATERSHED
A basin, drainage or
catchment area that is the
land area that contributes
runoff to an outlet point
Outlet point
Watershed
boundary

4. WATERSHEDS
Area of land draining into a stream at a given location. In US called
watershed.
Also known as Catchment, Catchment area, Catchment basin, Drainage area,
River basin, Water basin
Rainfall that falls in a watershed will generate runoff to that watershed outlet.
Topographic elevation is used to define a Watershed boundary (land survey
or LIDAR)
Scale is a big issue for analysis
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5. We all live in a watershed!
Area of land from which all
water drains, running downhill, to
a shared destination - a river,
pond, stream, lake, or estuary

6. FUNCTIONS
Captures precipitation – its characteristics influence how much is
captured
Stores water once it infiltrates into soil (important to plants)
Slowly releases water into streams, rivers, oceans

7. WHY ARE WATERSHEDS IMPORTANT?
Activities within a watershed impact runoff and water quality of water leaving
the watershed
Must manage at a watershed level rather than other boundaries to attain
goals related to runoff and water quality

8. TYPES OF WATERSHED
•Forested watershed
•Urban watershed
•Agricultural watershed
•Rural watershed
•Coastal/swamp/desert watershed
•Combination of above
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9. HYDROLOGIC ANALYSIS
Two important hydraulic parameters in hydrologic analysis
– Outfall/drainage outlet,
i.e. the common point of discharge
– Watershed boundary
– any rain that falls within the boundary will be directed towards point of discharge
– Because of various nature of river system, a watershed may have any number of
sub-watershed within it
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11. Watershed Characteristics
 Size
 Slope
 Shape
 Soil type/Land use
 Storage capacity
Reservoir
Divide
Natural
stream
Urban
Concrete
channel
1 mile

12. WATERSHED SIZE
Watershed area (km2, ha)
Runoff generation on these watersheds can be considered in two phases:i) land
phase and ii) channel phase
Small watersheds (< 250 km2)
They have dominant land phase and overland flow, have relatively less conspicuous channel
phase.
They are highly sensitive to high-intensity, short-duration rainfalls.
Large watersheds (>250 km2)
They have well-developed channel networks and channel phase, and, thus, channel storage is
dominant.
They are less sensitive to high-intensity rainfalls of short duration.
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13. WATERSHED SLOPES
The slope govern how fast water will drain to the channel
• steep slopes - peaked hydrograph
• gentle slopes - flat hydrograph
• Consider the average gradient of hill slopes
(slope: vertical/horizontal distance)
• Formula for land slope, S:
 Where:
 L = total length of contours (m),
 CI= contour interval (m)
 A= watershed area (m2)
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14. • Important hydrologic
characteristic
• Elongated Shape
• Concentrated Shape
• Affects Timing and
Peak Flow
• Determined by geo -
morphology of stream
WATERSHED SHAPES

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Sub-watershed

17. SUB-WATERSHED
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18. WATERSHED DELINEATION
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19. LANGAT RIVER BASIN
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20. RUNOFF What is runoff?
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21. WHAT IS RUNOFF?
Runoff = draining or flowing off of precipitation from a catchment area through a
surface channel enters into stream channel.
Output from catchment in a given unit of time.
Based on the time delay between the precipitation and the runoff, the runoff is
classified into two categories; as
(a) Direct runoff : runoff which enters the stream immediately after the rainfall. It
includes surface runoff, prompt interflow and rainfall on the surface of the stream.
Direct storm runoff and storm runoff are also used to designate direct runoff.
(b) Base flow : The delayed flow that reaches a stream essentially as groundwater
flow is called base flow.
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22. COMPONENTS OF RUNOFF
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23. FACTORS AFFECTING CATCHMENT RUNOFF
a) Precipitation characteristics
b) Shape and size of catchment
c) Topography
d) Geologic characteristics
e) Meteorological characteristics
f) Storage characteristics of a catchment
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24. RUNOFF ESTIMATION Rational method

25. RUNOFF ESTIMATION METHOD
Rational method
Infiltration Approach
Hydrograph method
NRCS Curve Number (Formerly SCS) Method
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26. RATIONAL METHOD
Used for determination of peak flow rate
 Assumption: A constant intensity of rain uniformly distributed over an area
 maximum runoff: occur when the rainfall duration equals the time of
concentration
For small size (<50 km2) catchments
This not cover what is MSMA (Manual Saliran Mesra Alam Malaysia)/Urban
Stormwater Management Manual.

27. RATIONAL METHOD
The maximum possible flow generated by rainfall event of a watershed
• Knowledge of Qp is required for drainage design to avoid/minimize project
from flooding
• Rational method: is a prediction method and based on characteristics of
watershed and rainfall
Assumptions:
• Waters is small (<200 acres)
• Peak flow occurs when the entire area is contributing
• Rainfall intensity is uniform over a time of concentration
• A rational coefficient represent rainfall:runoff ratio
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28. RATIONAL METHOD
Standard Rational Method
Qp = C i A
Where
 Qp=peak discharge
 C=coefficient of runoff
 i = mean intensity of precipitation for
duration equal to tc
 A=drainage area
To compute Qp, requires tc,i and C
Rational runoff Coefficient, C
– Defined as the rate of rainfall over a
watershed
to rate of runoff from that watershed
– The value is highly dependent on
land use and
slope (Table)

29. RATIONAL METHOD
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30. RATIONAL METHOD

31. RUNOFF COEFFICIENT
Coefficient that represents the fraction of runoff
to rainfall
Depends on type of surface
When a drainage area has distinct parts with
different coefficients…
Use weighted average
A
A
C
..
A
C
A
C
C
i
n
n
2
2
1
1
Σ
+
…
+
+
=

32. Runoff
Coefficient

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35. TIME OF CONCENTRATION (TC)
Time for water to flow from hydraulically most distant
point on the watershed to the point of interest
Assumes peak runoff occurs when i lasts as long or longer
than tc

36. TIME OF CONCENTRATION, TC
For other catchment, use Kirpich Equation (1940)
tc=0.01947 L0.77S-0.385
where
 tc in min
 L= maximum length of travel time in m
 S= slope catchment = ∆H/L
 ∆H = difference of elevation between the most remote point on the catchment
and the outlet

37. TIME OF CONCENTRATION, TC
Sometimes its written as
tc= 0.01947 K1
0.77
Where K1=
L = max length of travel (m)
∆H = different of elevation
H)
/
(L3
∆

38. TIME OF CONCENTRATION, TC
38

39. TIME OF CONCENTRATION (TC)
Depends on:
Size and shape of drainage area
Type of surface
Slope of drainage area
Rainfall intensity
Whether flow is entirely overland or whether some is channelized

40. RAINFALL INTENSITY, I
Corresponding to a duration tc and the desired probability of
exceedence P
Return period, T=1/P
Found from rainfall intensity—duration-frequency (IDF) curve

41. INTENSITY-DURATION-FREQUENCY CURVE
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42. RAINFALL INTENSITY, I
Average intensity for a selected frequency and duration
Based on “design” event (i.e. 50-year storm)
 Overdesign is costly (what else?)
 Underdesign may be inadequate

43. RAINFALL INTENSITY, I
Based on values of tc and T
tc = time of concentration
T = recurrence interval or design frequency
As a minimum equal to the time of concentration, tc,
(mm/hr)

44. RECURRENCE INTERVAL (DESIGN EVENT)
2-year interval -- Design of intakes and spread of water on
pavement for primary highways and city streets
10-year interval -- Design of intakes and spread of water
on pavement for freeways and interstate highways
50 - year -- Design of subways (underpasses) and sag
vertical curves where storm sewer pipe is the only outlet
100 – year interval -- Major storm check on all projects
ARI = Average recurrent interval
- Average length of time between rain events
that exceed the same magnitude, volume and
duration

45. DESIGN ACCORDING
TO MSMA
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46. EXAMPLE 1:
RATIONAL METHOD
An urban catchment has an area of 85 ha. The slope of the
catchment is 0.006 and the maximum length of travel of water
is 950m. The maximum depth of rainfall with a 25-year return
period is as below
Duration
(min)
5 10 20 30 40 60
Depth of
rainfall
(mm)
17 26 40 50 57 62
 If a culvert for drainage at the outlet of this area is to
be designed for a return period of 25years, estimate
the required peak-flow rate, by assuming runoff
coefficient is 0.3

47. SOLUTION
tc using Kirpich formula:
tc=0.01947 L0.77S-0.385
= 0.01947 x (950)0.77 x (0.006)-0.385
= 27.4 minutes
By interpolation, i = (50-40)/10 x 7.4 + 40 = 47.4 mm
Average intensity, i tc,p = 47.4/27.4 x60 = 103.8 mm/hr
Q = 0.3 x 103.8 x 0.85/3.6 = 7.35 m3/s
47

48. EXAMPLE 2:
RATIONAL METHOD
If the urban area of example 1, the land use of the area and the
corresponding runoff coefficients are as given below, calculate the
equivalent runoff coefficient.
Land Use Area (ha) Runoff coefficient
Roads 8 0.70
Lawn 17 0.10
Residential Area 50 0.30
Industrial Area 10 0.80

49. SOLUTION
49
C =
C1A1 + C2A2 + ….. + CnAn
ΣAi
=
0.7 (8)+ 0.1(17)+0.3(50)+0.8 (10)
(8+17+50+10)
= 0.36

50. EXAMPLE 3
50
A catchment area of 120 ha has a time of concentration of 30 min and runoff
coefficient of 0.3. If a storm of duration 45 min results in 3.0 cm of rainfall over the
catchment, estimate the resulting peak flow rate.
i = 30 mm/(45 min/hr x 60) = 40 mm/hr
C = 0.3
A = 120 ha
Q = 0.3(40)(120)/360 = 4 m3/s

51. WORKED EXAMPLE
Determine the design peak for flow generated from residential area of 10 hectares in Kuala
Lumpur for design return period 50 years. Assume 80 m of overland flow followed by 400 m
of flow in open drain. Catchment area average slope is 0.5%.
Solution:
1. Determine tc = to + td = 8 + 7 = 15 min
From overland flow chart: to = 8 minutes
td = L/v (Manning equation), Assume v = 1 m/s, then td = 400 s = 6.7 min. Use 7 min
2. Refer IDF curve to obtain i. i = 200mm/hr
3. Choose rational coefficient, C (Table) = 0.7
4. Compute Qp = C I A
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53. IDF CURVE KUALA LUMPUR
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54. TRY
Problems 7.2 & 7.4
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55. THANK YOU Any question?
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