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ERT 246 Hydrology & Water Resources
Engineering
Siti Kamariah Md Sa’at
School of Bioprocess Engineering, UniMAP
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Unit Hydrograph
Cont.
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More Example 4:
Two storm each of 6-hr duration and having rainfall excess values of 3.0cm and 2.0 cm respectively occur successively.
The 2-cm ER rain follows the 3-cm rain. The 6-hr UH for the catchment is the same as given in previous example. Calculate the resulting DRH.
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Unit Hydrograph of Different Durations
Under condition where lack of adequate data in developement of unit hydrograph
D-hour unit hydrograph is used to develop unit hydrographs of differing durations nD
Two method available:1. Method of superposition
2. The S-Curve
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Method of superposition
If a D-h unit hydrograph is available, and its desired to develop unit hydrograph of nD, its is easily accomplished by superposing n unit hydrographs with each graph separated from the previous on by D-h.
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D = 2-Hr Unit HydrographD = 2-Hr Unit Hydrograph
Adjusted Net Rainfall one inch over basin
Qp
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Change UH DurationChange UH Duration
Consider 1 hr UH
Add and Lag two UH
by one hour
Sum and divide by 2
Results in 2 hr UH
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Example 5
Given the ordinates of a 4-hr unit hydrograph as below derive the ordinates of a 12-hr unit hydrograph for the same catchment
Time (hr) 0 4 8 12 16 20 24 28 32 36 40 44
Ordinates of 4-hr UH
0 20 80 130 150 130 90 52 27 15 5 0
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Equilibrium HydrographEquilibrium HydrographUniform Rain
Inflow = Outflow
Equiv to summing n
hydrographs in T
Produces S curveOne Hydrograph
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S-Curve
Also known as S-hydrograph Hydrograph produced by continous effective rainfall at a constant rate
for infinite period. Curve obtained by summation of an infinite series of D-h UH spaced D-h
apart.
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S-Curve Construction
Obtained by adding a string of D-h UH each lagged by D-hours from one another.
If Tb= base period of the UH, addition of only Tb/D UH are suffcient to obtained S-curve
U(t) = S(t)-S(t-D) or S(t) = U(t)+S(t-D)
Where S(t-D)= S-curve addition at time t S(t) = Ordinate of D-h UH at time t
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S-Curves for UHS-Curves for UH
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S-CurvesS-Curves
• Convert 2 hr Unit
hydrograph to 3-hr• Lag each 2-hr UH by
Duration D• Add to produce S-curve
S-curve
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Example 6
Solve previous example (Example 5) with S-curve method:
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Hydrograph Hydrograph ConvolutionConvolution
1
2
3
31 2
Add up the ordinates of all three to produce storm hydrograph
STORMHYDRO
Add and Lag Method
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Multi-Period Multi-Period StormStorm
• Pg - F = Net Rainfall
• RF units = UH duration
(i.e. 1 hour)
• Adjust UH by Net RF
• Add and Lag UH
• Produce Storm
Hydrograph
UH
STORM
NET RF
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Development Effects on UHDevelopment Effects on UH
Natural Partial Fully Developed