ERT 246 Hydrology & Water Resources

Engineering

Siti Kamariah Md Sa’at

School of Bioprocess Engineering, UniMAP

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