Unit Hydrographs of Different Durations

Lack ofadequate data normally precludes development ofunit hydrographscovering a wide range ofdurations for a given catchment. Undersuch conditions aD hour unit hydrograph is used to develop unit hydrographs of differing durations nD. Two methods are available for this purpose.

 Method of Superposition

If a D-h unit hydrograph is available and it is desired todevelop a unit hydrograph of nDh, where n isan integer, it is easily accomplished by superposing n unit hydrograph with each graph separated from the previous on by D-h.

Example 1

The ordinates of a 6-h unit hydrograph are given

Derive a 12-h unit hydrograph for the catchment.

Answer 

S-curve

If it is desired to develop a unit hydrograph of durationmD, where m is a fraction, the method of superposition cannot be used. A different technique known as the S-curve method is adopted in such cases, and this method isapplicable forrational values of m. 

The S-curve, also known as S-hydrograph is a hydrograph produced by a continuous effective rainfall at a constant rate for an infinite period. It is a curve obtained by summation of an infinite series of D-h unit hydrographs spaced D-hapart.

Fig .1 shows such a series of D-hhydrograph arranged with their starting points D-hapart.

 At any given time the ordinates of the various curves occurring at that time coordinate are summed up to obtain ordinates of the S-curve. A smooth curve through these ordinate results in an S-shaped curve called S-curve.

Fig. .1S-curve.

This S-curve is due to a D-h unit hydrograph. It has an initial steep portion and reaches a maximum equilibrium discharge at a time equal to the first unit hydrograph. The average intensity of ER producing the S-curve is 1/D cm/h and the equilibrium discharge,

Where A is area of catchment in km2 and D is duration in hours of ER of the unit hydrograph used in deriving the S-curve.

 By definition an S-curve is obtained by adding a string of D-h unit hydrographs each lagged by D-hours from one another. Further, if Tb = base period of the unit hydrograph, addition of only Tb/D unit hydrographs are sufficient to obtain the S-curve. However, an easier procedure based on the basic property of the S-curve is available for the construction of S-curves.

or

 (26.1)

The term S (t-D)could be called S-curve addition at time t

For all

 Example 2

The ordinate of 2-h unit hydrograph of a basin are given:

Compute a 4-h unit hydrograph ordinate and plot: (i) the S-curve (ii) the 4-h UG