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Although records of rainfall exists to some extent, the actual record of rainfall is seldom available in such sufficiency (50 years) as to enable the Engineer to infer precisely the worst flood conditions for designing bridges.

2.2.1.1 The current practice generally followed for calculating the discharge at the bridge site is by using empirical formulae as detailed below for various regions.

(A) Inglis Formula (for Western Ghats and Tapi Valley)

Where Q = Discharge in cusecs (ft3/s) A = Catchment area in sq. miles.

(B) Modified Ingis Formula : (Upper parts of Western Ghats)

Where Q = Discharge in cusecs (ft3/s) A = Catchment area in sq.miles.

(C) Dicken’s Formula (for Vidarbha & Marathwada Regions)

Where Q = Discharge in cusecs (ft3/s) A = Catchment area in sq. miles.

C = Constant whose value varies from 800 to 1600 = 800 to 1000 for rainfall 25" to 50"

= 1000 to 1400 generally this value taken in M.P can be adopted for Vidarbha adjacent to Madhya Pradesh = 1400 to 1600 in Western Ghats.

The discharge is then calculated at the assumed H.F.L. by using Manning’s formula. The discharge calculated by Manning’s formula is tallied with the discharge obtained from above empirical formulae. By trial and error the H.F.L. is fixed.

The discharge calculated by the Manning’s formulae is tallied with the discharge by above empirical formulae for the Catchments Area up to the bridge site. In the areas where ‘Inglis flood’ is not expected, the discharge calculated by Manning’s formulae is tallied with either Modified Inglis formula or Dicken’s formula. If the discharge calculated by Manning’s formulae is less than the above empirical formulae discharge, the H.F.L. is raised suitably to get the ‘designed H.F.L.’ and vice-versa. The bridge is designed on the basis of H.F.L. so fixed with due consideration to observed flood level.

2.2.1.2 Discharge by Unit hydrograph Method

The Unit Hydrograph, frequently termed as the unit graph, is defined as the hydrograph of storm run-off at a given point in a river, resulting from an isolated rainfall of unit duration occurring uniformly over the catchment, and producing a unit run-off. The unit run-off adopted is 1 cm depth over a catchment area. The term “Unit-Rainfall Duration” is the duration of rainfall excess resulting in the unit hydrograph. Usually, unit hydrographs are derived for specified unit durations, say, 6 hours, 12 hours. etc., and derived unit hydrographs for durations other than these are converted into unit hydrographs of the above unit durations. The duration selected should not exceed the period during which the storm is assumed to be approximately

4 A A 4000 Q + =

[ ]

uniform in intensity over various parts of the catchment. A 6 hours unit duration is suitable and convenient for studies relating to catchments larger than 250 sq. km.

The unit hydrographs represents the integrated effects of all the basin constants, viz. drainage area, shape, stream pattern channel capacities, stream and land slopes.The derivation and application of the unit hydrograph is based on the following principles :

1) All the characteristics of the catchment of a river are reflected in the shape of the hydrograph of run- off.

2) At a given point on a river for all storms having the same duration of rainfall excess above this point and uniformly distributed with respect to time, the storm run-off. This implies that rainfall excess of say 2 cm within the unit of duration will produce a run-off hydrograph having ordinates twice as great as those of the unit hydrograph. Also, if individual hydrographs are obtained from separate periods of uniform rainfall excess that may occur throughout a storm discharge ordinates of the hydrograph are proportional to the total volumes of period, and these are properly arranged with respect to time, the ordinates of the individual hydrographs can be added to give ordinates representing the total storm run-off hydrograph for the entire storm period.

Three methods are generally available for giving unit hydrographs at any point in a river. a) By analysis of rainfall and run-off records for isolated unit storms.

b) By analysis of the run-off compound hydrographs.

c) By computation of synthetic unit hydrographs when sufficient rainfall and run-off data are not available.

The determinations of design flood, after the unit hydrograph has been derived, involves the following steps :

a) Division of catchment into sub-areas, if necessary.

b) Derivation of design storm and its apportionment to sub-area.

c) Determination of minimum retention rate and calculation of rainfall excess of design storm. d) Arrangement of design storm.

e) Application of rainfall excess to unit hydrographs for each sub-area.

f) Routing of flood for each sub-area to the point of collection of the whole catchment.

A rational determination of critical design storm for a catchment requires a comprehensive study of major storms recorded in the region and an evolution of effects of locals conditions upon rainfall rate. This is particularly necessary in the case if design storms covering a large area of several thousand square km. In the case of areas less than a few thousand square km certain assumptions can be made regarding rainfall patterns and intensity variations without being inconsistent with meteorological causes. They simplify design-storm estimation, but would entail high degree of conservation.

2.2.1.3 Discharge by Mannings :

The discharge calculated as above from Inglis/Modified Inglis formula has to fairly tally with the discharge calculated by Manning’s formula i.e. area-velocity method with use of hydraulic characteristics of stream. Hydraulic characteristics of the channel influencing the maximum discharge are-

(a) Velocity of flow, (b) Slope of stream,

(c) Cross sectional area of stream, (d) Shape and roughness of stream.

Where n = Rugosity coefficient depending on roughness of bed & bank values shall be as given in table-2.1

R = A/P i.e. Hydraulic mean depth. S = Hydraulic gradient

Q = Discharge m3/s.

A = Area of cross section in m2

V = velocities of respective compartments in m/s.

Variation in the velocity across the depth of Channel is indicated in the fig 2.2

2 1 3 2 S R n 1 m/s) (in V