# Important Flood Empirical Formulas

## Rational formula:

This formula is used for small catchment area for designers of sewers. Rational formula is:

Q = 0.27 CIA.

where C = constant depending on the nature of the catchment (0.1-0.9) and 1 for paused area.

I = Intensity of rainfall (mm/hr) and

A = Area of catchment, ha In English system

Q = C2A A in acres. I in in/hc Q in cfs

## Catchment Area formula:

This involves the catchment area only. They are derived for specific are and cannot be used university.

Q = CAn Where C and n are constants.

Some of the formulas are:

## Dicken formula:

Q = 825 A0.75 for A in sq-miles. Q = 11.4 A0.75 (cfs) for A in Sq-km

## Morgan’s formula:

- Q= 3000A0.5 (cfs) A in sq-miles. Morgan formula can be modified for return period as:
- Design flood = QP [T/500]1/3 Where Q = 3000 A0.5
- W.P creagar formula: This formula was solved by creagon from the study of peak flood in USA.Qp = CA ’ 10.894 in cumecs. Were C = 40 to 130 (lower value for ordinary. Flood and hgh value for intense & accite flood. A’ = catchment area in sq=miles = 0.39A Where A= catchment area in Km2
- Javis Formula:

QP = C √A in cumes. Where c varies between 1.77(min) and 177(max) limiting on 100% chance of flood and required are given by the value of c of 177.

## Modified Myers formula:

QP = 177P √A in cumces. Where P -1 for stream has greatest flood P < 1 for stream has smallest flood

## Flood routing:

Flood routing is a procedure to determine the magnitude of flow at point from knows as assumed.

## Hydrographs

This procedure known as flood routing. Routing by lumped system methods is called hydrolauce (lumped) routing.

## Routing by distribution:

This method is called hydrolauce (distributed) routing. For hydrology routing, input I(t), output Q(t) and storage S(t) as Functions of time related by continuity equation:

σS/σt = I(t)- Q(it).

I(t)- can be determined from inflow hydrograph Q(t)- can be determined from outflow hydrograph.

## Hydrologic & hydraulic flood analysis:

Hydrologic and hydraulic flood analysis are required for planning, design & management facilities. Analysis are needed to determine mar-flood elevation and depth, areas of inundation, sizing channels, levee height, design of highway crossing & culverts and many other.

## Return Period:

It is the time between two successive peak flow exceeding a certain return period.It is also called recurrence interval.

## Flood frequency:

It is also called probability of occurrence and expressed as

P(Q) = 1/T

where T is return period. And P(Q) is probability of occurrence 0 exceeds.

The probability of non-exceedence = P(Q—) = 1-P(Q) =1-1/T

## Plotting of Position:

The frequency of occurrences & return period is called plotting of position.

## a) Werball plotting position formula:

P(Q)= m/1+n ; where m is rank of flow in descending order, n is total number of events.

## b) Gungoston’s formula:

P(Q)= m-0.44/ m+0.12 = m-a/n+1-2a. For a= 0.44. c) Bolm formula: P(Q)= m-0.375/n+0.25 = m-a/n+1-2a A= 0.37

## Formula based on catchment Area & shape:

## Pettis formula:

Organized in northern US by Pettis & it is P(Q)= C(PB)5/4 cumces. Where P is probable 100 year max-one day rainfall in cm B= average width of basin in KM C= 1.5 for humid area and 0.2 for desert area. This formula is applicable to area ranging from 1600 to 16000Km2 If area is wider at lower end then the formula under predicts the result if the area is wider at upper then the formula over predicts A correction of 10 to 137 are required for wide variation.

## Catchment parameter formula:

The formula developed in Great Britain which takes into account the magnitude as well as characteristics of catchment area like shape etc. EMF= 0.835(area) 0.878+ (RMSD) 0.78* (soul) 6.533+ (1+URBA) 1.3007(S1000)

## Soil:

Soil index (composite index determine from soil survey maps) = (0.15S1+0.35S2+0.45S3+0.45S4+0.5S5)/ (S1+S2+S3+S4+S5) Where s1,s2,s3,s4,s5 represent categories of soil which represent proportion of soil type i.e amount of clay sand and graul etc in the soil. S1085 : slope between 10% & 85% of length of stream.

## Statistical studies of flood:

In these methods, the predictions of floods are made upon the available records of the past floods. These methods can be safely used to determine the max flood that is expected on rioes with a given frequency if sufficient pat record is available.