1.5.5 Maximum Flood Discharge & Yield

Flood Estimation

Maximum flood discharge is required for spillway design. As by any method exact amount and intensity of flood is difficult to predict, expected flood and its consequent damages can only be judged and approximated. Hence discretion and judgment of design engineer is utmost important.

Estimation of peak flow or flood can be made by following methods

1. By physical indication of past floods – ancient monuments on river banks bear past flood marks. Old people in villages know maximum water levels in past 35-50 years. Water line corresponding to high floods can be drawn on c/s of river. From such c/s water flow area, wetted perimeter and hydraulic mean depth can be computed. Knowing longitudinal slope of the channel, mean velocity can be calculated from Chezy’s or other suitable formula. This velocity can be used to multiply probable area of water section at the time of past flood to calculate flood discharge.
2. By empirical formulae – Many formulae have been derived for estimating flood flows. They can be safely applied to the areas for which they have been derived. As many variables are involved which depends upon country, past flows, topography, geological charactristics etc that can not be generalised.

Q = CAⁿ

Where Q= flood discharge, A = catchment area, n= flood index, C= flood coefficient

C & n depends upon various factors such as size, shape & location of catchment, topography of catchment, intensity & duration of rainfall.

Some of the empirical formulae are

Dicken’s formula – Q = CA ^{3/4 ( C=11.5 North India, C=14 to 19.5 Central India, C= 22 to 26 Western Ghats)}

Ingli’s formula –

Fanning’s formula Q = CA ^5/6

3. Determination of peak flood discharge using envelope curves

Data on Indian rivers was collected and two envelope curves, one for basins in South India and the other for northern and central India was developed. Here only drainage area is considered and other basin characteristics have been ignored, hence results will not be precise, but can be used for preliminary guidance. These curves should be revised time to time as more and more data becomes available.

4. Flood frequency studies- Probability concepts are used to study probable variations in flow so that design can be completed on calculated risk.

Flood frequency denotes likelihood of flood being equaled or exceeded. Denoted by F.

Recurrence interval denotes the number of years in which a flood can be expected once. This is denoted by T_r and is equal to T_r = ¹⁰⁰/_F

Determination of recurrence interval – If record of annual flood for N number of years is given, arrange them in decreasing order of their magnitude and mark their serial order. If a particular flood has serial no m in above order then its recurrence interval can be found by

California method T_r= or Hazens method T_r= or Gumbel’s method T_r = where C= Gambel’s correction factor.

To find any design flood of desired frequency, a plot of Q versus T_r or (F) is prepared on probability paper. From this plot unknown flood for any value of T_r can be found out.

5. Determination by Unit hydrograph method

Hydrograph is a graph in which discharge and velocity is plotted along Y axis and the time is plotted along X axis. The time may be in day, month or in hour. From the flood hydrograph we can find out

1. Rate of flood at site at any time.

2. Total volume of flood flow

3. Maximum rate of flow caused by flood.

The rise and fall of flood.

Yield

Yield is defined as the total quantity of water available from catchment area at the outlet in period of one year. This quantity is expressed as volume in units of Mm³(Million meter cube 10⁶ m³) or ha-m (hectare-meter 10⁴ m²). Yield can be estimated from either river gauging (mass curve analysis) or rainfall analysis. Yield computation is important as storage capacity depends upon it. While taking up any irrigation project, preliminary calculations are made by using empirical formulae, once it is finalized exact calculations are made by river gauging and correlating the rainfall run off, yield and verify correctness of the yield assumed for planning purposes.

Dependable yield

Dependable yield represents that value of yield which will be available for a given number of years per rainfall cycle. There are two methods of calculating dependable yield. first by assuming certain dependability percentage and second by adopting rainfall of an average bad year.

Dependability percentage - Suppose while designing a dam and a reservoir if design is based on minimum value of yield it will lead to small height and low cost of dam but will not utilize the yield fully every year. Whereas if design is based on maximum value of yield the height of dam will be large and reservoir will be filled up to 5% of time and more investment will be unnecessarily blocked.

For example if at a site minimum and maximum yield is 100 and 500 Mm³ in 50 years, then for economy and optimum utilisation of resources the design should be based on dependability percentage (p) between 100% and 2% . Small and medium reservoirs are designed for p=60% while larger ones are designed for p=75%.

Average bad year – For small project where detailed data is not available, design may be based on rainfall of average bad year. A bad year is one in which the rainfall is less than 80% of the average annual rainfall. Thus rainfall for an average bad year will be equal to 80% of average annual rainfall and yield available from this rainfall will be dependable yield. This method is more approximate than earlier.

Stream Gauging

Stream gauging means to determine the characteristics of stream flow. It includes determining discharge ( Q = A x V) that means area and velocity of flow.

Following are the common methods to determine discharge of river, canal or channel

Area-velocity method

Weir method

Chemical method

Venturi flume method

In determining area of a stream we’ll consider two factors of it namely width and depth.

Width Measurement – To determine width of a open channel having width up to 150m a wire rope is stretched across the channel and segments are marked on the wire rope by means of pendants. Precaution for sag correction is taken. For more than 150m width, pivot point method based on similar triangles is used.

Depth measurement –

By Sounding Rod – In this method a graduated wooden rod 5-8 am in diameter, enameled steel pipe or flat gauge is used. Graduations are in meters and centimeters. The bottom of sounding rod is fitted with 10-15cm diameter disc, to prevent its sinking in bed. The depth is directly measured by lowering sounding rod in the channel. This method is used for shallow channels.

By lead line – For deeper channels having high velocity, observations are done with the help of weighted lead line or log line which essentially consists of copper cores covered with hemp and weight fixed at one end. These lines do not shrink when wet, neither they stretch when under weight and also remain free from knots. The lead weight is in shape of frustum of a cone 5-10 kg depending upon velocity of flow.

By echo sounder – This method is based on principle of electricity . Echo sounder transmits sound waves from the water surface to the bed of channel. When these sound waves reflect back from the bed they are arrested by the transmitter. Time of transmission and time of reception is plotted on a graph. The depth of channel is worked out from these records. This method is generally adopted by ships to determine depth of channel.

Measurement of velocity

To obtain average velocity of the channel, 3 to 4 velocities are taken. Velocity of flow can be determined by one of the following methods.

By surface floats – These are usually wooden discs 7.5 to 15cm in diameter. Its weight and shape is such that it is least affected by disturbing forces such as eddies, winds etc. They are painted or flag is fitted at top in order to distinguish it from distance. Three wire ropes PQ, RS & XY are stretched at 15m apart across the channel as shown in fig over poles. The width of channel is divided into eight/ten equal parts by handing pendants. Another wire rope say AB is stretched at about 7m upstream of PQ. Floats are release from AB from the middle of each part and their timing from PQ to RS is recorded using stop watch. Floats shall be picked up at XY. Surface velocity of current is then calculated by

Mean velocity is obtained by multiplying the coefficient 0.8.

By velocity rods – Velocity rods are are wooden or steel tubes of 2.5 to 5cm in diameter. Length of velocity rod is kept 0.94D where D is depth of channel. Weights are provided at the bottom, so as to keep rods in vertical position with 2.5cm part above water. To facilitate visibility flag is provided at top. As depth of channel is varying, rods of different lengths are required. The velocity rods are released in the same way as floats and time taken in travelling from one section to another is noted and velocities at each section is calculated. Velocity rods give direct mean velocity of the channel.

Double or subsurface floats - In this method two floats are used one on the surface and another at distance 0.2m D distance from bed.

By current meter – Current meter mainly consists of a wheel carrying series of cups that revolves on a vertical axis by the force of the current, contact breaker, tail vane and the counter weights. A chart known as rating chart is supplied with current meter, which gives the relation between the velocity of the water and the number of revolutions of the wheel per minute.

When the current meter is suspended in water, the velocity of flow causes the wheel to rotate. Current meter is fitted with a device to record number of revolutions of the horizontal wheel due to velocity of flow. Generally velocities at 0.2D and 0.8D are determined and average value is taken as mean velocity.

N=No of revolutions made by wheel per second, a & b are constant given by manufacturer.

The boat is generally used for small velocities but for higher velocities and rough waters boat is generally anchored.

N.B. - Weir and venturi flume method is not discussed as same has been covered under hydraulics.