1 HYDROLOGICAL CYCLE

Total 1400 million/ 3 Km
World Water balance
For a given catchment in a time interval Dt,

1.1 Water budget equation

Inflow – Outflow = Storage [continuity equation]

This continuity equation expressed in terms of various phase of hydrological cycle is called water budget equation/hydrological budget equation.

P-R-E-T-G= DS

P = Precipitation,
R= Surface water inflow,
Es = Evaporation,
Ts = Transpiration,
G = Ground water appearing as surface water,
I = Infiltration
In terms of rainfall-runoff relationship water budget equation can be represented as
R = P-L
L = Losses = water not available to runoff due to (I, E, T and depression storage)

[Q] Which of the following is true?

(a) Precipitation = evaporation + run off ü SSC2018-23SepE
(b) Precipitation = infiltration + runoff
(c) Runoff = Evaporation + precipitation
(d) Evaporation = precipitation + runoff

1.2 Forms of Precipitation

1.2.1 Rain

It is the most common form of precipitation.

In this the water droplet size are larger than 0.5 mm and smaller than 6 mm.

Types	Intensity
Light Rain	Trace to 2.5 mm/h
Moderate Rain	2.5 mm/h to 7.5 mm/h
Heavy Rain	>7.5 mm/h

Rainfall intensity Unit is mm/h.

1.2.2 Snow

Snow is frozen water vapour. It contains a mixture of H₂O and air molecules. It creates beautiful snowflakes. 0.06 – 0.15 g/cm³ an average of 0.1 g/cm3

1.2.3 Drizzle

Fine Sprinkles of numerous water drops of size less than 0.5 mm and intensity is less than is 1 mm/h.

1.2.4 Glaze

When rain or drizzles comes in contact with the cold ground at 0℃ and from an ice coating.

1.2.5 SLEET

It is frozen raindrops of transparent grains which form when rains fall through air at subfreezing temperatures.

1.2.6 Hail

Size more than 8 mm.

1.2.7 Mist

0.005 – 0.05mm

1.2.8 Graupel

2 – 5mm

Types	Discerption
Light Rain	0.5 mm
Snow	0.06 – 0.15 g/cm3
Drizzle	0.5 mm, i < 1 mm/h.
Glaze	cold ground at 0℃
Sleet	frozen raindrops
Hail	8 mm.
Mist	0.005 – 0.05mm
Graupel	2 – 5mm

1.3 Instrument name Used for measuring

SN	Instrument name	Used for measuring
1	Anemometer	Wind velocity
2	Pluviometer	Rainfall depth
3	Lysimeter	Evapotranspiration
4	Atmometer/ Open pan	Evaporation
5	Phytometer	Transpiration
6	Hygrometer/ Psychomotor	Relative humidity
7	Tensiometer	capillary potential
8	Pyranometer	Radiation from sun

2 RAINFALL

Avg. annual rainfall ज्ञात करने के लिए 35year तक का data collect किया जाता है।

India avg. annual rainfall 118cm – 120cm

India में orographic rainfall होती है।

2.1 TYPE OF RAINFALL

2.1.1 Convectional Rainfall

The air being heated becomes light and rises in convection currents. As it rises, it expands and loses heat and consequently, condensation takes place and cumulus clouds are formed. This process releases latent heat of condensation which further heats the air and forces the air to go further up.

Convectional precipitation is heavy but of short duration, highly localized, and is associated with a minimum amount of cloudiness. It occurs mainly during summer and is common over equatorial doldrums in the Congo Basin, the Amazon basin, and the islands of south-east Asia.

2.1.2 Orographic Rainfall

When the saturated air mass comes across a mountain, it is forced to ascend and as it rises, it expands (because of a fall in pressure) and the temperature falls, and the moisture is condensed.

This type of precipitation occurs when warm, humid airstrikes an orographic barrier (a mountain range) head-on. Due to the initial momentum, the air is forced to rise. As the moisture-laden air gains height, condensation sets in, and soon saturation point is reached.

The surplus moisture falls as orographic rainfall along the windward slopes. The chief characteristic of this sort of rain is that the windward slopes receive greater rainfall. After giving rain on the windward side, when these winds reach the other slope, they descend, and their temperature goes up.

2.1.3 Frontal Precipitation

When two air masses with different temperatures meet, turbulent conditions are produced. Along the front convection takes place and causes precipitation. For instance, in northwest Europe, cold continental air and warm oceanic air converge to produce heavy rainfall in adjacent areas.

2.1.4 Cyclonic Rain

Cyclonic Rainfall is convectional rainfall on a large scale. The precipitation in a tropical cyclone is of conventional type while that in a temperate cyclone is because of frontal activity. 1. Cyclonic precipitation

precipitation pressure difference

2.1.5 Monsoonal Rainfall

This type of precipitation is characterized by the seasonal reversal of winds which carry oceanic moisture (especially the southwest monsoon) with them and cause extensive rainfall in the south and Southeast Asia. (Would learn more while studying Indian Monsoons).

2.1.5.1 Note: –

2.1.5.2 Index of wetness

Index of wetness [I.O.W.]

I.O.W	Year
<100%	Bad
=100%	Normal
>100%	Good

2.2 MEASUREMENT OF RAINFALL

Rainfall measurement, rain gauge, ombrometer, pluviometer, udometer Raingauge

Rain gauge Type

2.2.1 Recording Type

The recording gauges produce a continuous plot of rainfall against time and provide valuable short duration data on intensity and duration of rain a for hydrological analysis of storms. The commonly used recording gauge are:

1. Natural Syphon Type Rain gauge

This type of recording rain-gauge is also known as float type gauge.

=> Here the rainfall collected by a funnel shaped collector is lead into a float chamber causing a float to rise.

=> As the float rises, a pen attached to the float through a lever system records the elevation of the float on a rotating drum driven by a clockwork mechanism.

Note: This type of rain gauge is adopted as standard recording type rain gauge in

India.

2. Tipping bucket method

-The record from Tipping bucket gives data on the intensity of rainfall.

-The main advantages of this type of instrument is that it gives an electronic pulse output that can be recorded at a distance from the rain gauge

3. Weighing bucket method

This instrument gives a plot of the accumulated rainfall against the elapsed time, i.e. mass curve of rainfall (accumulated precipitation against time).

The catch from the funnel empties into a bucket mounted on a weighing scale. The weight of the bucket and its contents are recorded on a clockwork- driven chart.

Note: The weighing type is suitable for measuring all kinds of precipitation (rain, sleet etc.)

2.2.2 Non-recording type

नॉन रिकॉर्डिंग रैन गेज सिर्फ Rainfall की depth दिखाते है।

1. Symon’s Rain gauge

Standard Non-recording rain gauge
Symon’s rain gauge SSC-2011, SSC-2018-23SEP-M

The non-recording gauge extensively used in India is the symon’s gauge.
For uniformity, the rainfall is measured every day at 8 : 30 am (1ST) and is recorded
as the rainfall of that day.

Standard recording rain gauge -Natural syphon

3.Total rain gauge minimum 10% rain gauge recording type

2.3 OPTIMUM NO. OF RAIN GAUGE

C_v= Coefficient of variation
E = Standard error

For Accurate rainfall measurement rain gauge, we need infinite.

Double mass curve rainfall is used to find out the consistency of rainfall.

2.4 MEAN PRECIPITATION OVER AN AREA

To convert point rainfall values at various station into an average value ove a catchment the following three methods are used.

2.4.1 Athematic method

2.4.2 Thiessen polygon method

इस method में पहले सभी rainfall station को straight line द्वारा जोड़ा जाता है। और इस बहु भुज को simple triangle में बाटते है। फिर इस triangle की सहायता से avg rainfall ज्ञात किया जाता है।

2.4.3 Isohyet method

Isoheytal is a line joining points of equal rainfall magnitude.

इस method Isohyet की सहायता Avg. rainfall को ज्ञात किया जाता है। rain gauge की संख्या अधिक होने पर यह best method होता है।

Isohyet

– Same rainfall depth point को मिलाने वाली रेखा Isohyet कहलाती है। SSC-2018-25SEP-M

Isoplith

– same evapo transpiration वाले point को मिलाने वाले रेखा Isoplith कहलाती है।

Isochrone

– Outlet पर same time में पहुंचने वाले बिंदुओं को मिलाने वाली रेखा Isochrone कहलाती है।

Mass curve of rainfall is a plot of accumulated precipitation against time.
Isobar map is the plot of line marking places of equal barometric pressure.
Theissen polygon is the area of catchment bounded by perpendicular bisector of line joining rain gauge and catchment boundary

2.4.4 Rain gauge density

Particular area में लगे rain gauge की संख्या rain gauges density कहलाती है।

Area	Rain gauge density
Plain	1 RG/ 520 km²
Area having 1000m elevation	1 RG/ 260-390 km²
Hilly	1 RG/ 130 km²

IMD Used the Rain Gauges Whose Collector Aperture Is 100-200 Km².

As it can be seen from the above table, for plain 1 no of rain gauge required for an area of 520 km2. Hence, number of rain gauge stations required for an area of 5200 km2 in planes ∴ N = 5200/520 = 10 stations.

2.5

3 EVAPORATION

Surface evaporation

Factors affecting evaporation
Evaporation surface area
Evaporation wind velocity
Evaporation Temprature
Evaporation Vapour pressure

3.1 Measurement of evaporation

Evaporation is measured using an open pan. The most commonly used evaporation pan is the Class A evaporation pan.

Class A evaporation pan is cylindrical in shape having 120.7 cm diameter and has a depth of 25 cm.

This pan rests on a carefully levelled, wooden base and is mostly enclosed by a metal fence to prevent animals from drinking from it.

1. Class A evaporation pan method

इस method में G.I. का pan काम में लिया जाता है जिसका diameter 1210 mm a depth 255 mm होती है। diameter 1210 mm

2. ISI evaporation pan method

इस method में copper के pan का use किया जाता है जिसका diameter 1220 mm a depth 255mm होती है।

3. Colorado -Sunken method

[lake evaporation = C_P x pan evaporation

Method	C_P	Diameter (mm)	Depth (mm)
Class A pan	.70	1210 mm	255 mm
ISI pan	.80	1220 mm	255 mm
Colorado Sunken	.78	920 Sq.	460 mm

3.2 Prevention of evaporation

Cetyl Alcohol is used to reduce the evaporation rate. Evaporation chemical Hexadecanol- Cetyl alcohol

[Q] Calculate the evaporation (mm) from a pond, if the pan evaporation is 45 mm, the pan coefficient is 0.70. SSC-201727Jan-M

(a) 13.5 (b) 19.28 (c) 31.5 (d) 64.28

Sol-(c) Evaporation from field

= Pan coefficient * Pan evaporation

= (0.70 * 45) = 31.5 mm.

Hence, the evaporation from a pond is 31.5 mm.

[Q] An irrigation canal Is 80 km tong. It has an average surface width of 15 m. If the evaporation measured In a Class A pan Is 5 mm/day the volume of water evaporated. In a month of 30 days (take pan coefficient as 0.7)

Sol-(c) Evaporation from class A pan = 5 mm/day
Lake evaporation = Cp * Pan evaporation
= (0.70 * 5) = 31.5 mm.

Total evaporation in 30 days x 30

0.7*5*10^-3*80.10³*15*30

=126000 m³

3.3 Transpiration

पेड़ पौधों का पतियों से पानी का वाष्प रूप में निकालना transpiration कहलाता है।
Phytometer के द्वारा transpiration ज्ञात किया जाता है।
Lysimeter के द्वारा evapo-transpiration ज्ञात किया जाता है।

3.4 Evapotranspiration Equation:

There are large number of evapotranspiration equations available, they are purely empirical and not theoretical. The most used equation is Penman’s Equation.

Penman’s Equation:

Penman’s equation is based on sound theoretical reasoning and is obtained by combination of energy and mass transfer approach.

PET=AHn+EaγAγ��=��+��γ�γ

PET = Daily potential evapotranspiration (in mm per day)

A = Slope of the saturation vapour pressure vs. temperature curve at the mean air temperature (in mm of Hg per °C)

Hn = Net radiation

Ea = Parameter including wind velocity and saturation deficit.

γ = Psychromrtic constant = 0.49 mm of Hg/°C

3.5 Aridity index [A.I.]-

AET= Actual evapo transpiration

PET= potential evapo transpiration
इसके द्वारा agricultural draught को ज्ञात किया जाता है।

An aridity index (AI) is a numerical indicator of the degree of dryness of the climate at a given location.

The relation between actual evapotranspiration and potential evapotranspiration with different soil moisture conditions is as follows:

If the water supply to the plant is adequate, soil moisture will be at field capacity then, the ratio of AET to PET = 1.
If the water supply to the plant is inadequate, then the ratio of AET to PET is less than 1.
In clayey soils, AET/PET is almost equal to 1.
When the soil moisture approaches the permanent wilting point, AET tends to 0.

4 INFILTRATION

पानी के ground level से ground water table तक जाने को किया infiltration कहलाती है। व जिस दर से पानी जाता है। उसे infiltration rate कहा जाता है।

4.1 Infiltration capacity-

Infiltration maximum rate to infiltration capacity कहा जाता है। Infiltration capacity को Horton curve द्वारा ज्ञात किया जाता है।

4.2 ϕ-index & W- index

यह दोनों ही avg rainfall को बताते है। जिससे ऊपर हुए rainfall हमें runoff के रूप में प्राप्त होती है।

ϕ-index	W- index
Initial Loss is not Separated.	Initial Loss is Separated.
It is Calculated from the Rainfall excess period

Infiltration rate (infiltration capacity) so defined that the area of hyetograph above.
f-index gives the depth of surface runoff/direct runoff/effective rainfall/rainfall excess.

Hence, area of hyetograph below f-index approximately gives depth of infiltration.

Rainfall excess period- यह वो time duration है इसमें कुछ runoff प्राप्त होता है।

Flooding-Type Infiltrometer (f_f)

As the flooding-type infiltrometer measures the infiltration characteristics at a spot only, a large number of pre-planned experiments are necessary to obtain representative infiltration characteristics for an entire watershed.

Disadvantages of flooding-type infiltrometers are

The raindrop impact effect is not simulated
The driving of the tube or rings disturbs the soil structure

Rainfall Simulators(f_r)

Rainfall simulators are one of the most popular research devices for studying the impacts of rainfall on the activation of runoff, infiltration, and sediment transport mobilization in the landscape.

Rainfall simulator type infiltrometers give lower values than flooding type infiltrometers. This is due to the effect of the rainfall impact and turbidity of the surface water present in the former. i.e f_f > fr

5 STREAM GAGING

Stream gaging is a technique used to measure the discharge, or the volume of water moving through a channel per unit time, of a stream. The height of water in the stream channel, known as a stage or gage height, can be used to determine the dischage in a stream.

5.1 STREAM FLOW MEASUREMENT

The science of water measurement and water flow stream is known as Hydrometry.

It is a only part of hydrological cycle that can accurately.

5.1.1 Stage measurement

The height above which Stream flow is measured is called stage.

Stage measurement Stream के bottom से पानी की top surface के बीच की दूरी Stage measurement method कहलाती है।

5.1.2 MANUAL RECORDING

1. Staff gauge

A staff gauge is a vertical scale installed in a water body, such as a river or stream, to measure the water level or stage. It typically consists of a numbered scale marked on a vertical staff or pole installed in the water. The height of the water surface above a reference point on the staff gauge is referred to as the stage, and it is an essential parameter for monitoring river or stream flow.

2. Wire gauge

It is a gauge used to measure the water-surface elevation from above the surface such as from a bridge or similar structure. In this a weight is lowered by a reel to touch the water surface. A mechanical counter measures the rotation of the wheel which is proportional to the length of the wire paid out.

5.1.3 AUTOMATIC STAGE RECORDERS

3. Bubble gauge

In this, compressed air or gas bleeds out at a very slow rate at the bottom of the river. A pressure gauge measures the gas pressure which in turn is equal to the water column above the outlet.

4. Float gauge

Stream velocity का measurement current meter के द्वारा किया जाता है।

Most common type. Float operated in stilling basin is balanced by a counterweight over the pulley of the recorder. Displacement of float due to rising and lowering of water surface elevation caused angular displacement of pulley and input shaft of the recorder.

5.2 MEASUREMENT OF VELOCITY

5.2.1 Float

This method involves the use of a floating object, such as a float or buoy, to track the movement of the water and calculate the velocity.

Canster Float

Or Rod Float.

5.2.2 Current Meter

This consisting A rotating element which rotates due to reaction of river or stream.

The number of rotations is made by current meter is counted in order to find out the values of Rotation per second RPS.

A current meter is an instrument used to measure the velocity of flow at a required point in the flowing stream.

In general, it consists of a wheel or revolving element containing blades or cups, and a tail on which flat vanes or fins are fixed.

A current meter measures the velocity at a single point, and several measurements are required to calculate the total flow.

The procedure is to measure and plot on graph paper the cross-section of the stream and imagine that it is divided into strips of equal width. The average velocity for each strip is estimated from the mean of the velocity measured at 0.2 and 0.8 of the depth in that strip. This velocity, times the area of the strip, gives the flow for the strip and the total flow is the sum of the strips.

For shallow water, a single reading is taken at 0.6 of the depth instead of averaging the readings at 0.2 and 0.8 of the depth.

Mid-Depth Velocity (20 – 80% of Depth); Many hydrologists and scientists often prefer to calculate the average velocity at the mid-depth of the stream, which typically corresponds to a depth between 20% and 80% of the total water depth. This is a common choice because it provides a good representation of the main flow velocity in the stream, as it avoids the potentially slower-moving surface layer and the slower-moving near-bed layer.

In a large river, the depth of river is 15 m. Up to which depth the current meter should be lowered to measure the average velocity?

Given; depth of river = 15 m Average velocity will be calculated at 0.2 × 15 = 3 m and 0.8 × 15 = 12 m. Hence option (4) is the correct answer.

(a)Vertical axis current meter

It is a device used to measure the speed and direction of water currents in a vertical profile.

Vertical axis current meters are oriented perpendicular to the direction of the current.

Price current Meter

Gurley Current meter

Normal Range of is 0.15 m/s to 4.0 m/s.

Disadvantage – The instrument shows a positive velocity if lifted in still water.

(b)Horizontal axis current meters,

which are aligned with the flow of water,

5.3 3. DISCHARGE MEASUREMENT

5.3.1 Direct Method

1. Velocity area method

It is a popular method of river discharge measurement. It is also called “Standard Current meter method”.

In this method section of river is divided into number of segments.

The segment width us not greater than 1/15 to 1/20 of the width of river.

Discharge of each segment is less than is 10%.

Difference in velocities of each segment is not less than is

2. Moving boat method

In this method a current meter is installed on boat which moves one bank to another bank of river.

An angle of indicator is also provided in the boat which records direction of resultant velocity.

3. Ultrasonic Method

In this method transducer is introduced in on the both side of rivers.

4. Dilution Method

This method is based on law of conservation of mass in this method a chemical compound called Tracer such as sodium chloride, sodium di chromate is coloured with dye etc is introduced in the stream at given location.

5.3.2 Indirect Method

In this method, we include such technique which find the discharge with the help of relationship between discharge and depth.

1. Slope area method

The Slope-Area Method is a technique used to estimate river discharge by measuring the slope of the water surface along a known reach (section) of a river and combining it with the cross-sectional area of the flow.

This method is used to estimate flood discharge based on high water marks left over in the past.

This method is based on the principle of the continuity equation, which states that the product of cross-sectional area and velocity is constant for steady flow.

In this method we find the discharge with help of manning’s equation.

This equation is used to relate the depths at either end of river reach to the flowing discharge in that reach and in this way by knowing the depth, we find out the discharge.

The selection of reach is the most important part of the slope area method. Following criteria should be followed.

The accuracy of high water marks must be good.

The reach should be straight and uniform so far as possible, if it is not possible then choose a gradually contracting section.

As the length of reach increases, the accuracy in the discharge measurement also increases.

A reach length should be greater than 75 times the mean depth.

2.Weir and Notches

The Weir and Notches Method involves the use of structures like weirs and notches to create a constriction in the river or stream flow. The water flow over these structures is then measured to estimate the discharge. Weirs are typically solid barriers that span the width of the river, creating a rectangular or trapezoidal opening over which water flows. Notches are openings with specific shapes cut into plates or structures to regulate and measure flow.

5.4 FLOOD/RUNOFF MEASUREMENT

Peak Discharge is a function of area it is comes dues to various studies carries by departments.

5.4.1 1. Rational method

Where K= runoff coefficient

cp = critical rainfall

A = catchment area in hectare

Formula is only for critical rainfall condition valid

Critical rainfall – rainfall duration time of concertation rainfall critical rainfall

5.4.2 Empirical formula

(a) Dicken’s formula

(1865)- Mainly used in northern India

A= Area in km²
C_D= Dickens Constant 6 to 30
Q = in m³/s

Region	Value of C_D
North Indian Plains	6
North Indian Hilly Regions	11-14
Central	14-28
Coastal Andhra and Orissa	22-28

(b) Ryve’s method

(South Regions)-

= 6.8 area within 80 km of east coast

= 8.5 area within 80 – 160 km of east coast

= 10.2 for limited area near hills

For Tamil Nadu and Andhra Regions parts of Karnataka and Andhra Pradesh.

(c) Inglis method

(1930) Western Ghats mainly for fan shaped basin- Q= 124.A^1/2

3. Probability method

P=Probability
T= Return period or recurrence interval
n = No.of year

Reliability- [1-P]ⁿ

Risk-1-[1-P]ⁿ

6 HYETOGRAPH

Graph between rainfall intensity rainfall duration graph SSC-2016-2March-M
•A hyetograph is a plot of the average intensity of rainfall against the time interval.

The hyetograph is derived from the mass curve and is usually represented as a bar chart.
The area under a hyetograph represents the total precipitation received in the period.

6.1 Mass curve of rain fall

A mass curve of rain fall is a plot of the accumulated precipitation against time.

Mass curve of rainfall are used in extracting the information on the duration and magnitude of a storm.

6.2 Depth-Area Curve

The Depth-Area Curve is a graphical representation of the relationship between the depth of water in a river or stream and the corresponding area of the cross-section of the water body. In hydrology, the depth-area curve is an essential tool for estimating the flow rate of a stream or river.

6.3 Depth-Area-Duration (DAD) relationship

Depth of rainfall at a rain gauge station is called point rainfall.
A depth area duration curve expresses graphically the relation between progressively decreasing average depth of rainfall occurs progressively increasing area from the centre of the storm outward to its edge for a given duration of rainfall.

जैसे जैसे Area बढ़ेगा तो Depth कम होती जाती है।

For a rainfall of a given duration, the average depth decreases with the area is an exponential function given by
P = P_o. e^-KAn

P = Average depth in catchment over area A (km²).

P_o = Highest amount of rainfall in catchment at the storm curve

K_n = Constant

6.4 Double mass curve

Inconsistency of record is corrected by using double mass curve technique.

Thus, after correction, the previous record become consistent with present day environmental and land use condition.

Double mass curve plots between accumulated precipitation of the station (i.e. EP_X) on y axis v/s the accumulated values of the average of the group of base stations (i.e. EP_avg)

Some of the common cause for inconsistency of the records are
Shifting of rain gauge station to a new location.
Neighbourhood of the station undergoing a marked change.
Replacement of old instrument by new one.
Change in the ecosystem due to calamities such as forest fires, landslides etc.
Occurrence of observational error from a certain data.

6.5 Intensity Duration Curve

Rational method of estimating peak runoff off, may be used precisely for areas than 50 hectares. SSC-2016-4March-M

Q_p = Peak rate of runoff in (cumecs)

K = Coefficient of runoff.

A – Drainage area of basin in hectare

Pc = Mean rainfall intensity in (cm/hr) for duration equal to T.
The duration of rainfall for the use of rational formula must be Tc (time of concentration) or more.

This formula is not applicable for area more than about 5000 hectares.

Time of concentration is the period after which the entire area starts contributing to the run off.

[Q] If the length of overland flow from the critical point to the mouth of drain is 13.58 km and difference in level between the critical point and drain mouth is 10 m, the inlet time is According to Kirpich equation SSC-2016-4March-M

This is the most popularly used formula relating the time concentration of the length of travel and slope of the catchment.

[Q] The intensity of the rainfall for successive. 1 hour’s period of a 6 hours storm is 2, 6, 8, 9, 7 and 3 cm/hr. The runoff is 4 cm/hr. Calculate f -index (cm./hr). SSC-2017-25Jan-M

Given that: Duration of storm = 6 hr.
Runoff = 4 cm/hr.
Total surface runoff = 4 * 6 = 24 cm
Hyetograph for the given intensity of rainfall.
Assume f -index to be lower than 2 cm/hr.
For sum off of 4 cm/hr, total run off will be calculated for the effective duration.
Thus, assuming, f < 2 cm /hr

Then,

(2 – f) + (6 – f) + (8 – f) + (9 – f) + (7 – f) + (3- f) = 4×6

=> 35-6 f = 24

=> f = 1.833 cm/hr < 2 cm/hr

But, while assuming, 2 cm/hr b< f < 3 cm/hr. effective duration of rainfall is 5 hr.

(6- f)+ (8- f)+ (9- f)+ (7- f)+ (3- f)

= 4×5

=> 33 —5 f = 20

=> f = 2.6 cm/hr

This assumption is also correct,

again, assuming 3 cm/hr. < f < 6 cm hr. effective

duration of rainfall will be 4 hr.

Thus,

(6 – f) + (8 – f) + (7 – f) + (9 – f) = 4 x 4

=> 30 -4 f = 16

=> f =3.5 cm/hr.

Which is also correct. But for single rainfall f – index should be unique. Thus there might be

problem in question.

[Q] Calculate the runoff (cm) from a rainfall of 3 hours. The intensity of the rainfall is 2 cm/hr. The evaporation and infiltration losses are 8 mm and 16 mm respectively.

(a) 1.2 (b) 2.8 (c) 3.6 (d) 6.8 SSC-2017-27Jan-M

Given,

Rainfall intensity = 2 cm/hr

duration of rainfall = 3 hr

evaporation loss (£) = 8 mm =0.8 cm

infiltration loss(Z) = 16 mm = 1.6 cm

by water budget method P — R-E-T-G = Ds
Precipitation (P) = 2 * 3 = 6 cm

Hence 6-R-0.8-0-1.6 = 0
Runoff (R) = (6 – 2.4) cm = 3.6 cm

[Q] What is the rainfall intensity (mm/hr) according to the formula given by British Ministry of Health, if the time of concentration is 540 seconds? SSC-2017-27Jan-E

(a) 20 (b) 30 (c) 40 (d) 50

6.6 British ministry of health formula

(for storm duration of 5 to 20 minutes)

(for storm duration of 20 to 100 minutes)

I-> Intensity of rainfall, mm/hr

f-> duration of storm in minutes

Given that:

Duration of storm = 540 seconds = 9 minutes

I = 40 mm/hr.

Hence, the intensity of rainfall is 40 mm/hr.

Note: Time of concentration: The period after which the entire catchment area will start contributing to the runoff is called as the time of concentration.

[Q] Rainfall of Intensity 20mm/hr occurred over a watershed of 1 km per square of duration of 6 hours. It measures a direct runoff for a volume of 30,000 m3 in the stream. Find the precipitation NOT available for runoff in this case? SSC-2018-25Sep-M

Solution-Rainfall intensity = 20 mm/h

Duration = 6 hours

Total rainfall depth = 20 * 6 = 120 = 12 cm

Direct runoff = 30,000 m³

Runoff depth = = 3

Precipitation not available for runoff

= 12 – 3 = 9 cm

[Q] Which of the following statement is true for the linear reservoir? SSC-2017-23Jan-E

(a) Storage is proportional to inflow discharge

(b) Storage is proportional to outflow discharge
(c) Storage is proportional to square of inflow discharge

(d) Storage is proportional to square of outflow discharge

Solution-For the linear reservoir, storage varies linearly with the outflow discharge. Such a storage is known as linear storage or linear reservoir (or reservoir type storage) in which storage is only function of outflow discharge.

Note: Linear channel: The channels in which inflow hydrograph passes through a reach with only translation and no attenuation.
In linear reservoir, s= kQ By Muskingum equation

7 HYDROGRAPH

– Graph between runoff discharge duration graph

Hydrograph- runoff discharge duration graph

Rising limb is depends on catchment area & rainfall intensity.

Falling limb is only depends on catchment area.

7.1 Factor’s affecting shape of hydrographs

7.1.1 1. Shape of catchment area

7.1.2 2.Stream Density

7.1.3 3.Draingae Density

As drainage density increase peak discharge increase.

7.1.4 Run off Depth by Hydrograph

h= depth in cm
A = catchment area in km2
o= discharge in m3/sec
t= time in hr
= area of hydrograph

7.2 Unit Hydrograph

Unit duration unit depth के लिए of hydrograph unit hydrograph कहलाता है।

यह time invariance व linear response पर आधारित होता है।

The basic principle of Unit Hydrograph Theory is-

TIME INVARIANCE
LINEAR RESPONSE

इसे Sherman ने दिया इसके द्वारा किसी भी duration व depth का Hydrograph बनाया जाता है।

The main objective of UH is to predict the flood Hydrograph.

Flood Hydrograph – Base Flow = Direct Runoff Hydrograph (DRH)

Direct Runoff Hydrograph (DRH) /(ER) Effective Rainfall = Unit Hydrograph (UH)

UH * ER = DRH + BF = FH

S-curve hydrograph Constant discharge a Indefinite A infinite duration के लिए बना graph S-curve hydrograph कहलाता है।

7.2.1 S- Curve (Synthetic Hydrograph)

It is a Hydrograph which is made by a continuous effective rainfall, at a constant rate for an infinite period.

Graph made by using Mathematical equation is known as synthetic hydrograph.

SNYDER developed this.

Discharge of S Curve

(m³/hr)

(m³/sec)

7.2.2 Instantaneous Unit Hydrograph

It is a hydrograph resulting from surface runoff of instantaneous excess rainfall of 1 cm.

[Q] A 4-hour unit hydrograph of a drainage basin is triangular in form with a height of 50 m³/sec and a base of 15 hours. the area (in km²) of the drainage basin is.

Sol. A hydrograph is a graphical representation of discharge (Q) and time (t).
1/100×Area of drainage basin =12×50×15× (60×60)
1/100×A=1800×50×15
A = 135 × 10⁶ m²
A = 135 km²

8 FLOOD ROUTING

Flood routing is a hydrological process that involves the analysis and prediction of the movement, attenuation, and spreading of floodwaters as they progress through a river or stream channel. This is important for understanding how floods evolve over time and space, which is crucial for effective flood management and mitigation.

There are two main types of flood routing: hydrologic flood routing and hydraulic flood routing.

8.1 Hydrologic Flood Routing:

Definition- Hydrologic flood routing deals with the prediction of flood waves as they move through a river basin, without considering the details of the channel and floodplain geometry.

It is only used continuity equation only.

Methods- Hydrologic routing models often use mathematical equations and computational methods to simulate the movement of water through the river system. These models may take into account factors such as precipitation, soil moisture, land use, and other hydrological parameters.

8.2 Hydraulic Flood Routing:

Definition- Hydraulic flood routing focuses on the detailed analysis of floodwaves within a river or stream channel, considering the physical characteristics of the channel and floodplain.

It is only used continuity and momentum equations.

Methods- Hydraulic routing models use principles of fluid mechanics to simulate the movement of water through a channel. These models consider the channel geometry, roughness, and other hydraulic parameters. Numerical methods, such as finite difference or finite element methods, may be employed to solve the governing equations.

8.2.1 The objectives of flood routing include:

8.2.1.1 Flood Forecasting:

Predicting the timing, magnitude, and spatial distribution of floods.

8.2.1.2 Flood Warning:

Providing timely warnings to communities at risk.

8.2.1.3 Floodplain Management:

Understanding how floodwaters will interact with the floodplain.

8.2.1.4 Infrastructure Design:

Designing bridges, dams, and other structures to withstand and manage floods.

Flood routing is an essential component of flood risk assessment and management. It helps authorities and communities make informed decisions about land use planning, emergency response, and infrastructure development to minimize the impact of floods on people and property.

8.3 Time of Concentration

Time of Concentration is the time required by the entire drainage area to contribute to the runoff is called the time of concentration or time required by the most extreme point in the drainage to reach the point of interest.

In Other Words, it is the maximum time taken by the rainwater to reach the outlet of the basin.

Time of concentration = overland flow time + channel flow time Overland flow is also called sheet flow.

It is the phase of runoff when water flows as a sheet on plain land. Channel flow time is the time during which runoff flows in open channel up to the gauging site.

Time of concentration depends upon the slope, the catchment characteristics and the flow path. For a hydrograph analysis, time of concentration is defined as the time duration from the end of excess rainfall to the point of inflection.

Kirpich equation is an empirical equation used to determine the time of concentration in runoff hydrograph and it is given as:

T = 0.01947L _0.77 S ^-0.385

Where, t = time of concentration in minutes L = the maximum length of water travel in m. S = the slope of the catchment and it is given as ΔH is the difference in elevation between most remote points on the catchment outlet.

8.4 Muskingum equation

The Muskingum method is a hydrologic channel-routing method for flood routing. It’s a mathematical model that estimates the attenuation of flood waves in a river channel.

The method is commonly used for small to medium-sized river basins.

The Muskingum method uses a mass conservation approach to route an inflow hydrograph. It accounts for hysteresis, or the “looped” storage vs. outflow relationships that most rivers have.

The method relates the storage of a reach to its inflow and outflow rates.

The storage is expressed as a function of both inflow and outflow discharge.

The method uses a weighting factor, x, to distribute the volume of the reach between the wedge and prism. The number used for x is a constant, based on historical records.

8.5 A 10% flood frequency

Flood frequency is a statistical expression of the average time between floods of a certain magnitude. Flood-frequency analysis uses records of annual peak discharges to estimate the probability of flooding at specific river locations.

The recurrence interval, or return period, is the average number of years between floods of a certain size. The actual number of years between floods can vary due to climate change.

A 10% flood frequency means that there is a 10% chance of a flood occurring in any given year. A 10-year flood is a high streamflow that can overflow the banks of a waterway.

Ques- The probability of a 10-year flood occurring at least once in the next 4 years is 34.39%. This is close to 35%.

The probability for the annual maximum flood magnitude to occur =

Calculation:

Q =1-p = 0.9

Probability of flood at least once in next 4 years = 1 – no flood in next 4 years

= 1 – q⁴

= 1 – (0.9)⁴

= 0.35

8.6 Recurrence Interval (T)

Recurrence interval if a given storm is the time interval during which the given storm is likely to be equalled or exceeded. If we say that at a given station, the maximum precipitation of 30 cm has recurrence interval of 8 year, we mean that on this station, the changes of rainfall are such that once in eight years, rain is likely to be equalled or exceeded.

This does not mean that a rain equal to 30 cm or more will occur after every eight year. It may occur twice in one set of eight year or may not occur for consecutive 12 year or so.

(ii) Recurrence interval or return period are defined as, T = 1/P ⇒ PT = 1 Where, P = Probability of exceedance

Probable Maximum Flood (PMF):

This is the flood resulting from the most severe combination of critical meteorological and hydrological conditions that rare reasonably possible in the region.

It is computed by using the Probable Maximum Storm (PMS) which is an estimate of the physical upper limit to storm rainfall over the catchment.

Standard Project Flood (SPF):

This is the flood resulting from the most sever combination of meteorological and hydrological conditions considered reasonably characteristic of the region.

The SPF is computed from the Standard Project Storm (SPS) over the watershed considered and may be taken as the largest storm observed in the region of the watershed.

It is not maximized for the most critical atmospheric conditions but it may be transposed from an adjacent region to the watershed under consideration.

Design Flood:

For large dams: IDF should be based on PMF.

For intermediate dams: IDF should be based on SPF.

For small dams: IDF may be taken as 100 years return period flood.

∴ The probable maximum flood is more than standard project flood.

9 TYPE OF GRAPHS

Type of Curve	Graph	Application
Mass Curve	Accumulated rainfall v/s Time.	A mass curve of inflow can be prepared from the flow hydrograph of a stream for a large number of consecutive previous years
Double Mass Curve	Avg. Annual data of Missing Station Vs Avg. Annual data of surrounding station	To check the Consistency of Rainfall Data
Hydrograph	Discharge (runoff) v/s Time.	Flood Routing (inflow and Outflow Hydrographs), Estimation of Peak Flood Discharge.
Hyetograph	Rainfall Intensity(mm/hr) Vs Time(hr)	Rainfall Intensity, Area gives rainfall in mm
Unit Hydrograph	Plot of instantaneous discharge (runoff) v/s time.	Estimation of Run-offs
Flow Duration Curve		Maximum and Minimum flow in Hydroelectric Power Plants

SN	Instrument name	Used for measuring
1	Anemometer	Wind velocity
2	Pluviometer	Rainfall depth
3	Lysimeter	Evapotranspiration
4	Atmometer/ Open pan	Evaporation
5	Phytometer	Transpiration
6	Hygrometer/ Psychomotor	Relative humidity
7	Tensiometer	capillary potential
8	Pyranometer	Radiation from sun