Hydrology & Irrigation Engineering Formulas for Civil Engineering Exam

# Hydrology & Irrigation Engineering Formulas for Civil Engineering Exam | Irrigation Engineering - Civil Engineering (CE) PDF Download

``` Page 1

Short Notes on Engineering Hydrology

Precipitation & General aspects of Hydrology
Index of Wetness
• index of wetness =

• % Rain deficiency = 100 - % index of wetness

Aridity index

Where, A.I = Aridity index

PET = Potential Evapo- transpiration
AET = Actual Evapotranspiration
a. AI = 0 ? Nonarid
b. 1 = A.I = 25 ? Mild Arid
c. 26 = A.I = 50 ? Moderate arid
d. A.I > 50 ? Severe Arid

Optimum Number of rain Gauge: (N)

where, Cv = Coefficient of variation,
Page 2

Short Notes on Engineering Hydrology

Precipitation & General aspects of Hydrology
Index of Wetness
• index of wetness =

• % Rain deficiency = 100 - % index of wetness

Aridity index

Where, A.I = Aridity index

PET = Potential Evapo- transpiration
AET = Actual Evapotranspiration
a. AI = 0 ? Nonarid
b. 1 = A.I = 25 ? Mild Arid
c. 26 = A.I = 50 ? Moderate arid
d. A.I > 50 ? Severe Arid

Optimum Number of rain Gauge: (N)

where, Cv = Coefficient of variation,
? = Allowable % Error,

s Standard deviation of the data, n = Number of stations,

mean of rainfall value

Estimation of missing rainfall data

where, N1,N2 ,… Nx..Nn are normal annual percipitation of 1,2,…x…n respectively.

P1,P2 …Pn are rainfall at station 1,2,…. N respectively.

And Px is the rainfall of station x.

Case: A minimum number of three stations closed to station ‘x’

If any of N1, N2, N3…
Nn > 10% of Nx
Mean rainfall Data
To convert the point rainfall values at various into an average value over a
catchment the following three methods ar in use

(i) Arithmetic Avg Method: when the rainfall measured at various stations in a
catchment area is taken as the arithmetic mean of the station values.

Where, P1,P2 …Pn are rainfall values

Of stations 1,2…n respectively.

In practice this method is used very rerely.
Page 3

Short Notes on Engineering Hydrology

Precipitation & General aspects of Hydrology
Index of Wetness
• index of wetness =

• % Rain deficiency = 100 - % index of wetness

Aridity index

Where, A.I = Aridity index

PET = Potential Evapo- transpiration
AET = Actual Evapotranspiration
a. AI = 0 ? Nonarid
b. 1 = A.I = 25 ? Mild Arid
c. 26 = A.I = 50 ? Moderate arid
d. A.I > 50 ? Severe Arid

Optimum Number of rain Gauge: (N)

where, Cv = Coefficient of variation,
? = Allowable % Error,

s Standard deviation of the data, n = Number of stations,

mean of rainfall value

Estimation of missing rainfall data

where, N1,N2 ,… Nx..Nn are normal annual percipitation of 1,2,…x…n respectively.

P1,P2 …Pn are rainfall at station 1,2,…. N respectively.

And Px is the rainfall of station x.

Case: A minimum number of three stations closed to station ‘x’

If any of N1, N2, N3…
Nn > 10% of Nx
Mean rainfall Data
To convert the point rainfall values at various into an average value over a
catchment the following three methods ar in use

(i) Arithmetic Avg Method: when the rainfall measured at various stations in a
catchment area is taken as the arithmetic mean of the station values.

Where, P1,P2 …Pn are rainfall values

Of stations 1,2…n respectively.

In practice this method is used very rerely.
(ii) Thiessen Polygon Method: In this method, the rainfall recorded at each
station is given a weightage on the basis of an area closest to the station.

Where, P1,P2 …Pn are the rainfall data of areas A1,A2…An. The thiessen-polygon
method of calculating the average percipitation over an area is superior to the
arithmetic average method.

(iii) Isohyetal Method: An isohyet is a line joining points of equal rainfall
magnitude. The recorded values for which areal average P is to be detarmined are
then maked on the plot at appropirate stations.Neighbouring stations outside the
catchment are also considered.

Page 4

Short Notes on Engineering Hydrology

Precipitation & General aspects of Hydrology
Index of Wetness
• index of wetness =

• % Rain deficiency = 100 - % index of wetness

Aridity index

Where, A.I = Aridity index

PET = Potential Evapo- transpiration
AET = Actual Evapotranspiration
a. AI = 0 ? Nonarid
b. 1 = A.I = 25 ? Mild Arid
c. 26 = A.I = 50 ? Moderate arid
d. A.I > 50 ? Severe Arid

Optimum Number of rain Gauge: (N)

where, Cv = Coefficient of variation,
? = Allowable % Error,

s Standard deviation of the data, n = Number of stations,

mean of rainfall value

Estimation of missing rainfall data

where, N1,N2 ,… Nx..Nn are normal annual percipitation of 1,2,…x…n respectively.

P1,P2 …Pn are rainfall at station 1,2,…. N respectively.

And Px is the rainfall of station x.

Case: A minimum number of three stations closed to station ‘x’

If any of N1, N2, N3…
Nn > 10% of Nx
Mean rainfall Data
To convert the point rainfall values at various into an average value over a
catchment the following three methods ar in use

(i) Arithmetic Avg Method: when the rainfall measured at various stations in a
catchment area is taken as the arithmetic mean of the station values.

Where, P1,P2 …Pn are rainfall values

Of stations 1,2…n respectively.

In practice this method is used very rerely.
(ii) Thiessen Polygon Method: In this method, the rainfall recorded at each
station is given a weightage on the basis of an area closest to the station.

Where, P1,P2 …Pn are the rainfall data of areas A1,A2…An. The thiessen-polygon
method of calculating the average percipitation over an area is superior to the
arithmetic average method.

(iii) Isohyetal Method: An isohyet is a line joining points of equal rainfall
magnitude. The recorded values for which areal average P is to be detarmined are
then maked on the plot at appropirate stations.Neighbouring stations outside the
catchment are also considered.

Infiltration, Run off and Hydrographs

Infiltration

Infiltration is the flow of water into the ground through the soil surface.

• Horton’s Equation: Horton expressed the decay of infiltration capacity with
time as an exponential decay given by

Where,

fct = infiltration capacity at any time t from start of the rainfall
fco = initial infiltration capacity at t = 0
fct = final steady state value
td = Duration of rainfall
kh = constant depending on soil.

Infiltration indices

In hydrological calculations involving floods it is found convenient to use a constant
value of filtration rate for the duration of the storm. The defined average infiltration
rate is called infiltration index and two types of indices are in common use
Page 5

Short Notes on Engineering Hydrology

Precipitation & General aspects of Hydrology
Index of Wetness
• index of wetness =

• % Rain deficiency = 100 - % index of wetness

Aridity index

Where, A.I = Aridity index

PET = Potential Evapo- transpiration
AET = Actual Evapotranspiration
a. AI = 0 ? Nonarid
b. 1 = A.I = 25 ? Mild Arid
c. 26 = A.I = 50 ? Moderate arid
d. A.I > 50 ? Severe Arid

Optimum Number of rain Gauge: (N)

where, Cv = Coefficient of variation,
? = Allowable % Error,

s Standard deviation of the data, n = Number of stations,

mean of rainfall value

Estimation of missing rainfall data

where, N1,N2 ,… Nx..Nn are normal annual percipitation of 1,2,…x…n respectively.

P1,P2 …Pn are rainfall at station 1,2,…. N respectively.

And Px is the rainfall of station x.

Case: A minimum number of three stations closed to station ‘x’

If any of N1, N2, N3…
Nn > 10% of Nx
Mean rainfall Data
To convert the point rainfall values at various into an average value over a
catchment the following three methods ar in use

(i) Arithmetic Avg Method: when the rainfall measured at various stations in a
catchment area is taken as the arithmetic mean of the station values.

Where, P1,P2 …Pn are rainfall values

Of stations 1,2…n respectively.

In practice this method is used very rerely.
(ii) Thiessen Polygon Method: In this method, the rainfall recorded at each
station is given a weightage on the basis of an area closest to the station.

Where, P1,P2 …Pn are the rainfall data of areas A1,A2…An. The thiessen-polygon
method of calculating the average percipitation over an area is superior to the
arithmetic average method.

(iii) Isohyetal Method: An isohyet is a line joining points of equal rainfall
magnitude. The recorded values for which areal average P is to be detarmined are
then maked on the plot at appropirate stations.Neighbouring stations outside the
catchment are also considered.

Infiltration, Run off and Hydrographs

Infiltration

Infiltration is the flow of water into the ground through the soil surface.

• Horton’s Equation: Horton expressed the decay of infiltration capacity with
time as an exponential decay given by

Where,

fct = infiltration capacity at any time t from start of the rainfall
fco = initial infiltration capacity at t = 0
fct = final steady state value
td = Duration of rainfall
kh = constant depending on soil.

Infiltration indices

In hydrological calculations involving floods it is found convenient to use a constant
value of filtration rate for the duration of the storm. The defined average infiltration
rate is called infiltration index and two types of indices are in common use

(i) W-index: In an attempt to refine the f-index the initial losses are separated
from the total abstractions and an average value of infiltration rate, called W-index,
is defined as

Where, P = Total storm precipitation (cm)
R = Total storm runoff (cm)
Ia = initial losses (cm)

te = Duration of rainfall excess

W-index = Avg. rate of infiltration (cm/hr)

(ii) f-index: The f index is the average rainfall above which the rainfall volumes is
equal to the runoff volume. The f index is derived from the rainfall hyetograph with
the edge of the resulting run- off volume.

? - ?nd?x =
I - R
24

Where, R = Runoff in cm from a 24- h rainfall of intensity I cm/day

Runoff

Runoff means the draining or flowing off of precipitation from a catchment area
through a surface channel. It thus represents the output from the catchment in a
given unit of time.
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## Irrigation Engineering

7 videos|35 docs|31 tests

## FAQs on Hydrology & Irrigation Engineering Formulas for Civil Engineering Exam - Irrigation Engineering - Civil Engineering (CE)

 1. What are some common formulas used in hydrology and irrigation engineering?
Ans. Some common formulas used in hydrology and irrigation engineering include: - Rational formula: Q = CiA, where Q is the peak discharge, C is the runoff coefficient, i is the rainfall intensity, and A is the drainage area. - Manning's equation: V = (1/n) * R^(2/3) * S^(1/2), where V is the velocity, n is Manning's roughness coefficient, R is the hydraulic radius, and S is the slope of the channel. - Penman-Monteith equation: ET0 = (0.408 * ∆ * (Rn - G) + γ * (900 / (T + 273)) * u2 * (es - ea)) / (∆ + γ * (1 + 0.34 * u2)), where ET0 is the reference evapotranspiration, ∆ is the slope of the saturation vapor pressure curve, Rn is the net radiation, G is the soil heat flux density, γ is the psychrometric constant, T is the air temperature, u2 is the wind speed at 2 meters above the ground, es is the saturation vapor pressure, and ea is the actual vapor pressure. - Hazen-Williams equation: Q = 0.849 * C * d^2.63 * S^0.54, where Q is the flow rate, C is the Hazen-Williams coefficient, d is the pipe diameter, and S is the pipe slope. - Crop water requirement equation: ETc = Kc * ETo, where ETc is the crop water requirement, Kc is the crop coefficient, and ETo is the reference evapotranspiration.
 2. How is the Rational formula used in hydrology and irrigation engineering?
Ans. The Rational formula is used in hydrology and irrigation engineering to estimate the peak discharge from a drainage area. It is commonly used for sizing stormwater drainage systems and designing hydraulic structures. The formula is expressed as Q = CiA, where Q is the peak discharge, C is the runoff coefficient, i is the rainfall intensity, and A is the drainage area. The runoff coefficient represents the fraction of rainfall that becomes runoff, and it depends on factors such as land use, soil type, and vegetation cover. The rainfall intensity is typically obtained from rainfall frequency analysis or local rainfall data. By applying the Rational formula, engineers can determine the maximum amount of water that needs to be handled by a drainage system or irrigation infrastructure.
 3. What is Manning's equation and how is it used in hydrology and irrigation engineering?
Ans. Manning's equation is a widely used empirical formula in hydrology and irrigation engineering to calculate the velocity of flow in open channels. It is expressed as V = (1/n) * R^(2/3) * S^(1/2), where V is the velocity, n is Manning's roughness coefficient, R is the hydraulic radius, and S is the slope of the channel. The hydraulic radius is defined as the cross-sectional area divided by the wetted perimeter. Manning's roughness coefficient represents the resistance to flow in the channel and depends on the roughness characteristics of the channel and the type of vegetation present. By applying Manning's equation, engineers can estimate the velocity of flow in open channels, which is essential for designing irrigation canals, drainage systems, and river channels.
 4. How is the Penman-Monteith equation used in hydrology and irrigation engineering?
Ans. The Penman-Monteith equation is a standard method used in hydrology and irrigation engineering to estimate the reference evapotranspiration (ET0). ET0 represents the amount of water lost through evaporation and transpiration from a well-watered, large grass surface under standard conditions. The equation takes into account various climatic parameters such as net radiation, air temperature, wind speed, vapor pressure, and slope of the saturation vapor pressure curve. By using the Penman-Monteith equation, engineers can estimate the ET0, which serves as a basis for determining the water requirements of crops and designing irrigation systems. It is widely adopted by agricultural and irrigation professionals to optimize water management and irrigation scheduling.
 5. How is the Hazen-Williams equation used in hydrology and irrigation engineering?
Ans. The Hazen-Williams equation is a commonly used empirical formula in hydrology and irrigation engineering to calculate the flow rate in pressurized pipes. It is expressed as Q = 0.849 * C * d^2.63 * S^0.54, where Q is the flow rate, C is the Hazen-Williams coefficient, d is the pipe diameter, and S is the pipe slope. The Hazen-Williams coefficient represents the roughness of the pipe and depends on the material and condition of the pipe. By applying the Hazen-Williams equation, engineers can estimate the flow rate in pressurized pipes, which is essential for designing water supply systems, irrigation networks, and sprinkler systems. The equation is widely used due to its simplicity and practicality.

## Irrigation Engineering

7 videos|35 docs|31 tests

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