detail description on open channel flow with lots of problems

open channel flow

1. 3. Hydrological losses 8hrs
Theprecipitatedwaterthatreachestheearthsurfacefromtheatmospheredoesnotremainstableonthesurface,i.e.thiswateragainevaporatesbacktothe
atmospherefromthesoilsurface,vegetationcover/bodiesaswellasfromthesurfaceofwaterbodies.Someportionofwaterinfiltratesintothegroundand
rechargestheundergroundsources.Somewatertakesitswaytowardsthestreamsorriversthroughsurfaceflowandreachestheseaandoceans.
Hence, the precipitated water flows as runoff from the surface of earth towards the river / streams after allowing water forinterception, depression storage
and infiltration. The precipitated water that does not produce runoff is defined as hydrological losses.
3.1 Initial losses (interception and depression losses):
Asalreadydiscussedabovethatsurfacerunoffstartstoflowaftermeetingallthelosses.i.einitiallyafterprecipitationwaterdoesnotflowtowardsstream/
riverfromthesurface.Waterstrikesontheobjectslayingontheearthlikestones,leaves,buildingsetc.donotreachtheearthsurfacebutevaporatesfrom
suchbodiescalledinterception.Afterfullywettingtheobjectswatergetitswaytowardstheearthsurface.Watermustfillthevoidsofsoils,depressions
spotstohavesurfacerunoff.Duringsurfaceflowtowardsriver/streams,infiltrationalsotakesplaceseepingintothegroundfromthetopsoil.Theinitial
waterthatreachingearthfromtheatmospherewhichiswetted/soakedbyobjectsandstoredindepressedsurfacestartsevaporatingfromthereandlostfrom
theearthsurfaceareinitiallosses.
3.2Evaporationprocess:
Theprocessofchangingthestateofwatereithersolidorliquidtothevapor/gaseousstateatthefreesurfacebelowtheboilingpointiscalledevaporation.
Thisvaporgoestotheatmosphereformingclouds.Itisduetogaininghighkineticenergybythewatermoleculestoloosetheirmolecularattractionfrom
thewatersurfaceandvaporizedtowardsatmosphere.
3.2.1Meteorologicalparametersforevaporation:
1.Radiation:Itisprocessoftransferofenergyfromthesourcetowardtheobjects.Theenergytransmitfromthesunbysolarradiationwhichcontrolsthe
weatherandclimateoftheearth.Radiationdirectlyaffectsthetemperatureoftheevaporatingsurfaces.
2.Temperature:Temperatureofthewaterbodyandthesurroundingareaaffectstheevaporationrate.Withincreaseinwatertemperaturerateof
evaporationalsoincreasestothecertainextent.Forthesametemperature,evaporationfromthewaterbodymaynotbeequalandsameinallseasons
becausethesurroundingairtemperatureisdifferentindifferentseasons.

2. 3. Humidity : It is the measure of moisture content present in the atmospheric air. The dry air contains less moisture hence the capacity of holding
evaporated water will be higher than the moist air. During evaporation process if the humidity is low than evaporation rate increases.
4. Vapor pressure: The pressure exerted by the molecules of water vapor leaving the surface is vapor pressure. If the vapor pressure present in theair is less than that
of water surface, evaporation continues. As soon as the va[por pressure reaches the saturation vapor pressure , evaporation stops. According to Dalton,
EL= C(ew-ea) ; mm of evaporable water /day
Where, ew= Saturated vapor pressure (evaporated water) mm of Hg ; uptolimit ew= eaevaporation takes place
ea= Actual vapor pressure (air) ew> eacondensation takes place.
C = Constant depends on surface of evaporation.
5. Wind speed: If wind takes place during the evaporation process, vapor from the surface of water trying to escape up to the atmosphere is easily displaced by the
wind. Hence, wind helps to accelerate the evaporation rate to a certain extent only.
3.2.2 Energy Budget method and Mass transfer approach ( Dalton’s Law)
a) Energy budget method:
Based on principle of conservation of energy. The energy available for evaporation is determined by considering incoming , out going and stored energy in the system
of water bodies over a known period of time.
Incoming energy = out going energy + change in stored energy
Energy balance to evaporating surface in a period of a day for a water body as shown is given by,
Hn= Ha + He + Hg +Hs + Hi Hs = Heat stored in water body; Hi = advected energy / net heat conducted
Hn= net radiation = Hc(1-r) –Hb ; Ha= Sensible heat transfer from water to air out of the system.
r Hc= Reflected radiation He = heat energy used up in evaporation
Hc= Incoming solar radiation , Hb = Back radiation from water body
r = Albedo / reflection coefficient ; Hg = Heat flux into the ground

3. For short time periods , Hs and Hi can be neglected. All other terms can be measured or evaluated.
Ha can be estimated using Bowen’s ratio given by
�=
??????�
??????�
=
??????�
??????.??????.�??????
Again, Bowen’s ratio can be estimated by �=�
�??????−��
(�??????−��)
On solving, evapotation loss can be determined by �??????=
??????�−??????�−??????�−????????????
??????.??????(�+�)
2. Mass transfer method: This method is based on the theories of turbulence mass transfer in the boundary layer to calculate the mass of water transfer from
the surface of surrounding.
Dalton’s law states that the rate of evaporation is proportional to the saturation deficit. i.e
ELα(es-ea)
EL= C ( es –ea)
C = Constant depends upon wind speed and barometric pressure.
es-ea= Saturation deficit.
i)Meyer’s formula: EL = C ( 1+
�??????
��
) (es-ea) where, U9 = mean wind velocity 9 m above ground km/h
ii)Rhower’sformula EL = 0.771(1.465-0.000732P) ( 0.44+0.0733U) (es-ea)
where, P = barometric pressure mm of Hg , U = wind velocity 0.60m above ground km/h

4. 3.2.3 Experimental methods using Evaporimeters / Evaporation Pan
Evaporimeters:
These are the containers of shallow depth which contains water and are placed near / on the water bodies. The water evaporates from the evaporimeter to the atmosphere and in the
same time water from the water bodies also evaporates within the same temperature, radiation, humidity , wind effects etc.
The water is filled in the evaporimeters to a certain depth and change in depth of water due to evaporation with in the specifictime period is measured .
Now evaporation from the water body / lake is estimated by multiplying evaporated depth of pan and pan coefficient.
Lake evaporation = pan coefficient x evaporation from pan
Types of pan :
i) Cass A evaporation pan : made up of galvanized iron sheet; placed 15cm above ground. Hook gauge in a stilling well is used for the measurement of depth of water.
Cp = 0.60-0.80 = 0.70
ii)Colorado sunken pan :made of galvanized iron sheet buried into ground such that water level is at the ground level. Cp = 0.75-0.86 = 0.78
iii)ISI standard pan: made up of copper sheet 0.9mm, tinned inside and painted white outside and pan is placed 10cm above ground. From the top pan is covered by wire mesh.
Cp = 0.65 to 1.1 = 0.80
iv)USGS floating pan: Square shape 900x900 and depth 450mm supported by drum floats and water level of pan is kept at the same level of lake. It isvery expensive due to its
complication of installation. Cp = 0.70-0.82 = 0.80
US Class A pan
Colorado Sunken Pan ISI Standard Pan

5. 3.3 Evapotranspiration:
Transpiration is the vaporization of water contained in plant tissue towards the atmosphere. Plants lost their water through stomata and transpiration mainly occurs
during daylight hours.
Evapotranspirationis the combined form of evaporation and transpiration. In the hydrology and irrigation practice, evaporation from the surrounding soil / water body
with the vegetations on them where transpiration also occurs at the same time is very difficult to distinguish / calculation.So, both of them are considered under the
single heading of evapotranspiration and also called consumptive use.
Potential evapotranspiration: The rate of evapotranspiration from the surface covering by the growing crops which is provided with sufficient water supply i.e
moisture content of soil is not limited.
Actual evapotranspiration: The real evapotranspiration occurring in a specific situation is called actual evapotranspiration.
When soil moisture is sufficient so that it is at Field capacity moisture content level ; then AET = PET
Measurement of Evapotranspiration:
Lysimeter: It is the small cylindrical container of size 60 to 90 cm diameter and 180cm deep in which plants are sown. This tank is filledwith the soil and buried into
the ground such that its top level is kept at the same level of the surrounding ground surface. Plants grown in lysimeter arethe same as in the surrounding field.
Evapotranspiration is estimated in terms of amount of water required to maintain constant moisture condition of field capacity with in the tank.
Evapotranspiration = (precipitation + irrigation input –runoff –increase in soil storage –ground water lost)

6. Penman’s Equation:
It is the combined method of energy budget and mass transfer approach for finding evapotranspiration analytically. Potential evapotranspiration is given by the
following equation
??????��=
????????????�+���
??????+�
Where, A = slope of saturation vapor pressure vs temperature curve at mean air temperature.
Hn= net radiation in mm of water /day
Ea= parameter including wind velocity and saturation deficit.
γ= Psychrometric constant = 0.49mm of Hg /
o
C
Net radiation is given by ??????�=??????��−��+�
�
??????
−??????��
�
�.��−�.�??????���[�.��+�.??????�
�
??????
]
Where, Hc= incident solar radiation mm of water / day
r = Reflection constant / Albedo depends on surface of reflection.
a = Constant depends on latitude фof the place = 0.29 cos ф
b = a constant having value of 0.52
n = actual duration of bright sun shine hours
N = maximum possible hours of bright sunshine
??????= Stefan Boltzman’sconstant = 2.01 x 10
-9
Ta = Temperature of the air in Kelvin = 273 +
o
C
Eais estimated by the equation; ��=�.���+
��
���
(��−��)
where, U2 = mean wind speed 2m above the ground surface in km/day

7. 3.4 Infiltration : It is the process of entering water into the soil from the ground surface of the earth. The infiltrated water is first utilized to fulfill the soil moisture
deficiency and excessive water then only moves downwards by force of gravity towards the underground water table. Infiltration provides water for sub surface runoff/
delay flow to the rivers or streams as well as under ground recharge. Similarly, it helps to reduce flood and erosion by reducing surface runoff and provides water to the
plants.
Factors affecting infiltrations are :
1.Rainfall characteristics: a) Rainfall intensity b) Duration of rainfall c) forms of precipitation
2.Soil characteristics : Type, Porosity, texture, permeability, grain size etc.
3.Surface condition: compacted, vegetated, cracks, baren lands, slope of land etc.
4. Soil moisture present: High/ low moisture content , dry surface, land use pattern,
5. Climate : dry / hot season, wet seasons
6. Water table
7. Quality of water : present of salt lowers infiltration, turbidity reduces
8. Animals and human activities : burrowing animals, Cattle grazing , farming, constructions etc.
3.4.1: Horton’s Equation
Infiltration capacity (fc): It is the maximum rate at which water can be absorbed by the soil at a particular point under the given conditions. It is expressed in cm/hr.
Infiltration rate: (f): The actual rate of infiltration is called infiltration rate which may be smaller than or equals to infiltration capacity of soil.
If intensity of rainfall is greater and equal to infiltration capacity; f = fc
if intensity of rainfall is less than fc ; f = i
Infiltration rate f = F/t
Where, F = Total depth of infiltrated water in time of t hrs.

8. Measurement of infiltration using Horton’s Equation:
Horton an American in (1930-1939) states that the infiltration capacity of the soil begins at some rate foat time toand deccreasesexponentially until it reaches a constant rate of fc ; which is
expressed by equation
��=��+��−���
_
??????�
fo
total infiltration in time t = F = ∫�(t) dt �=��+��−���
_
??????�
= ∫���??????+∫�??????−���
_
????????????
dt f
??????=��.??????+
????????????−????????????
??????
(1−�
_
????????????
)
For large time t , e
-kt
becomes very negligible and can be neglected . Above equation reduces to �=��.�+
��−��
??????
F= area under curve
??????=
��−��
�−��.�
f(t)
fc
1. Determination of fo, fc and k using stastisticalapproach t = o t= t
f = fc + (fo-fc ) e
–kt
Horton’s equation
f-fc = (fo-fc ) e
–kt
taking log on both sides ; ln (f-fc) = ln ((fo-fc ) e
–kt
) using least square method: m = -k = [N∑��−∑�∑�]÷??????∑�
2
-(∑�)2
ln (f –fc) = –kt + ln (fo-fc)
y = mx + c compare it with y= mx +c straight line equation C = [∑�−??????∑�]÷??????
C = ln (fo-fc)
fo–fc = e
C
fo= fc + e
C

9. 3.4.2 Infiltration indices: ф-index and W-index
Infiltration indexes are used to find the infiltration capacities of soil. They are
1.ф-index : It is the average rainfall intensity above which the rainfall volume equals the run off volume. Which is based on the assumptionthat for a
specified rainfall / storm with given initial conditions, the rate of infiltration remains constant through out the storm periods, i.e. фremains constant.
for i < ф, f = i, i.eno runoff because all the water is infiltrated in to the soil.
For i> ф, runoff occurs i.e. R = i–f
The amount of rainfall in excess of index is known as effective rainfall or rainfall excess. ф-index = (P-R) / Te
Where, P = precipitation , Te = Time of effective rainfall
R = Runoff
Excess rainfall volume above ф-index = Runoff volume
Intensity of rainfall
mm/hr
ф-index average infiltration rate of soil
1hr 2hr 3hr 4hr 5hr
Time
fig: Rainfall hyetograph showing ф-index

10. Determination of ф-index
Trial and error approach is used to determineф-index.
Procedure:
i)For the First trial, find ф-index using formula ф-index = (P-R) / T
ii)Compute rainfall excess using each observed rainfall, time interval and calculated ф-index
Rainfall excess = P –фx ΔT
iii) Compute total rainfall excess Re
iv) Compare total rainfall excess with direct runoff .
v) If Re is not equal to direct runoff , take another trial value of ф-index.
if Re > runoff , increase ф-index
if Re < runoff , decrease ф-index
vi) Repeat the process till Re = runoff. When, Re= runoff , that assumed ф-index is the correct one.
2. W-index: It is the improvement version of ф-index, which is also the average rate of infiltration during the period when the rainfall intensity exceeds the
infiltration rate in which initial losses such as interception and surface storage are considered. It is given by
W-index = (P -R-Ia) / Te Where, Ia = initial losses ( interception and depression storage)

11. 3.4.3 Infiltrometers
Infiltrometers are the experimental device used to measure the infiltration capacity of soil. It is of two types.
1.Flooding type infiltrometer: a) Single ring infiltrometer. b) Double ring infiltrometer.
2.Rainfall simulator type infiltrometer.
1. It is the hollow cylindrical metal ring which is inserted into the ground soil for measuring infiltration rate of that soil.
a)Single ring infiltrometer: Consists of hollow cylindrical ring of 30cm diameter and 60 cm long which is inserted into the soil. Water is supplied to the depth of
5cm from the top surface and pointer is set at that level. As the infiltration proceeds, the volume of water is again added up to the pointer level using burette. By
knowing the volume of water added at different time interval , graph is plotted between infiltration rate Vs time and the experiment continued till to the uniform
rate of infiltration is obtained. ф30cm ф30cm
5cm
GL 5cm
50cm
b) It consists of two concentric hollow cylinders of same
length. Water is added to both cylinders to maintain the
same height. The data used for infiltration is taken from
the inner cylinder only. Outer cylinder helps not to
spread water from the inner cylinder. Fig: Single ring infiltrometer Fig: Double ring infiltrometer
Other procedure is same as that of single ring infiltrometer for measuring infiltration rate.

12. 2. Rainfall simulator type infiltrometer:
The rainfall simulator is the mechanism of providing artificial rain in the form of spray of water of different intensities, drop sizes and durations. Plot of 4m x 2m is
selected and water is applied to this field by the rainfall simulator with various intensities falling from 2m height. The amount of infiltration is determined by using
water budget equation as,
Infiltration = Rainfall –surface runoff
Fd= Pd –Srd–Sol where, Fd = depth of infiltration
Pd = rainfall depth
Srd = Surface runoff depth
Sol = other losses, depression storage, detention, abstraction
Infiltration capacity = total infiltrated depth / total time of experiment.