unit 3 - losses from precipitation (evaporation)

7/25/2019 Unit 3 - Losses From Precipitation (Evaporation)

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Losses from Precipitation

EVAPORATION


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Course Learning Outcome 1CLO 1

On completion of this chapter, students will be able to

evaluate water cycle for a catchment by estimation ofprecipitation and the lossesusing measurement,

empirical and analytical methods.


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Program Outcome 1

PO 1

To acquire and apply engineering fundamentals

to complex civil engineering problems(Engineering knowledge).


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Lesson OutcomesOn completion of this chapter ,you will be able to:

identify factors influencing evaporation

measure the rate of evaporation using various measurement

techniques

estimate the rate of evaporation using

empirical equations

analytical methods

suggest strategies to reduce evaporation from water resources


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Losses from Precipitation Evaporation

Evapotranspiration

Infiltration

Depression storage


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EVAPORATIONEvaporation is the process in which a liquid changes to the

gaseous stateat the free surface,below the boiling pointthrough

the transfer of heat energy.

Evaporation is particularly significant over large bodies of water

such as lakes, reservoirs and the ocean.

Knowledge on evaporation is useful for:Planning and design of many water resources projects

Capacity of reservoirs for water supply & irrigation

Allowance for evaporation should be made to avoid serious errors.


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Factors Affecting Evaporation

1. Vapour pressures at water surface and atmosphere

2. Air & water temperatures

3. Atmospheric pressure

4. Wind speed

5. Quality of water

6. Size of the water body


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1. Vapor Pressures at Water Surface & Atmosphere

The rate of evaporation (E) is proportional to the difference

between the saturated vapour pressureat water temperature (ew) and

the water vapour pressurein the air (ea).

)( aw eeCE )( aw eeCE E = inmm/day;ewand ea= in mm Hg ; C= constant

Evaporation: ew> ea

Condensation: ew< ea

Water Vapour Pressure (ea):

Pressure exerted by water vapour at air temperature.

Saturated Vapour Pressure (ew):

Pressure exerted by water vapour at water surface temperature.

Factors ffecting Evaporationactors ffecting Evaporation


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waterE (high correlation)

atm E (low correlation)

2. Air & Water Temperature

Patm(e.g. at high altitudes) E

3. Atmospheric Pressure

water

E

atm

E

Factors ffecting Evaporationactors ffecting Evaporation


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4. Size of the Water Body

Deep water bodies have more heat storage than shallow

ones.

A deep lake may store radiation energy received in summer

and release it in winter causing less evaporation in summer

and more evaporation in winter compared to a shallow lake

exposed to a similar situation

Factors ffecting Evaporation

actors ffecting Evaporation


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Help in removing the evaporated water vapor close to the

surface of the water bodies and consequently create greater

scope for further evaporation.

Vwind E

However, if the wind velocity is large enough to remove all

the evaporated water vapour (critical speed), any further

increase in wind velocity does not influence the evaporation.

Vwind E retains

5. Wind Speed

Vwind

E

Critical velocity




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Soluble salts in water E

Specific gravity E

Under the same conditions, evaporation from sea water isabout 2-3% less than that from fresh water.

6. Quality of Water - Soluble Salts




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Estimation of EvaporationThe amount of water evaporated from a water surface can beestimated by the following methods:

Measurement

Empirical equations

Analytical methods

Meteorological data such as humidity, wind movement, air &water temperature and precipitation are also noted along withevaporation measurements.


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Measurement of Evaporation

Evaporation is estimated by using evaporimeters.

Evaporimeters are water-containing panswhich

are exposed to the atmosphereand the loss of

water by evaporation measured in them at regular

intervals.

Some common types of evaporimeters are:

Class A Evaporation Pan Colorado Sunken Pan

US Geological Survey Floating Pan

Measurement

easurement


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It is a standard pan of 12.1-cm diameter and 25.5-m depth used by the US

Weather Bureau.

The depth of water is maintained between 18 -20 cm.

The pan is normally made of unpainted galvanized iron sheet or anti-corrosive

metal (where corrosion is a problem). The pan is placed on a wooden platform of 15 cm height above the ground to

allow free circulation of air below the pan.

Evaporation measurements are made by measuring the drop in depth of water

with a hook gauge in a stilling well.

Class A Evaporation Pan

Measurement

easurement


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Principles of Evaporation Pan

The pan is installed in the field

The pan is filled with a known quantity of water

Record the surface area of pan and the water depth

The water is allowed to evaporate during a certain period

of time (usually 24 hrs) After 24 hrs, the remaining quantity of water is measured

The amount of evaporation per unit time is calculated(i.e. the difference between the two measured water

depths for a given period of time)

Measurement

easurement


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Day 1 Day 2

Measurement

easurement


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Take water out of thepan when the water

depth rises too much

Add water when thewater depth in the

pan drops too much

Measurement

easurement


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Colorado Sunken Pan

The Colorado Sunken Pan is 920 mm2and 460 mm deep, made up of

galvanized iron sheet andburied into the ground within 100 mm of

the top.

Difficult to detect leak, tall grass and dustmight disturb

measurement, expansiveto install

Radiation and aerodynamic characteristics are similar to

those of a lake

Measurement

easurement


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Square pan (900 mm side and 450 mm depth) or circular pan is

set afloat in a lake.

The water level in the pan is kept at the same levelas the lake

leaving a rim of 75 mm.

Simulate the radiation and aerodynamic characteristicsof

large body of water

High cost of installation and maintenance

Difficult to perform measurements

Measurement

easurement


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Evaporation pans are not exact models of large reservoirs and

therefore have the following drawbacks:

The heat-storing capacity differs from that of the lake.

The height of the rim in a pan affects the wind action over the

surface and it casts a shadow over the water surface. Heat transfer characteristics of the pan material is different from

that of the lake.

Therefore, the evaporation observed from a pan has to be corrected by

pan coefficient to get the evaporation from a lake under similarclimatic and exposure conditions.

Limitations of Evaporation Pans

nevaporatioPan

nevaporatioLakepC

Types of pan Average Cp Range

Class A Pan 0.70 0.60-0.80

Colorado Sunken Pan 0.78 0.75-0.86

USGS Floating Pan 0.80 0.70-0.82

Measurement

easurement


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Other Errors in Pan Evaporation that cannot be

corrected:

Films of dust

Oil from sprays

Screen covers placed over the pans to keep

out birds can cause errors in observation

Birds/Ducks bathing in pans

Measurement

easurement


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Methods of Evaporation Estimation

Empirical Equations:

Daltons Formula

Meyers Formula RohwersFormula

Analytical Methods:

Water-Budget Method

Energy-Budget Method

Mass Transfer Method


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Latent Heat of Evaporation (Lv):

Amount of energy needed for liquid water to change phase to

vapour.

Lv= (2.501 x 106) - 2370Ta

Lv= 25012.37Ta

Note: Ta= air temperature in C

Water Vapour Pressure (ea):

Actual vapour pressure exerted by water vapour at air temperature.

[J/kg]

[kJ/kg]

Relevant Parameters


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Saturated Vapour Pressure (ew):

Vapour pressure exerted by water vapour at water surfacetemperature.

Contains maximum moisture.

How to find ew?

1. Refer to Table 3.3 in textbook (pg. 72), or

2. Use this equation,

Note: Tw= Water temperature in C

w

w

w

T

Te

3.237

27.17exp611

[Pa or N/m2]

w

w

w

T

Te

3.237

27.17exp584.4 [mm of Hg]


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Table 3.3 (Pg72): ewandASaturated vapour pressure of water (ew)

Water sueface

temperature (oC)

Saturated vapour pressure ew

(mm of Hg)

Slope, A

(mm/oC)

0 4.58 0.30

5.0 6.54 0.45

7.5 7.78 0.54

10.0 9.21 0.60

12.5 10.87 0.7115.0 12.79 0.80

17.5 15.00 0.95

20.0 17.54 1.05

22.5 20.44 1.24

25.0 23.76 1.40

27.5 27.54 1.61

30.0 31.82 1.85

32.5 36.68 2.07

35.0 42.81 2.35

37.5 48.36 2.62

40.0 55.32 2.95

45.0 71.20 3.66

A

= Slope of ewvs. temperature


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Relative Humidity ():

The ratio of the actual water vapour pressure of the air, eato that at saturated, ew.

Unit %

100w

a

e

e

100

.wa

ee


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Empirical Formulae for

Evaporation Estimation

Daltons Formula

Meyers Formula (1915)

RohwersFormula (1931)


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EL = K f(u) (ew- ea)

EL= Lake evaporation (mm/day)

ew= Saturated vapour pressure (mm of Hg)

ea= Water vapour pressure (mm of Hg)

f(u)= Wind speed correction function

K= Daltons coefficient

Daltons Formula


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EL = Lake evaporation for 1-m2area (mm/day)

KM = Meyers coefficient accounting for different waters

0.36 for large deep waters

0.50 for small, shallow waters

ew = Saturated vapour pressure (mm Hg)

ea = Water vapour pressure (mm Hg)

u9 = Monthly mean windvelocity in km/h at 9 m above ground

161)( 9

ueeKE awML

161)( 9

ueeKE awML


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n

huu nh

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n

huu nh

uh= wind velocity at a height habove the ground (h < 500 m)

un

= wind velocity at nmeter above ground


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ExampleA reservoir with a surface area of 250 hectares (large waters, KM

= 0.36) had the following average values of parameters during a

week:

Water temperature = 20oC (Tw= 20oC)

Relative humidity 40% ( = 0.4)

Wind velocity at 1.0 m above ground = 16 km/h (u1= 16 km/h)

Estimate:(a) the average daily evaporationper unit m2of the lake

(b) the volume of water evaporated from the lake during that one

week.


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Solution

Hgofmm54.17

203.237

2027.17exp584.4

3.237

27.17exp584.4

w

ww

T

Te

Hgofmm

humidity)(Relative

02.7

54.174.04.0

4.0

wa

w

a

ee

e

e

km/h7/1

7/1

19

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9.21)9(0.161

9

uu

n

huu nh

mm/day97.8

169.21102.754.1736.0

161)( 9

ueeKE awML

3m000,157

102501000

97.87

4

(a) By Meyers formula:

(b) Evaporated volume in 7 days


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EL= Lake evaporation 1-m2area (mm/day)

Pa = Mean barometric reading (mm Hg)

ew = Saturated vapour pressure (mm Hg)

ea = Water vapour pressure (mm Hg)u0.6 = Wind velocity in km/h at 0.6 m above ground


EL= 0.771 (1.465-0.000732pa) (0.44+0.0733u0.6) (ew- ea)

Empirical Equations

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6.0

6.0

n

uu nh

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6.0

6.0

n

uu nhuh= wind velocity at a height habove the ground (h < 500 m)

un = wind velocity at nmeter above ground


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Empirical Formulae for


Daltons Formula




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Analytical Methods for


Water-Budget Method Energy-Budget Method



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This method is the simplest, but least reliable.

The method is an application of the principle of

continuity (conservation of mass).

Accuracy increases with time.

Water-Budget Method

Ground

Ground Surface

VogVig

VosVis

P ELTL

CROSS SECTION OF A LAKE

W t B d t M th d


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Daily Precipitation (P),

Daily Lake Evaporation (EL),

Daily Transpiration Loss (TL),

Daily Surface Inflow into the Lake (Vis),

Daily Surface Outflow from the Lake (Vos),

Daily Groundwater Inflow into the Lake (Vig),

Daily Groundwater Outflow from the Lake (Vog),

Increase in lake storage in a day (S)

Ground

Ground Surface

Vog Vig

VosVis

P ELTL


Water-Budget Method


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The continuity equation can then be written as,

P+ Vis+ Vig= Vos+ Vog+EL+ S+ TL

It can also be arranged as,

EL =P + (Vis- Vos) + (Vig- Vog)TL - S

Vig,Vogand TLare difficult to define and can only be roughly

estimated.

In view of the various uncertainties in the estimated values and

thepossibilities of errors in measured variables, the water-

budget method CANNOTgive very accurate results.

Water-Budget Method


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The method is an application of the principle of

conservation of energy, which include

consideration on the incoming energy, outgoing

energyand energy stored in the water body over a

known time of interval.

Results are satisfactory, with errors of the order

of 5% when applied to periods less than a week.



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Hg

Hi

Hs

HeHa

HbrHc

Hc

Hn = HcrHc-Hb= Hc (1r)-Hb


Hn = Net heat energy received by the water surface

Hc = Solar radiation

Hb = Back radiation (long wave) from water body

r = Reflection coefficient (albedo)

Ha = Sensible heat transfer from water surface to air = HeHe = Heat energy used up in evaporation = LvELHs = Heat stored in water body

Hg = Heat flux into the ground

Hi = Net heat conducted out of the system by water flow (advected energy)

***All the energy terms are in calories/mm2/day***

Hn=Ha+He+Hg+Hs +HiHn

Energy-BudgetMethod


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Hn=Ha+He+Hg+Hs +Hi

Negligible if the time periods are short

Bowens ratio, to correct the measurement

pa= Atmospheric pressure (mm of mercury) = 760 mm Hg

ew

= Saturated vapour pressure (mm of mercury)

ea= Actual vapour pressure (mm of mercury)

Tw= Temperature of water surface (C)

Ta = Temperature of air (C)


aw

awa

L

a

ee

TTp

LE

H

4101.6


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Typical values of Bowens ratio, :

Area

Tropical Oceans

Tropical Wet Jungles

Temperate Forests

Grassland

Semi-arid areas

Deserts

0.1

0.1 - 0.3

0.4 - 0.8

0.4 - 0.8

2-6

10



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The final equation after simplifications,

= Bowens ratio

w = density of water (1000 kg/m3)

Lv = latent heat of evaporation


1vw

isgn

L

L

HHHHE

Lv= (2.501 106)2370 Ta

Lv= 25012.37 Ta

Ta= air temperature in C

[J/kg]

[kJ/kg]


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ExampleCalculate the daily evaporation rate (in mm/day) from an open

surface, if the net radiation is 200 W/m2, relative humidity of

40%, water surface temperature is 30 oC and the air temperature

is 25 oC. Assume no other sensible heats or ground heat flux.


Daily evaporation rate = ??? mm/day

Hn= 200 W/m2

= 40%Tw= 30 oC

Ta= 25 oC

Hs=Hg= 0 W/m2


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Mass-transfer method is based on theories of turbulent mass

transfer in boundary layers to calculate the mass water vapor

transferred from the surface to the surrounding atmosphere

It estimates evaporation from modeling mass & momentumtransportof water vapour from evaporating surface by

convection.

Convection- the circulatory motionthat occurs in a fluid at a nonuniform

temperature owing to the variation of its density and the action of gravity

The equation is developed by EL= f(u) (ew- ea)

Mass Transfer (Aerodynamic) Method


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k = Von Karman constant (= 0.4)

pa = atmospheric pressure (100 kPa)

a = density of air (refer to table of water properties)

w = density of water (1000 kg/m3)

u = wind speed atZlevel

Z = height at which wind speed is measured

Zo = roughness height

)(

/ln

622.02

2

aw

owa

aL ee

ZZp

ukE


M T f (A d i ) M th d


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ExampleCalculate the evaporation rate from an open surface with airtemperature 20oC, water surface temperature 25oC, relative

humidity 40%, atmospheric pressure 100 kPa and wind speed

3 m/s, all measured at height 2 m above the water surface.

Assume a roughness height of 0.03 cm.


Daily evaporation rate = ??? mm/day

Tw= 25 oC

= 40%

Pa= 100 kPau2= 3 m/s

k= 0.4

Z= 2 m

Za= 0.03 cm = 0.0003 m

)(

/ln622.0

2

2

aw

owa

aL ee

ZZpukE


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Summary of Methods of Evaporation Estimation

Measurement using evaporimeter:

Class A Evaporation Pan

Colorado Sunken Pan


Empirical Equations:

Daltons Formula

Meyers Formula

RohwersFormula

Analytical Methods: Water-Budget Method




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Reduction of Evaporation from

Water Resources

Under certain circumstances, some countries (e.g. aridcountries) tend to control the amount of water loss fromthe evaporation process.

Why do we need to reduce evaporation?

Economic concerns

Conservation of water BUT, total prevention of evaporation is impossible.


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Water Conservation through the

Reduction of Evaporation

Reduction of Surface Area

Construction of reservoirs with minimum ratio of area to

storage

Storing water below ground

Storing water in one large reservoir instead of several

small reservoirs

Selecting proper reservoir sites


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Mechanical Covers

Roofs applied over the small reservoir

Examples:permanent, temporary, floating rafts, floatingparticles, etc)

Chemical Films

Application of thin chemical film (e.g. cetyl alcohol) on watersurface to reduce evaporation.

Characteristics of the films: strong, flexible, close back if

punctured, pervious to O2and CO2, colourless, odourless,

nontoxic etc

Water Conservation through

the Reduction of Evaporation

unit 3 - losses from precipitation (evaporation)

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