Losses from Precipitation EVAPORATION
Course Learning Outcome 1 CLO 1
On completion of this chapter, students will be able to evaluate water cycle for a catchment by estimation of precipitation and the losses using measurement , empirical and analytical methods. methods .
Program Outcome 1 PO 1
To acquire and apply engineering fundamentals to complex civil engineering problems (Engineering knowledge). knowledge).
Lesson Outcomes On completion of this chapter ,you will be able to:
identify factors influencing evaporation
measure the rate of evaporation evaporati on using various measurement techniques
estimate the rate of evaporation using
•
empirical equations
•
analytical methods
suggest strategies to reduce evaporation from water resources
Losses from Precipitation
Evaporation
Evapotranspiration
Infiltration
Depression Depressi on storage
EVAPORATION Evaporation is the process in which a liquid changes to the gaseous state at the free surface, below the boiling point through 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.
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
1. Vapor Pressures at Water Surface & Atmosphere 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.
The rate of evaporation ( E ) is proportional to the difference between the saturated vapour pressure at water temperature (ew) and the water vapour pressure in the air (ea). E C (ew ea )
E = in mm/day ; ew and ea = in mm Hg ; C = constant
Evaporation: ew > ea Condensation: e < e
2. Air & Water Temperature
water E (high correlation)
E
atm E (low correlation)
E
water
3. Atmospheric Pressure
Patm (e.g. at high altitudes)
E
atm
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
5. Wind Speed 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
E Critical velocity
Vwind
6. Quality of Water - Soluble Salts
Soluble salts in water
E
Specific gravity
E
Under the same conditions, evaporation from sea water is about 2-3% less than that from fresh water.
Estimation of Evaporation The amount of water evaporated from a water surface can be estimated 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 with evaporation measurements.
Measurement of Evaporation
Evaporation is estimated by using evaporimeters.
Evaporimeters are water-containing pans which are exposed to the atmosphere and 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
Class A Evaporation Pan
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.
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)
Day 1
Day 2
Add water when the water depth in the pan drops too much
Take water out of the pan when the water depth rises too much
Colorado Sunken Pan
The Colorado Sunken Pan is 920 mm2 and 460 mm deep, made up of galvanized iron sheet and buried into the ground within 100 mm of the top. Radiation and aerodynamic characteristics are similar to those of a lake Difficult to detect leak , tall grass and dust might disturb measurement, expansive to install
US Geological Survey Floating Pan
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 level as the lake leaving a rim of 75 mm. Simulate the radiation and aerodynamic characteristics of large body of water High cost of installation and maintenance Difficult to perform measurements
Limitations of Evaporation Pans 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 similar climatic and exposure conditions. C p
Lake evaporation Pan evaporation
Types of pan
Average C p
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
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
Methods of Evaporation Estimation
Empirical Equations: Dalton’s Formula Meyer’s Formula Rohwer’s Formula
Analytical Methods: Water-Budget Method Energy-Budget Method Mass Transfer Method
Relevant Parameters
Latent Heat of Evaporation (Lv ):
Amount of energy needed for liquid water to change phase to vapour. Lv = (2.501 x 10 6) - 2370T a
[J/kg]
Lv = 2501 – 2.37T a
[kJ/kg]
Note: T a = air temperature in C
Water Vapour Pressure (ea ):
Actual vapour pressure exerted by water vapour at air temperature.
Saturated Vapour Pressure (ew ): Vapour pressure exerted by water vapour at water surface temperature. Contains maximum moisture. How to find ew? 1. Refer to Table 3.3 in textbook (pg. 72), or 2. Use this equation, ew
17.27 T 611 exp 237.3 T w
w
ew
17.27 T 4.584 exp 237.3 T w
w
[Pa or N/m2]
Note: T w = Water temperature in C
[mm of Hg]
Table 3.3 (Pg72): ew and A Saturated 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
0.71
15.0
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
= Slope of
Relative Humidity ( ):
The ratio of the actual water vapour pressure of the air, ea to that at saturated, ew. Unit %
ea ew
100
ea
.ew 100
Empirical Formulae for Evaporation Estimation
Dalton’s Formula Meyer’s Formula (1915) Rohwer’s Formula (1931)
Dalton’s Formula E L = K f (u) (ew- ea) E L = ew = ea = f(u) = K =
Lake evaporation (mm/day) Saturated vapour pressure (mm of Hg) Water vapour pressure (mm of Hg) Wind speed correction function Dalton’s coefficient
Meyer’s Formula (1915) u9 E L K M (ew ea )1 16 E L = Lake evaporation for 1-m2 area (mm/day) K M = Meyer’s coefficient accounting for different waters 0.36 for large deep waters 0.50 for small, shallow waters
ew ea u9
= Saturated vapour pressure (mm Hg) = Water vapour pressure (mm Hg) = Monthly mean wind velocity in km/h at 9 m above ground 1/ 7
h u h un n
uh = wind velocity at a height h above the ground (h < 500 m) un = wind velocity at n meter above ground
Example A reservoir with a surface area of 250 hectares (large waters, K M = 0.36 ) had the following average values of parameters during a week:
Water temperature = 20oC (T w = 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 evaporation per unit m2 of the lake
(b)
the volume of water evaporated from the lake during that one week .
Solution 17.27T w 237.3 T w
ew 4.584 exp
17.27 20 4.584 exp 237 . 3 20 17.54 mm of Hg e
a
0.4
0.4 e
7.02 mm of Hg
(Relativehumidity)
(a) By Meyers’ formula:
E L K M (ew ea )1
u9
16
21.9 0.3617.54 7.021 16 8.97 mm/day
e
w
e
a
w
0.4 17.54
7
1/ 7
h uh un n
8.97 1000
250 104
157,000 m3
1/ 7
9 u9 u1 1
(b) Evaporated volume in 7 days
16.0(9)1/ 7 21.9 km/h
Empirical Equations
Rohwer’s Formula (1931) E L= 0.771 (1.465-0.000732 pa) (0.44+0.0733u0.6) (ew- ea) E L = Lake evaporation 1-m2 area (mm/day) P a = 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 1/ 7
uh0.6
0.6 un n
uh = wind velocity at a height h above the ground (h < 500 m) un = wind velocity at n meter above ground
Empirical Formulae for Evaporation Estimation
Dalton’s Formula Meyer’s Formula (1915) Rohwer’s Formula (1931)
Analytical Methods for Evaporation Estimation
Water-Budget Method Energy-Budget Method Mass Transfer Method
Water-Budget Method
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. P E L
T L V os
V is
V og
V ig CROSS SECTION OF A LAKE
Ground Surface
Ground
Water-Budget Method P E L
T L V os
V is
V og
V ig
Ground Surface
Ground
CROSS SECTION OF A LAKE
Daily Precipitation (P), Daily Lake Evaporation (E L ), Daily Transpiration Loss (T L ), Daily Surface Inflow into the Lake (V is ), Daily Surface Outflow from the Lake (V os ), Daily Groundwater Inflow into the Lake (V ig ), Daily Groundwater Outflow from the Lake (V og ), Increase in lake storage in a day ( S)
Water-Budget Method
The continuity equation can then be written as, P + V is + V ig = V os + V og + E L + S + T L
It can also be arranged as, E L = P + (V is - V os) + (V ig - V og ) – T L - S
V ig ,V og and T L are difficult to define and can only be roughly estimated. In view of the various uncertainties in the estimated values and the possibilities of errors in measured variables, the water budget method CANNOT give very accurate results.
Energy-Budget Method
The method is an application of the principle of conservation of energy, which include consideration on the incoming energy, outgoing energy and 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 .
H n
H n = H a + H e + H g + H s + H i
H b
H c
rH c
H a
H n = H c – rH c - H b= H c (1 – r) - H b
H e
H s H i
H g
d o h t e M t e g d u B y g r e n E
CROSS SECTION OF A LAKE
H n = Net heat energy received by the water surface H c = Solar radiation H b = Back radiation (long wave) from water body r = Reflection coefficient (albedo) H a = Sensible heat transfer from water surface to air = H e H e = Heat energy used up in evaporation = Lv E L H s = Heat stored in water body H g = Heat flux into the ground H i = Net heat conducted out of the system by water flow (advected energy) ***All the energy terms are in calories/mm2/day ***
Energy-Budget Method H n = H a + H e + H g + H s + H i Negligible if the time periods are short
H a
LE L
6.1104 pa
T w T a ew ea
Bowen’s 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) T w = Temperature of water surface ( C) T a = Temperature of air (C)
Energy-Budget Method
Typical values of Bowen’s ratio, : Area
Tropical Oceans
0.1
Tropical Wet Jungles
0.1 - 0.3
Temperate Forests
0.4 - 0.8
Grassland
0.4 - 0.8
Semi-arid areas
2-6
Deserts
10
Energy-Budget Method
The final equation after simplifications,
E L
H n H g H s H i
w Lv 1
= Bowen’s ratio w = density of water (1000 kg/m3)
Lv = latent heat of evaporation Lv = (2.501
106) – 2370 T a
Lv = 2501 – 2.37 T a
T a = air temperature in C
[J/kg] [kJ/kg]
Energy-Budget Method
Example Calculate the daily evaporation rate (in mm/day) from an open surface, if the net radiation is 200 W/m 2, 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 H n = 200 W/m2
= 40% T w = 30 oC T a = 25 oC H s = H g = 0 W/m2
Mass Transfer (Aerodynamic) Method
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 & momentum transport of water vapour from evaporating surface by convection. Convection - the circulatory motion that 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 E L = f (u) (ew- ea)
Mass Transfer (Aerodynamic) Method 2
E L
k
0.622k au pa w ln Z / Z o
2
(ew ea )
= 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 at Z level
Z = height at which wind speed is measured Z o = roughness height
Mass Transfer (Aerodynamic) Method
Example Calculate the evaporation rate from an open surface with air temperature 20oC, water surface temperature 25 oC, 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 T w = 25 oC
= 40% P a = 100 kPa u2 = 3 m/s
E L
k = 0.4 Z = 2 m Z a = 0.03 cm = 0.0003 m
0.622k 2 au pa w ln Z / Z o
2
(ew ea )
Summary of Methods of Evaporation Estimation
Measurement using evaporimeter:
Class A Evaporation Pan
Colorado Sunken Pan
US Geological Survey Floating Pan
Empirical Equations: Dalton’s Formula Meyer’s Formula Rohwer’s Formula Analytical Methods: Water-Budget Method Energy-Budget Method Mass Transfer Method
Reduction of Evaporation from Water Resources
Under certain circumstances, some countries (e.g. arid countries) tend to control the amount of water loss from the evaporation process. Why do we need to reduce evaporation? Economic concerns Conservation of water BUT, total prevention of evaporation is impossible.
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
