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3. Evaporation

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3. Evaporation Evaporation 49 __________________________________________________________________ . 3. EVAPORATION Evaporation occurs when water is converted into water vapor at the evaporating surface, the contact between water body and overlapping air. At the evaporative surface, there is a continuous exchange of liquid water molecule into water vapor & vice versa. The two main factors influencing evaporation from an open water surface are the supply of energy to provide the latent heat of vaporization, and the ability to transport the vapor away from the evaporative surface. The latent heat of vaporization lv is the amount of heat absorbed by a unit mass of a substance. Solar radiation is the main source of heat energy. The magnitude of annual evaporation is highly dependent on the prevailing climate in and around the water body. Evaporation has significant impact on water resources development especially in arid and semi-arid regions. Evaporation from Lake Nasser in Egypt (arid region) is about 3000 mm/year, where as evaporation from Lake Koka is about 1500 mm/year, which is half of that from Lake Nasser. Evaporation rate is a function of several meteorological and environmental factors such as net radiation, saturation vapor pressure, actual vapor pressure of air, air and water surface temperature, wind velocity and atmospheric pressure. Section 3.1 discusses definition and measurements of these variables. 3.1 Definition of some meteorological variables The atmosphere forms a distinctive, protective layer about 100 km thick around the Earth. To the hydrologist, the troposphere (the first 11 km) is the most important layer because it contains 75% of the weight of the atmosphere and virtually all its moisture. On average, the temperature from ground level to the tropopause falls steadily with increasing altitude at the rate of 6.5 oC /km. This is known as the lapse rate. Evaporation 50 __________________________________________________________________ . Evaporation at high altitudes is promoted due to low atmospheric pressure as expressed in the psychrometric constant. The effect is, however, small and in the calculation procedures, the average value for a location is sufficient. A simplification of the ideal gas law, assuming 20°C for a standard atmosphere, can be employed to calculate atmospheric pressure P: (3.1) where: P atmospheric pressure [kPa], z elevation above sea level [m], The psychrometric constant, , is given by: (3.2) where = Psychrometric constant [kPa °C-1], P = Atmospheric pressure [kPa], = Latent heat of vaporization, 2.45 [MJ kg-1], -3 -1 -1 cp = Specific heat at constant pressure, 1.013 10 [MJ kg °C ], and = ratio molecular weight of water vapour / dry air = 0.622. The specific heat at constant pressure is the amount of energy required to increase the temperature of a unit mass of air by one degree at constant pressure. Its value depends on the composition of the air, i.e., on its humidity. For average -3 -1 -1 atmospheric conditions a value cp = 11.013 10 [MJ kg °C ] can be used as an average atmospheric pressure is used for each location. 3 Air density: air density of moist air (kg/m )is estimated by a = 3.486 (p/(275 + T)) where p is the atmospheric pressure in kPa and T is air temperature in degrees Celsius. Evaporation 51 __________________________________________________________________ . Water vapor: the amount of water vapor in the atmosphere is directly related to the temperature. The water vapor content or humidity of air is usually measured as a vapor pressure, and the units used is millibar (mb). Specific humidity: The mass of water vapor per unit mass of moist air is called specific humidity qv and equals the ratio of the densities of water vapor v and of moist air a v qv = (3.3) a Vapor pressure: Dalton's law of partial pressures states that the pressure exerted by a gas (its vapor pressure) is independent of the pressure of other gases; the vapor pressure e of the water vapor is given by the ideal gas law as e = v Rv T (3.4) where T is the absolute temperature in K and Rv is the gas constant for water vapor. If the total pressure exerted by the moist air is p, then p-e is the partial pressure due to the dry air, and p - e = d Rd T (3.5) a = d + v (3.6) The gas constant for water vapor is Rd Rv = (3.7) 0.622 Evaporation 52 __________________________________________________________________ . where 0.622 is the ratio of the molecular weight of water vapor to the average molecular weight of dry air. Combining Eqs.(3.4), (3.5.) and (3.7) we get v p = ( + ) Rd T (3.8) d 0.622 The specific humidity qv is approximated by e q = 0.622 (3.9) v p where p = a Ra T The relationship between the gas constants for moist air and dry air is given by Ra = Rd (1 + 0.608qv ), Rd = 287 J/Kg.K (3.10) Saturation vapor pressure es : For a given air temperature, there is a maximum moisture content the air can hold and the corresponding vapor pressure is called saturation vapor pressure es . At this vapor pressure, the rates of evaporation and condensation are equal. Over a water surface the saturation vapor pressure is related to the air temperature with equation T es = 611 exp17.27 (3.11) 237.3 + T 2 Where es is in Pascal (Pa = N/m ) and T is air temperature in degree Celsius. Due to the non-linearity of the above equation, the mean saturation vapour pressure for a day, week, decade or month should be computed as the mean Evaporation 53 __________________________________________________________________ . between the saturation vapour pressure at the mean daily maximum and minimum air temperatures for that period. That is (3.12) Using mean air temperature instead of daily minimum and maximum temperatures results in lower estimates for the mean saturation vapour pressure. The corresponding vapour pressure deficit (a parameter expressing the evaporating power of the atmosphere) will also be smaller and the result will be some underestimation of the reference crop evapotranspiration. Therefore, the mean saturation vapour pressure should be calculated as the mean between the saturation vapour pressure at both the daily maximum and minimum air temperature. The relative humidity Rh: It is ratio of actual vapor pressure to its saturation value at a given air temperature T and is given by e Rh = (3.13) es Dew-point temperature Td : The dew-point temperature Td is the temperature at which space becomes saturated when air is cooled under constant pressure and with constant water-vapor content. It is the temperature having a saturation vapor pressure es equals to the existing vapor pressure e. Wet bulb thermometer measures the dew point temperature. Saturation deficit is the difference between the saturation vapor pressure at air temperature es and the actual vapor pressure represented by the saturation vapor pressure at Td which is the amount of water vapor in the air. The saturation deficit (es - e) represents the further amount of water vapor that the air can hold at the temperature Ta before becoming saturated. Evaporation 54 __________________________________________________________________ . Figure 3.1 Saturated vapor pressure as a function of temperature over water. Point C has vapor pressure e and temperature T, for which the saturated vapor pressure es. The temperature at which the air is saturated for vapor pressure e is the dew-point temperature Td. Figure 3.1 shows the saturation vapor pressure curve and the Td and T, es and e relationship. If the barometric pressure is kept constant and the temperature is reduced, i.e. if the air is cooled at constant barometric pressure, a stage will come when the air will become saturated with the same amount of vapor.If the cooling is continued, the vapor will get condensed on the contact surfaces. This condensation will be in the form of dew if the dew point is > O 0C; and it will be in the form of frost if the dew point is < 0 0C. Example 3.1 At a climatic station, air pressure is measured as 100 kPa, air temperature as 20 0C, and the wet-bulb, or dew-point, temperature as 16 0C. Calculate the corresponding vapor pressure, relative humidity, specific humidity, and air density. Solution: The saturated vapor pressure at T = 20 0C is given by T es = 611 exp(17.27 ) 237.3 + T Evaporation 55 __________________________________________________________________ . 17.27* 20 es = 611 exp( ) 237.3 + 20 = 2339 Pa and the actual vapor pressure e and the relative humidity are calculated using the dew- point temperature Td=16 C 17.27* 16 e = 611 exp( ) 237.3 + 16 = 1819Pa The relative humidity is = e/es = 1819 /2339 = 0.78 e q = 0.622 v p 1819 q = 0.622( ) v 100000 kg of water = 0.01133 kg moist air = 78% The air density is calculated from the ideal gas law p a = 287(1 + 0.608 qv )T(K) Evaporation 56 __________________________________________________________________ . 100000 = a 287(1 + 0.608* .01133)293 = 1.18 kg/m3 Note that the actual vapor pressure can be determined from the difference between the dry and wet bulb temperatures, the so-called wet bulb depression. The relationship is expressed by the following equation: ea = e° (Twet) - g psy (Tdry - Twet) (3.14) where ea = Actual vapour pressure [kPa], e°(Twet) = Saturation vapor pressure at wet bulb temperature [kPa], = Psychrometric constant [kPa °C-1], Tdry-Twet = Wet bulb depression, with Tdry the dry bulb and Twet the wet bulb temperature [°C]. The psychrometric constant of the instrument is given by: gpsy = apsy P (3.15) where apsy is a coefficient depending on the type of ventilation of the wet bulb -1 [°C ], and P is the atmospheric pressure [kPa].
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