Lecture 9 29-August-2016

EVAPORATION (contd…) We were discussing about evaporation from a pan. From the conservation of mass of water vapor in the control volume, we got the relation:

For the steady flow of air over the pan, we have

= 0

Therefore,

………………………… (1) From the conservation of mass equation for liquid water, we have got the relation, …………………………………….. (2)

Therefore, from Eqn.(1) and (2) we get,

…………………………….. (3)

From the conservation of heat energy in liquid,

+

Where,

|system is the rate at which heat is transferred into the liquid system.

|system is the rate at which fluid system does work on the surroundings. The work done by the fluid (liquid) system on its surroundings can be

divided into shaft work (Ws) and flow work (Wf). The work is due to work done by resultant pressure force as the system moves through space. Shaft work is any other work done by the fluid system other than the flow work. The flow work done by the liquid system is actually derived in the mechanics and is given as:

where, p is pressure.

Therefore,

+

For the case of Evaporation pan:

There is no work done by the liquid system on its surroundings. Therefore,

= 0

This is because there is no flow of water in the evaporation pan. i.e, V=0

Therefore,

The rate at which water surface elevation changes is much smaller as compared to the internal energy changes.

Therefore,

2 If Rn is the net radiation flux (W/m ) 2 Hs is the sensible heat to the air stream supplied by the water (W/m ) G is the ground heat flux to the ground surface

Then, for per unit area,

Assume that the temperature of water in the control volume is constant with respect to time. Therefore, the only change in heat stored within the control volume is the change in internal energy of the water evaporated. i.e., = where, is the latent heat of vaporisation.

Hence,

i.e. for unit area,

or =

i.e.

If and G are zero, then we have per unit area, then

Aerodynamic Method: As we know that evaporation depends on: o Supply of energy to provide latent hat of vaporization. o Ability to transport water vapor away from evaporative surface. The aerodynamic method deals with the second aspect. The fluid form of the expression for evaporation rate due to transport of water vapor is

where, is the evaporation rate due to vapor transport. B is the vapor transport co-efficient. is the saturated vapor pressure at the water surface.

is the vapor pressure at height z2 above the water surface (or ambient vapor pressure in air) Recall,

Combined Energy balance and Aerodynamic Method: In actual there will be both energy changes and vapor transport occurring. Therefore, the evaporation rate should include both. o If energy supply is non-limiting -Use aerodynamic method o If vapor transport is non-limiting -use energy-balance method.

The combined form is:

+

Where, is the evaporation rate [LT-1], where incoming radiation is absorbed by evaporation. is the evaporation rate [LT-1], due to aerodynamics situation. is the psychrometric constant ( 66.8 Pa/0C)

is the gradient of saturated vapor pressure curve.;