Heat and Mass Transport
living organisms and their environment, the following needs to be known:
the vapor concentration at the evaporating surface, the vapor concentration of the air, and the total resistance to vapor transfer between the
evaporating surface and the air. We showed earlier how to calculate vapor
concentration in the air from humidity and air temperature, or from dew
point or wet bulb temperature measurements. The vapor concentration
at the evaporating surface is calculated by knowing the temperature of
the surface and the water potential of the liquid phase from which water
is evaporating. As shown in Ch. 4, the humidity is often very near 1.0
at the evaporating surface, so the vapor concentration at the evaporating surface, in these cases, is just the saturation concentration at surface
temperature.
The conductances to water loss are generally series combinations of
boundary layer and surface conductances. We consider boundary layer
conductance in detail in Ch. 7. To give some indication of the sizes of
conductances in nature, a 1 cm thickness of still air has a conductance
around 100 mmol m-2 s-'. The boundary layer conductances of leaves
and of crops typically range from 500 to 1000 mmol m-2 s-' .
Equation (6.8) is used similarly. The temperature of the environment
and organism needs to be known as well as values for all resistances or
conductances between the organism and the environment.The total resistance may be a series combination of several component resistances, as it
is with vapor resistances. The magnitudes of these resistances, at least in
the boundary layer and in a layer of still air, are similar to those for vapor.
We now go through several example calculations to show how Eqs. (6.7)
and (6.8) are used.
Example 6.1. Find the rate of water loss from a crop. Assume the canopy
temperature is 30" C, the air vapor pressure is 1.0 kPa, canopy conductance is 1 mol m-2 s-', and boundary layer conductance is 0.5 mol m-2
s-' .
Solution. The humidity at the evaporating surfaces inside the leaves
is essentially 1, (Eq. (4.13), with @ = -1000 Jkg), so Cv, =
h,,es(Ts)/pa = 1 x 4.24kPa/lOlkPa = 0.042 mol/mol. The vapor
concentration in the air is Cva = 1 . Ok Pa/101kPa = 0.0099. The total
conductance for vapor exchange is the series combination of canopy and
boundary layer conductance:
1
gv =
1
I
= 0.33 mol m-2 s-'
1 mol m-2 s-I + 0.5 mol m-2 s-1
The evaporative loss is therefore
E = 0.33 mol m-2 s-'(0.042 - 0.009)
= 0.0107mol m-2 s-' = 10.7m mol m-2 s-' .
living organisms and their environment, the following needs to be known:
the vapor concentration at the evaporating surface, the vapor concentration of the air, and the total resistance to vapor transfer between the
evaporating surface and the air. We showed earlier how to calculate vapor
concentration in the air from humidity and air temperature, or from dew
point or wet bulb temperature measurements. The vapor concentration
at the evaporating surface is calculated by knowing the temperature of
the surface and the water potential of the liquid phase from which water
is evaporating. As shown in Ch. 4, the humidity is often very near 1.0
at the evaporating surface, so the vapor concentration at the evaporating surface, in these cases, is just the saturation concentration at surface
temperature.
The conductances to water loss are generally series combinations of
boundary layer and surface conductances. We consider boundary layer
conductance in detail in Ch. 7. To give some indication of the sizes of
conductances in nature, a 1 cm thickness of still air has a conductance
around 100 mmol m-2 s-'. The boundary layer conductances of leaves
and of crops typically range from 500 to 1000 mmol m-2 s-' .
Equation (6.8) is used similarly. The temperature of the environment
and organism needs to be known as well as values for all resistances or
conductances between the organism and the environment.The total resistance may be a series combination of several component resistances, as it
is with vapor resistances. The magnitudes of these resistances, at least in
the boundary layer and in a layer of still air, are similar to those for vapor.
We now go through several example calculations to show how Eqs. (6.7)
and (6.8) are used.
Example 6.1. Find the rate of water loss from a crop. Assume the canopy
temperature is 30" C, the air vapor pressure is 1.0 kPa, canopy conductance is 1 mol m-2 s-', and boundary layer conductance is 0.5 mol m-2
s-' .
Solution. The humidity at the evaporating surfaces inside the leaves
is essentially 1, (Eq. (4.13), with @ = -1000 Jkg), so Cv, =
h,,es(Ts)/pa = 1 x 4.24kPa/lOlkPa = 0.042 mol/mol. The vapor
concentration in the air is Cva = 1 . Ok Pa/101kPa = 0.0099. The total
conductance for vapor exchange is the series combination of canopy and
boundary layer conductance:
1
gv =
1
I
= 0.33 mol m-2 s-'
1 mol m-2 s-I + 0.5 mol m-2 s-1
The evaporative loss is therefore
E = 0.33 mol m-2 s-'(0.042 - 0.009)
= 0.0107mol m-2 s-' = 10.7m mol m-2 s-' .