Latent Heat Exchange
193
latent heat loss by sweating, but do not otherwise treat water loss under
heat stress.
Example 12.1. White crown sparrows migrate over long distances. In
flight, both water and energy are expended. If an average sparrow weighs
27 g, and can store 4 g of fat and 4 g of water (including the water
obtained from metabolism), will its range be limited by stored energy or
stored water? Assume the metabolic rate for flight is 6Mb and the energy
content of fat is 40 Wg. Also assume T, = 10" C, T, = 38" C, and
ea = 1 kPa.
Solution. The energy-limited flight time is equal to the total energy
available divided by the rate of energy consumption. The rate of energy
consumption is 6Mb. Assuming Mb = 50 w/m2, M = 300 w/m2. From
Eq. (12.13), the sparrow area is A = 0.1 x (0.027)~/~ = 0.009 m 2 . The
energy limited flight time is
4g x 40000
tamgy =
= 59,259 s = 16.4 hour.
300& x 0.009m 2
Water loss is from the skin and from the respiratory tract. The vapor
pressure of the air is given, and the vapor pressure at the evaporating
surfaces is e, (38) = 6.63 H a . Assuming a flight altitude of 1000 m, then
pa = 89 kPa. Again we ignore effects of coat and boundary layer on vapor
conductance, and use the sparrow skin conductance from Table 12.1.
Using these numbers, the rate of skin water loss is
mol
6.63kPa-1kPa
mol
E, = 0.0054 - x
= 0.00034 - .
m 2 s
89 kPa
m 2 s
Equation (12.15) can be used to get the respiratory water loss. The inspired air is at the vapor pressure of the atmosphere and the expired air
is saturated at the expired air temperature. From Fig. 12.3, the sparrow
expired air temperature at 10°C ambient is 21°C. The saturation vapor
pressure is 2.49 kPa. The rate of respiratory water loss is therefore
2. 49 kPa-1 kPa
rnol
E, = 300
89 Wa
= 00021 -
480000
x 0.05
m 2 s
The total rate of water loss is the sum of respiratory and skin loss, or
0.00045 rnol m-2 s-I. The stored water is 4 g +18 glmol = 0.22 mol.
The water limited flight time is
0.22 rnol
hater =
= 54321 s = 15 hours.
0.00045 $ x 0.009m 2
With this set of assumptions, it appears that water and energy are about
equally limiting. The assumptions were not arbitrary, but were taken from
literature on white crown sparrows, so the conclusions are probably not
far off. It should not be a surprise that the two limitations would be that
193
latent heat loss by sweating, but do not otherwise treat water loss under
heat stress.
Example 12.1. White crown sparrows migrate over long distances. In
flight, both water and energy are expended. If an average sparrow weighs
27 g, and can store 4 g of fat and 4 g of water (including the water
obtained from metabolism), will its range be limited by stored energy or
stored water? Assume the metabolic rate for flight is 6Mb and the energy
content of fat is 40 Wg. Also assume T, = 10" C, T, = 38" C, and
ea = 1 kPa.
Solution. The energy-limited flight time is equal to the total energy
available divided by the rate of energy consumption. The rate of energy
consumption is 6Mb. Assuming Mb = 50 w/m2, M = 300 w/m2. From
Eq. (12.13), the sparrow area is A = 0.1 x (0.027)~/~ = 0.009 m 2 . The
energy limited flight time is
4g x 40000
tamgy =
= 59,259 s = 16.4 hour.
300& x 0.009m 2
Water loss is from the skin and from the respiratory tract. The vapor
pressure of the air is given, and the vapor pressure at the evaporating
surfaces is e, (38) = 6.63 H a . Assuming a flight altitude of 1000 m, then
pa = 89 kPa. Again we ignore effects of coat and boundary layer on vapor
conductance, and use the sparrow skin conductance from Table 12.1.
Using these numbers, the rate of skin water loss is
mol
6.63kPa-1kPa
mol
E, = 0.0054 - x
= 0.00034 - .
m 2 s
89 kPa
m 2 s
Equation (12.15) can be used to get the respiratory water loss. The inspired air is at the vapor pressure of the atmosphere and the expired air
is saturated at the expired air temperature. From Fig. 12.3, the sparrow
expired air temperature at 10°C ambient is 21°C. The saturation vapor
pressure is 2.49 kPa. The rate of respiratory water loss is therefore
2. 49 kPa-1 kPa
rnol
E, = 300
89 Wa
= 00021 -
480000
x 0.05
m 2 s
The total rate of water loss is the sum of respiratory and skin loss, or
0.00045 rnol m-2 s-I. The stored water is 4 g +18 glmol = 0.22 mol.
The water limited flight time is
0.22 rnol
hater =
= 54321 s = 15 hours.
0.00045 $ x 0.009m 2
With this set of assumptions, it appears that water and energy are about
equally limiting. The assumptions were not arbitrary, but were taken from
literature on white crown sparrows, so the conclusions are probably not
far off. It should not be a surprise that the two limitations would be that