Page 121 - Biosystems Engineering

102 Cha pte r T h ree

Evaporation (E) is related to latent heat flux, E by E = E /(ρ λ ),
L L ω ν
3
where ρ is density of water [M/L ]. Substituting this into Eq. (3.6)
ω
and rearranging results in
⎛ dQ ⎞
−
E = ⎜ R − G H − ⎟ ρλ ν (3.7)
ω
n
⎝ dt ⎠
The ratio of sensible heat flux (H) to latent heat flux (E ) is called
L
the Bowen ratio (B) (i.e, H = BE ). Substituting this ratio results in
· L
⎛ dQ ⎞
⎜ ⎝ R − G − dt ⎠ ⎟
n
E = (3.8)
ρλ (1+ B)
ω
ν
The benefit of using the Bowen ratio in evaporation computations
is that B can be estimated independently as a function of temperature,
vapor pressure, and air pressure with empirical relationships.
3.4.3 Dalton’s Law
Dalton’s law is a simple way of computing evaporation from free
water surfaces:
E = C e −( e )
s a (3.9)
where E is the evaporation rate in millimeters per day, C is a constant,
and e and e are saturation vapor pressures at the temperature of the
s a
water surface and actual vapor pressure of the air, respectively, both
in kilopascal . For a given air temperature, there is a maximum mois-
ture content that air can hold. The air vapor pressure at this stage is
called saturation vapor pressure. At this pressure, evaporation and con-
densation rates are equal. It can be approximated as a function of
temperature by the following equation:

⋅
⎜
.
e = 0 611 exp ⎛ 17 27. + T ⎞ ⎟ (3.10)
T⎠
s
⎝ 237 3.
in which e is in kilopascals and T is in degrees Celsius. This equation is
s
valid for temperatures ranging from 0 to 50°C. The ratio of actual vapor
pressure to saturation vapor pressure is the relative humidity (R ):
h
e a
R = e (3.11)
h
s
The constant C in Eq. (3.9) can be estimated by C = 112.5 + 25.1u
7.6
for shallow ponds and C = 82.6 + 18.5u for small lakes and reser-
7.6
voirs, where u is the wind velocity at a height of 7.6 m above the
7.6
water surface in meters per second (Meyer 1942). The unit for C in
these equations is millimeters per month.