THE AQEOUS LIQUID AND VOLATILE LIQUID CONVERSION INTO VAPOR PRESURE AND FACTORS AFFECTING , THE PAN USED AND ITS CALCULATIONS

1. Evaporation

2. Evaporation
• Terminology
– Evaporation – process by which liquid
water passes directly to the vapor phase
– Transpiration - process by which liquid
water passes from liquid to vapor through
plant metabolism
– Sublimation - process by which water
passes directly from the solid phase to the
vapor phase

3. Factors Influencing Evaporation
• Energy supply for
vaporization (latent heat)
– Solar radiation
• Transport of vapor away from
evaporative surface
– Wind velocity over surface
– Specific humidity gradient
above surface
• Vegetated surfaces
– Supply of moisture to the
surface
– Evapotranspiration (ET)
• Potential Evapotranspiration
(PET) – moisture supply is not
limited
nR
E
Net radiation
Evaporation
Air Flow
u

4. Evaporation from a Water
Surface
• Simplest form of evaporation
– From free liquid of permanently saturated
surface

5. Evaporation from a Pan
• National Weather Service Class A
type
• Installed on a wooden platform in a
grassy location
• Filled with water to within 2.5 inches
of the top
• Evaporation rate is measured by
manual readings or with an analog
output evaporation gauge
h
Area, A
CS
w
a
AEm wv 
dt
dh
E 
nRsH
Sensible
heat to air
Net radiation Vapor flow rate
Heat conducted
to ground
G

6. Methods of Estimating Evaporation
• Energy Balance Method
• Aerodynamic method
• Combined method

7. Energy Method
• CV contains liquid and vapor phase water
• Continuity - Liquid phase
  
CS
w
CV
wv d
dt
d
m dAV
0
dt
dh
Aw No flow of liquid
water through CS
AEm wv 
E
dt
dh

hw
a
vm
dt
dh
E 
nRsH
G

8. Energy Method
• Continuity - Vapor phase
 
CS
avw qAE dAV
0
Steady flow of air
over water
AEw
  
CS
av
CV
avv qdq
dt
d
m dAV
 
CS
av
w
q
A
E dAV

1
 
CS
avv qm dAV
hw
a
vm
dt
dh
E 
nRsH
G

9.  
 
CS
u
CV
u
dgzVe
dgzVe
dt
d
dt
dW
dt
dH
AV



)2/(
)2/(
2
2
Energy Method
• Energy Eq.
0
hw
a
vm
dt
dh
E 
nRsH
G
.,0;0 consthV 
 
CV
wu de
dt
d
dt
dH

GHR
dt
dH
sn 
GHR sn 

10. Energy Method
• Energy Eq. for Water in CV
Assume:
1. Constant temp of water in CV
2. Change of heat is change in internal energy of water evaporated
hw
a
vm
dt
dh
E 
nRsH
G
vvml
dt
dH

GHR
dt
dH
sn 
GHRml snvv  AEm w
 GHR
Al
E sn
wv


1
Recall:
wv
n
r
l
R
E


Neglecting sensible and ground heat
fluxes

11. Wind as a Factor in Evaporation
• Wind has a major effect on evaporation, E
– Wind removes vapor-laden air by convection
– This Keeps boundary layer thin
– Maintains a high rate of water transfer from
liquid to vapor phase
– Wind is also turbulent
• Convective diffusion is several orders of magnitude
larger than molecular diffusion

12. Aerodynamic Method
• Include transport of vapor
away from water surface
as function of:
– Humidity gradient above
surface
– Wind speed across surface
• Upward vapor flux
• Upward momentum flux
nR
E
Net radiation
Evaporation
Air Flow
12
21
zz
qq
K
dz
dq
Km
vv
wa
v
wa


 
12
12
zz
uu
K
dz
du
K mama


 
 
 12
21
uuK
qqK
m
m
vvw




13. Aerodynamic Method
• Log-velocity profile
• Momentum flux
nR
E
Net radiation
Evaporation
Air Flow
 
 12
21
uuK
qqK
m
m
vvw










oZ
Z
ku
u
ln
1
*
 
 
2
12
12
ln 




 

ZZ
uuk
a
  
  2
12
12
2
ln
21
ZZK
uuqqkK
m
m
vvaw 



Thornthwaite-Holzman Equation
u
Z

14. Aerodynamic Method
• Often only available at 1
elevation
• Simplifying
nR
E
Net radiation
Evaporation
Air Flow
  
  2
12
12
2
ln
21
ZZK
uuqqkK
m
m
vvaw 



uqv and
 
  2
2
2
2
ln
622.0
o
aasa
ZZP
ueek
m




AEm w
 aasa eeBE 
  2
2
2
2
ln
622.0
ow
a
ZZP
uk
B



2@pressurevapor Zea 

15. Combined Method
• Evaporation is calculated by
– Aerodynamic method
• Energy supply is not limiting
– Energy method
• Vapor transport is not limiting
• Normally, both are limiting, so use a combination
method
ar EEE


 




wv
n
r
l
R
EE


 aasa eeBEE 
wv
hp
Kl
pKC
622.0

2
)3.237(
4098
T
e
dT
de ss


rEE


 3.1
Priestly & Taylor

16. Example
– Elev = 2 m,
– Press = 101.3 kPa,
– Wind speed = 3 m/s,
– Net Radiation = 200 W/m2,
– Air Temp = 25 degC,
– Rel. Humidity = 40%,
• Use Combo Method to find Evaporation
kJ/kg244110)25*36.22500(
237010501.2
3
6


x
Txlv
mm/day10.7
997*102441
200
3

xl
R
E
wv
n
r


17. Example (Cont.)
– Elev = 2 m,
– Press = 101.3 kPa,
– Wind speed = 3 m/s,
– Net Radiation = 200 W/m2,
– Air Temp = 25 degC,
– Rel. Humidity = 40%,
• Use Combo Method to find Evaporation
 
mm/day45.7
)day1/s86400(*)m1/mm1000(*126731671054.4 11

 
xEa
     
sm/Pa1054.4
1032ln997*3.101
3*19.1*4.0*622.0
ln
622.0 11
24
2
2
2
2
2
 

x
xZZP
uk
B
ow
a


Pa3167ase
Pa12673167*4.0*  asha eRe

18. Example (Cont.)
– Elev = 2 m,
– Press = 101.3 kPa,
– Wind speed = 3 m/s,
– Net Radiation = 200 W/m2,
– Air Temp = 25 degC,
– Rel. Humidity = 40%,
Pa/degC1.67
102441*622.0
103.101*1005
622.0 3
3

x
x
Kl
pKC
wv
hp

• Use Combo Method to find Evaporation
Pa/degC7.188
)253.237(
3167*4098
2



738.0



mm/day2.745.7*262.010.7*738.0 




 ar EEE



262.0
 


19. Example
– Net Radiation = 200 W/m2,
– Air Temp = 25 degC,
• Use Priestly-Taylor Method to find
Evaporation rate for a water body
rEE


 3.1 Priestly & Taylor
mm/day10.7rE 738.0



mm/day80.610.7*738.0*3.1 E

20. Evapotranspiration
• Evapotranspiration
– Combination of evaporation from soil surface and
transpiration from vegetation
– Governing factors
• Energy supply and vapor transport
• Supply of moisture at evaporative surfaces
– Reference crop
• 8-15 cm of healthy growing green grass with abundant water
– Combo Method works well if B is calibrated to local
conditions

21. Potential Evapotranspiration
• Multiply reference crop ET by a Crop Coefficient and a
Soil Coefficient rcs ETkkET 
3.10.2
t;CoefficienCrop


c
c
k
k
10
t;CoefficienSoil


s
s
k
k
ETActualET
ETCropReferencerET
http://www.ext.colostate.edu/pubs/crops/04707.html
CORN
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 20 40 60 80 100 120 140 160
Time Since Planting (Days)
CropCoefficient,kc