direct estimation of Wetbulb Temperature? 1

[70AARCUDA]

...although this is probably a WX-question, does anybody know of ANY equations (empirical or not) for directly estimating Wetbulb Temperature?

...the ONLY one I've found is this (E.A.Anderson,1968):

Tw = T - (T - Td)*(0.12 + 0.008*T)...all in degrees-F.

...all I'm seeking is reasonable, integer-value, accuracy.


Thanks,
"...just another electron counter!"

 

[MintJulep]

Knowing what? Can't get there if all you know is the drybulb temp. If you know any two properties of moist air, you can calculate any of the other properties, so no need for estimation.

I'm guessing that in the equation you provide, Td is the dewpoint temperature.

 

[70AARCUDA]

...local Airport WX only posts T and Td (yes, Td is dewpoint temp) but does NOT post Tw (I've asked).

...during summer months, T and Tw are needed to estimate cooler efficiency (actually saturation efficiency), not Td.

...just wondering if anyone knew of any useful empirical equations...only need integer value accuracy, because WX-dept only posts integer T and Td values.

 

[torpen]

Hello,

The following recipe is not straight but you have all the ingredients. You can adapt it if you only need integer value accuracy.


The equation of the ideal psychometric allows to calculate from the measures of T and Tw and for a given atmospheric pressure P the saturation water vapor pressure and then the dewpoint temperature.


Relation of the ideal psychometric

e'w(Td,P) = e'w(Tw,P) - A * P * (T-Tw) (1)
with,
T : dry-bulb temperature
Td : dewpoint temperature
Tw : wet-bulb temperature
e'w(T,P) : saturation water vapor pressure at T and P
A : psychometric constant
A = Cpa / (delta * L(Tw)) * (P - e'w(Tw,P)) / P
L : Latent heat of vaporization
L(Tw) ~ 2501.6E3 - 2.361 * Tw
delta : ratio of the mole weight of water vapor and air (delta = 0.62198)
Cpa : Heat capacity of dry air (Cpa = 1006 J/(kg.K))


corrective factor fw

fw = e'w / ew (2)

for standard atmospheric conditions : 1.004 < fw < 1.006
(for a pressure of 10 bar fw = 1.03)


Relation between saturation water vapor pressure ew (Pa) and temperature T (K)
ln(ew) = -6096.9385 * 1/T + 21.2409642 – 2.711193E–2 * T
+ 1.673952E10–5 * T^2 + 2.433502 * ln(T) (3)
for 173.15 K < T < 373.15 K

This equation comes from Sonntag (1990).
SONNTAG (D.). – Vapor pressure Formulationsbased on the ITS-90 and psychrometer formulate - Important new values of the physical constants of 1986. Z Meteorologie, 70, p. 5-340 à 344 (1990).


For a pressure P and with T and Tw known :
- calculate ew(T,P) and ew(Tw,P) with equation (3)
- find e'w(T,P) and e'w(Tw,P) with (2)
- determine e'w(Td,P) by using (1)
- calculate ew(Td,P) with equation (2)
- solve (3) to find Td

And you have for a given atmospheric pressure a table with the 3 temperatures T, Td and Tw.


Bibliography
Jensen, M.E., R.D. Burman, and R.G. Allen. 1990.
Evapotranspiration and irrigation water requirements.
ASCE Manuals and Reports on Engineering Practice No. 70.


Regards,

Torpen