Wet Bulb Formula - Order of Operation

[apprentice3]

Tw = T * arctan[0.151977 * (rh% + 8.313659)^(1/2)] + arctan(T + rh%) - arctan(rh% - 1.676331) + 0.00391838 *(rh%)^(3/2) * arctan(0.023101 * rh%) - 4.686035

T= Dry Bulb Temperature in Celcius
Tw = Wet Bulb Temperature in Celcius
rh% = Relative Humidity

I am being tasked with using the formula above to calculate the wet bulb temperature in a module based control program. The formula is too long to input directly into the equation module built into the control program. I am trying to figure out how to break this equation down in the order of operation to properly calculate the wet bulb temperature properly. It would really help me out if I can see this problem figured out with all of the work shown. In my test program I am using 21.11 degrees C for T and 50% for %rh. Based on some online calculators this should provide a wet bulb temperature of 14.65 degrees C. Can anyone assist me with figuring out this problem? Thanks for the help!

 

[topsquark]

Tw = T * arctan[0.151977 * (rh% + 8.313659)^(1/2)] + arctan(T + rh%) - arctan(rh% - 1.676331) + 0.00391838 *(rh%)^(3/2) * arctan(0.023101 * rh%) - 4.686035

T= Dry Bulb Temperature in Celcius
Tw = Wet Bulb Temperature in Celcius
rh% = Relative Humidity

I am being tasked with using the formula above to calculate the wet bulb temperature in a module based control program. The formula is too long to input directly into the equation module built into the control program. I am trying to figure out how to break this equation down in the order of operation to properly calculate the wet bulb temperature properly. It would really help me out if I can see this problem figured out with all of the work shown. In my test program I am using 21.11 degrees C for T and 50% for %rh. Based on some online calculators this should provide a wet bulb temperature of 14.65 degrees C. Can anyone assist me with figuring out this problem? Thanks for the help!

Calculate
T * atn[0.151977 * (rh% + 8.313659)^(1/2)]
atn(T + rh%)
atn(rh% - 1.676331)
0
0.00391838 * (rh%)^(3/2) * atn(0.023101 * rh%)

Add them and subtract the 4.686035

-Dan

 

[apprentice3]

if I use 21.11 for T and 50 for rh. Can you show the work to get the result? I still don’t follow how to get 14.65 as the result.

 

[Deleted member 4993]

if I use 21.11 for T and 50 for rh. Can you show the work to get the result? I still don’t follow how to get 14.65 as the result.

You follow the method described above by Dan and show us what do you get as a "result".

You may want to use a spreadsheet (like MS_Excel)- so that you can keep track of the progression of the numbers.

 

[Dr.Peterson]

Tw = T * arctan[0.151977 * (rh% + 8.313659)^(1/2)] + arctan(T + rh%) - arctan(rh% - 1.676331) + 0.00391838 *(rh%)^(3/2) * arctan(0.023101 * rh%) - 4.686035

T= Dry Bulb Temperature in Celcius
Tw = Wet Bulb Temperature in Celcius
rh% = Relative Humidity

I am being tasked with using the formula above to calculate the wet bulb temperature in a module based control program. The formula is too long to input directly into the equation module built into the control program. I am trying to figure out how to break this equation down in the order of operation to properly calculate the wet bulb temperature properly. It would really help me out if I can see this problem figured out with all of the work shown. In my test program I am using 21.11 degrees C for T and 50% for %rh. Based on some online calculators this should provide a wet bulb temperature of 14.65 degrees C. Can anyone assist me with figuring out this problem? Thanks for the help!

I found the presumed source here: https://journals.ametsoc.org/view/journals/apme/50/11/jamc-d-11-0143.1.xml



You copied the formula correctly; and the article confirms, as I would expect, that the arctan takes radians and RH% for your example would be called 50.

This is followed by a graph on which I can confirm that for T about 21 and RH% about 50, you should get T_w about 15. (I was wondering if your online calculator might use a very different formula.)

if I use 21.11 for T and 50 for rh. Can you show the work to get the result? I still don’t follow how to get 14.65 as the result.

I put the formula into Excel in this form:

=A2*ATAN((B2+8.313659)^(1/2))+ATAN(A2+B2)-ATAN(B2-1.676331)+0.00391838*(B2)^(3/2)*ATAN(0.023101*B2)-4.686035​

The result was 14.65368835. So the formula is good.

Now you need to show us what you are getting, and how; possibly I've already mentioned something you weren't taking into account, such as using radians. Once you're getting the right number, you can try coding it.

 

[Cubist]

Calculate
T * atn[0.151977 * (rh% + 8.313659)^(1/2)]
atn(T + rh%)
atn(rh% - 1.676331)
0
0.00391838 * (rh%)^(3/2) * atn(0.023101 * rh%)

Add them and subtract the 4.686035

-Dan

Dan must have accidentally deleted a minus sign while rearranging onto separate lines:-
- atn(rh% - 1.676331) OP note that you need a minus at the start of this line

 

[apprentice3]

I can't say that I even know what a radian is. I keep trying to run this formula through a calculator/ equation module. I think something is going wrong in the first part of the equation. I have listed my initial answers in BOLD below:

21.11 * arctan[0.151977 * (50 + 8.313659)^(1/2)] 1039.72
arctan(21.11 + 50) 89.19
arctan(50 - 1.676331) 88.81
0.00391838 *(50)^(3/2) * arctan(0.023101 * 50) - 4.686035 68.04

This kind of math is over my head. It has been years since I have been in school and I am trying to figure this out for a job that I am working on. I never thought I would ever need trigonometry.

Thanks for your assistance.

 

[Dr.Peterson]

It appears that you are using a calculator set to degrees. Find out how to put it in radian mode, and you should get the right numbers.

Whatever programming language you are using, if it has atan at all, it is probably going to use radians by default; but it may be important for you to show us something about that language to make sure what we suggest will really work.

Here are the correct values for each term:

T * arctan[0.151977 * (rh% + 8.313659)^(1/2)] =​	18.14554​
arctan(T + rh%) =​	1.556735​
- arctan(rh% - 1.676331) =​	-1.55011​
0.00391838 *(rh%)^(3/2) * arctan(0.023101 * rh%) =​	1.187558​
	-4.68604​
Tw =​	14.65369​

 

[topsquark]

Dan must have accidentally deleted a minus sign while rearranging onto separate lines:-
- atn(rh% - 1.676331) OP note that you need a minus at the start of this line

No missing signs as I was just listing terms, but I agree my terminology wasn't very good. When I say "add" I tend to think "add or subtract."

My bad.

-Dan

 

[apprentice3]

It appears that you are using a calculator set to degrees. Find out how to put it in radian mode, and you should get the right numbers.

Whatever programming language you are using, if it has atan at all, it is probably going to use radians by default; but it may be important for you to show us something about that language to make sure what we suggest will really work.

Here are the correct values for each term:

T * arctan[0.151977 * (rh% + 8.313659)^(1/2)] =​	18.14554​
arctan(T + rh%) =​	1.556735​
- arctan(rh% - 1.676331) =​	-1.55011​
0.00391838 *(rh%)^(3/2) * arctan(0.023101 * rh%) =​	1.187558​
	-4.68604​
Tw =​	14.65369​

Thank you for the reply! This helped me out a lot! I found out how to make my program calculate as shown above. I basically had to put a RAD(Formula) before each line to get it to calculate in radians. Thank you for all of the responses.