How to Calculate Dewpoint and Wet Bulb Temperature

Determine the wet-bulb and dewpoint temperature the given temperature is 40°C, relative humidity is 50% and then actual station pressure is 3 millibars.

Given,

 T = 40°C  rh = 50%  Psta = 3 hPA

1) To Find Td

 Substitute the given values in the formula

 Td = [243.5 x ln(e/6.112)] / [17.67 - ln(e/6.112)] e = (es x rh) / 100 es = 6.112 x e(17.67xT)/(T+243.5)   Where Td = Dewpoint Temperature  T = Temperature  rh = Relative Humidity  e = Vapor Pressure  es = Saturation Vapor Pressure

Step 1 :

Saturation Vapor Pressure (es) Calculation  es = 6.112 x e(17.67x40)/(40+243.5)  es = 6.112 x e2.493121693  es = 73.9490

Step 2 :

 Vapor Pressure (e) Calculation   e = (73.9490 x 50) / 100  e = 3697.45 / 100  e = 36.9745 

Step 3 :

 Dewpoint Temperature Calculation  Td = [243.5 x ln(36.9745/6.112)] / [17.67 - ln(36.9745/6.112)]  Td = 438.2938 / 15.87  Td = 27.6177°C

2) To Find Tw

Substitute the given values in the formula

 Ewg = 6.112 x e(17.67xTw)/(Tw+243.5)  eg = Ewg - Psta x (T - Tw) x 0.00066 x (1 + (0.00115 x Tw))  Tw = ΣN ∀ Ed ≠ 0  Ed = e - eg  Where Tw = Wet Bulb Temperature  T = Temperature  Psta = Actual station pressure  e = Vapor Pressure  Ed = Vapor Pressure Difference  N = Increment by 10 and consecutive Edis opposite sign, increment divide by 10.

Its upto reach Ed is zero or absolute value of Ed is greater than 0.05

Step 1 :

 Vapor Pressure (e) Calculation  From Dewpoint Temperature Calculation we get Vapor Pressure (e) value is, 36.9745

Step 2 :

Wet-bulb Temperature Calculation

Iteration : 0

Tw    = 0   

Ewg   = 6.112 x e(17.67x0)/(0+243.5)       = 6.112

eg     = 6.112 - 3 x (40 - 0) x 0.00066 x (1 + (0.00115 x 0))    = 6.0328

Tw    = 10 

Ed     = 36.9745 - 6.0328       = 30.9417

Iteration : 1

Tw    = 10 

Ewg   = 6.112 x e(17.67x10)/(10+243.5)    = 12.271

eg     = 12.271 - 3 x (40 - 10) x 0.00066 x (1 + (0.00115 x 10))       = 12.2116

Tw    = 10 + 10    = 20

Ed     = 36.9745 - 12.2116     = 24.7629

Iteration : 2

Tw    = 20 

Ewg   = 6.112 x e(17.67x20)/(20+243.5)    = 23.3695

eg     = 23.3695 - 3 x (40 - 20) x 0.00066 x (1 + (0.00115 x 20))     = 23.329

Tw    = 20 + 10    = 30

Ed     = 36.9745 - 23.329       = 13.6455

. . .

Iteration : 17

Tw    = 27.65     

Ewg   = 6.112 x e(17.67x27.65)/(27.65+243.5)    = 37.0444

eg     = 37.0444 - 3 x (40-27.65) x 0.00066 x (1 +(0.00115x27.65)) = 37.0192

Tw    = 27.65 - 0.01      = 27.64

Ed     = 36.9745 - 37.0192     = -0.0447

 In this Iteration 17 Ed value is less than 0.05, so to stop the iteration. Finally the Tw is 27.64°C.

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