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How to Calculate Dewpoint and Wet Bulb Temperature - Tutorial, Formula, Example

How to Calculate Dewpoint and Wet Bulb Temperature - Tutorial

Example :

Determine the wet-bulb and dewpoint temperature the given temperature is 40&deg;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 = &Sigma;N &forall; Ed &ne; 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.