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°C, relative humidity is 50% and then actual station pressure is 3 millibars.

Given,

T = 40°C rh = 50% P_sta = 3 hPA

1) To Find T_d

Substitute the given values in the formula

T_d = [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

T_d = 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 e^2.493121693 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 T_d = [243.5 x ln(36.9745/6.112)] / [17.67 - ln(36.9745/6.112)] T_d = 438.2938 / 15.87 T_d = 27.6177°C

2) To Find T_w

Substitute the given values in the formula

E_wg = 6.112 x e^{(17.67xT_w)/(T_w+243.5)} eg = E_wg - P_sta x (T - T_w) x 0.00066 x (1 + (0.00115 x T_w)) T_w = ΣN ∀ E_d ≠ 0 E_d = e - eg

Where

T_w = Wet Bulb Temperature T = Temperature P_sta = Actual station pressure e = Vapor Pressure E_d = Vapor Pressure Difference N = Increment by 10 and consecutive E_dis opposite sign, increment divide by 10.

Its upto reach E_d is zero or absolute value of E_d 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

T_w	= 0
E_wg	= 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
T_w	= 10
E_d	= 36.9745 - 6.0328	= 30.9417

Iteration : 1

T_w	= 10
E_wg	= 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
T_w	= 10 + 10	= 20
E_d	= 36.9745 - 12.2116	= 24.7629

Iteration : 2

T_w	= 20
E_wg	= 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
T_w	= 20 + 10	= 30
E_d	= 36.9745 - 23.329	= 13.6455

. . .

Iteration : 17

T_w	= 27.65
E_wg	= 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
T_w	= 27.65 - 0.01	= 27.64
E_d	= 36.9745 - 37.0192	= -0.0447

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

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