Wet-bulb temperature is the air temperature measured by a wet-bulb( cover the tip of the thermometer bulb with wetted cloth-muslin sleeve) that is freely exposed to the air and away from radiation and moisture.

OR

It is the temperature at which the water is evaporating into air @ given DBT & humidity ratio W. This process can bring the air to Saturation adiabatically @ the same temperature while the total pressure (partial pressure of water vapor + partial pressure of gas) is maintained constant.

As described above, the Wet-bulb temperature can be measured using a Sling Psychrometer with a wetted wick. And it is the easiest way to find it.

We will see how we can calculate Wet-bulb temperature from Dry-bulb temperature(DBT) and Relative Humidity (RH).

Consider we have,

DBT = 75° F,

RH ($\Phi$) = 70.5%

measured @ 10’ ft Sea level.

Then,

$p =$ $14.696*(1 - 6.8754 * 10^{-6} * Z)^{5.2559}$

Where, $z$ - altitude in ft

$= 14.696*(1 - 6.8754 * 10^{-6} * 10)^{5.2559}$

$= 14.691 \,psia$

$^{o}R = ^{o}F + 459.67$

$T_{DBT} = 75 + 459.67 = 534.67^{o}$

When the given temperature is between 32° F to 392° F

$\ln(p_{t}) = \dfrac{C_{8}}{t} + C_{9}$

$\quad\quad+$ $C_{10}*t + C_{11}*t^2 + C_{12}*t^3$

$\quad\quad+$ $C_{13}*\ln(t)$

Where,

t - Given temperature in °R

C8, C9, …, C13 are constants and their values are -10440.397, -11.29465, -0.027022355, 1.28904E-05, -2.47807E-09, 6.5459673 respectively

**Saturation pressure @ DBT = Saturation pressure**

$p_{s} = p_{dbt}$

$\ln(p_{dbt}) = \dfrac{-10440.397}{534.67} + -11.29465$

$\quad+$ $-0.027022355*534.67 + 1.28904E-05*534.67^2$

$\quad+$ $-2.47807E-09*534.67^3$

$\quad+$ $6.5459673*\ln(534.67)$

$p_{s} = p_{dbt} = 0.43 psia$

$\Phi = \dfrac{p_{w}}{p_{s}}$

Where,

$p_{w}$ - Partial pressure of water vapour (VP) in psia

$p_{s}$ - Saturation pressure in psia

$p_{w} = 0.705 * 0.43 = 0.303 \, lb/lb$

$W = \dfrac{0.621945 * p_{w}} {p-p_{w}}$

Where,

$p_{w}$ - Partial pressure of water vapour (VP) in psia

$W$ - Humidity ratio in lb/lb

$p$ - Standard atmospheric pressure at given altitude in psia

$= \dfrac{0.621945 * 0.303} {14.691-0.303}$

$= 0.0131 \, lb/lb$

When the given temperature is above 32° F

$W =\dfrac{(1093-0.556*WBT)*W_{wbt}-0.240*(DBT-WBT)}{1093+0.444*DBT-WBT}$

Where,

$W$ - Humidity ratio in lb/lb

WBT - Wet bulb temperature in °F

DBT - Dry bulb temperature in °F

$W_{wbt}$ - Humidity ratio at saturation corresponding to WBT

$0.0131 =\dfrac{(1093-0.556*WBT)*W_{wbt}-0.240*(75-WBT)}{1093+0.444*75-WBT}$

By iterating the above equation for various values of WBT, we can find WBT.

Assume that WBT is always less than or equal to DBT; let us do the iteration as stated below.

Find the saturated pressure at WBT using the below equation.

And find the Humidity ratio at WBT using the below equation.

If WBT = 75° F; We get $p_{WBT}$ = 0.43 & $W_{WBT}$ = 0.0187, then W becomes 0.0188.

If WBT = 74° F; We get $p_{WBT}$ = 0.416 & $W_{WBT}$ = 0.0181, then W becomes 0.0179.

If WBT = 73° F; We get $p_{WBT}$ = 0.402 & $W_{WBT}$ = 0.0175, then W becomes 0.0170.

…

…

…

If WBT = 68° F; We get $p_{WBT}$ = 0.339 & $W_{WBT}$ = 0.0147, then W becomes 0.0131.

This 0.0131 is the same as the Humidity Ratio calculated in the previous step. So we decide the **WBT = 68°F**.

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