<p><em>Edit: 1 May 2021</em></p>
<p>The following procedure uses the less accurate method from page 455 onward from the scanned sections of the book pictured below, from the original answer.</p>
<p>The procedure is a multistage process ideally suited to either a spreadsheet or programming code.</p>
<p>The equations use SI units.</p>
<p><em><strong>1. Calculate the saturated vapor pressure at the dry bulb temperature</strong></em></p>
<p>This is done using the equation:
<span class="math-container">$P''_{ws} \ = \ 0.61078\ e\ ^{17.27T_{dry}/(273.3+T_{dry})} \ \ kPa$</span></p>
<p>Where <span class="math-container">$T_{dry}$</span> is the dry bulb temperature.</p>
<p><em><strong>2. Calculate the saturated vapor pressure at the wet bulb temperature</strong></em></p>
<p>This is done using the equation:
<span class="math-container">$P'_{ws} \ = \ 0.61078\ e\ ^{17.27T_{wet}/(273.3+T_{wet})} \ \ kPa$</span></p>
<p>Where <span class="math-container">$T_{wet}$</span> is the wet bulb temperature.</p>
<p><em><strong>3. Calculate the moisture content of saturated air at the wet bulb temperature</strong></em></p>
<p>Use the equation: <span class="math-container">$r_o \ = \ \frac{18.016 \ (1.0048)P'_{ws}} {28.9664 \ (P_{atm}-1.0048)P'_{ws}} \ \ kg/kg$</span></p>
<p>Where <span class="math-container">$P_{atm}$</span> is atmospheric pressure</p>
<p><em><strong>4. Calculate the enthalpy of water vapor pressure at the wet bulb temperature</strong></em></p>
<p><span class="math-container">$H'_{wo} \ = \ -0.00000662 \ t_{wet}^3-0.000194 \ t_{wet}^2+1.8375 \ t_{wet}+2500.83 \ \ kJ/kg$</span></p>
<p><em><strong>5. Calculate the enthalpy of liquid water at the wet bulb temperature</strong></em></p>
<p><span class="math-container">$H'_{wl} \ = \ 0.0000063 \ t_{wet}^3-0.000727 \ t_{wet}^2+4.2058 \ t_{wet}+0.03 \ \ kJ/kg$</span></p>
<p><em><strong>6. Calculate the enthalpy of water vapor pressure at the dry bulb temperature</strong></em></p>
<p><span class="math-container">$H'_{wi} \ = \ -0.00000662 \ t_{dry}^3-0.000194 \ t_{dry}^2+1.8375 \ t_{dry}+2500.83 \ \ kJ/kg$</span></p>
<p><em><strong>7. Calculate the moisture content of saturated air at the wet bulb temperature</strong></em></p>
<p><span class="math-container">$r \ = \ \frac{r_o*(H'_{wo}-H'_{wl})-(1.005 \ t_{dry}-1.005 \ t_{wet})}{(H'_{wi}-H'_{wl})} \ \ kg/kg$</span></p>
<p><em><strong>8. Calculate the vapor pressure</strong></em></p>
<p><span class="math-container">$P_w \ = \ \frac{r \ P_{atm}} {1.0048 \ (18.016/28.9664+r)} \ \ kPa$</span></p>
<p><em><strong>9. Calculate the relative humidity</strong></em></p>
<p><span class="math-container">$\phi \ = \ P_w/P''_{ws}$</span></p>
<hr />
<p><em><strong>Previous Answer - scans from relevant pages from reference book</strong></em></p>
<p>I'm going to go old school with this one.</p>
<p>The following pictures are the relevant pages from: <em>Environmental Engineering in South African Mines</em>, The Mine Ventilation Society of South Africa, 1989, pp 451-455. They give the psychometric equations that are required to calculate relative humidity from wet &amp; dry bulb temperatures.</p>
<p><a href="https://i.sstatic.net/DfrY7.jpg" rel="nofollow noreferrer"><img src="https://i.sstatic.net/DfrY7.jpg" alt="enter image description here" /></a></p>
<p><a href="https://i.sstatic.net/sKMCm.jpg" rel="nofollow noreferrer"><img src="https://i.sstatic.net/sKMCm.jpg" alt="enter image description here" /></a></p>
<p><a href="https://i.sstatic.net/5Zupk.jpg" rel="nofollow noreferrer"><img src="https://i.sstatic.net/5Zupk.jpg" alt="enter image description here" /></a></p>
<p><a href="https://i.sstatic.net/g4fNs.jpg" rel="nofollow noreferrer"><img src="https://i.sstatic.net/g4fNs.jpg" alt="enter image description here" /></a></p>
<p><a href="https://i.sstatic.net/ZbbLp.jpg" rel="nofollow noreferrer"><img src="https://i.sstatic.net/ZbbLp.jpg" alt="enter image description here" /></a></p>
<p>For simplicity, I use the less accurate equations on p455, section 9.2.</p>
<p>As a slight diversion, the other way to measure <a href="http://science.waltermack.com/VirtualFieldTrip/whirling.html" rel="nofollow noreferrer">wet &amp; dry bulb temperatures</a> is to use a <a href="https://www.aweimagazine.com/article/use-of-whirling-hygrometers-1137/" rel="nofollow noreferrer">whirling hygrometer</a>. The wet bulb temperature is always read first because it will start to warm as soon as the hygrometer stops whirling.</p>
<p><a href="https://i.sstatic.net/oTa44.gif" rel="nofollow noreferrer"><img src="https://i.sstatic.net/oTa44.gif" alt="enter image description here" /></a></p>

CC BY-SA 4.0
2020-02-08T04:40:09.720Z
While screenshots of text are usually discouraged, this is the best possible answer for me at the moment, and I appreciate the speedy response! I'll take a look today and if nobody else does I'll add a summary answer based on what I've implemented, so that those who are visually impaired can have an answer as well. Thanks!
uhoh
CC BY-SA 4.0
2020-02-08T04:36:41.227Z
2021-04-30T18:08:13.657Z
2021-04-30T18:08:13.657Z
Fred
<p>The question <a href="https://earthscience.stackexchange.com/q/19145/6031">What is the second thermometer in the image from the Esperanza Antarctic temperature record?</a> shows what might be a wet/dry bulb setup.</p>

<p>I've given one to a friend to measure humidity for fun (it's me who thinks it's fun). I'd learned about them in Earth Science class a zillion years ago, so when I happened to see one recently I grabbed it.</p>

<p>I understand the very basics of how it can indicate humidity; the drier the air, the faster water will evaporate into it and so the colder the wet bulb will be with respect to the dry bulb.</p>

<p>To get a numerical value for humidity with this set up you use the coarse table on the front (there's a finer table on the back of the box) and look up the dry bulb temperature and the dry minus wet difference to find an approximate humidity. For example If I look up 19 and 2 °C for those respectively (roughly what's shown in the image) I get about 81% relative humidity.</p>

<p>But suppose I hooked up a camera to a Raspberry Pi and imaged the two thermometers, processed the image and determined the two temperatures and wanted to calculate the relative humidity without interpolating the table.</p>

<p><strong>Question:</strong> How is relative humidity determined from a wet and dry bulb readings? What are the steps and where's a good source for the equations and parameters involved?</p>

<p><em>Click for full size</em></p>

<p><a href="https://i.sstatic.net/Yu941.jpg" rel="noreferrer"><img src="https://i.sstatic.net/Yu941l.jpg" alt="wet/dry bulb setup to measure relative humidity"></a> </p>

CC BY-SA 4.0
2020-02-08T01:13:02.267Z
different but related: [How is the specific heat of a wet bulb determined?](https://earthscience.stackexchange.com/q/15349/6031) (which is currently unanswered) and also [How would I use data to find specific humidity and mixing ratio?](https://earthscience.stackexchange.com/q/13511/6031)
uhoh
<measurements><humidity><instrumentation><mathematics><environmental-sensors>
How is relative humidity determined from a wet and dry bulb readings?
uhoh
# How is relative humidity determined from a wet and dry bulb readings?

(Asked by: username_0 on 2020-02-08)

The question [What is the second thermometer in the image from the Esperanza Antarctic temperature record?](https://earthscience.stackexchange.com/q/19145/6031) shows what might be a wet/dry bulb setup.

I've given one to a friend to measure humidity for fun (it's me who thinks it's fun). I'd learned about them in Earth Science class a zillion years ago, so when I happened to see one recently I grabbed it.

I understand the very basics of how it can indicate humidity; the drier the air, the faster water will evaporate into it and so the colder the wet bulb will be with respect to the dry bulb.

To get a numerical value for humidity with this set up you use the coarse table on the front (there's a finer table on the back of the box) and look up the dry bulb temperature and the dry minus wet difference to find an approximate humidity. For example If I look up 19 and 2 °C for those respectively (roughly what's shown in the image) I get about 81% relative humidity.

But suppose I hooked up a camera to a Raspberry Pi and imaged the two thermometers, processed the image and determined the two temperatures and wanted to calculate the relative humidity without interpolating the table.

**Question:** How is relative humidity determined from a wet and dry bulb readings? What are the steps and where's a good source for the equations and parameters involved?

*Click for full size*

[![wet/dry bulb setup to measure relative humidity](https://i.sstatic.net/Yu941l.jpg)](https://i.sstatic.net/Yu941.jpg)

**Tags:** measurements, humidity, instrumentation, mathematics, environmental-sensors

> **Comments:**
> **username_0**: different but related: [How is the specific heat of a wet bulb determined?](https://earthscience.stackexchange.com/q/15349/6031) (which is currently unanswered) and also [How would I use data to find specific humidity and mixing ratio?](https://earthscience.stackexchange.com/q/13511/6031)  

---

## 1 answers

### Answer by username_1 on 2020-02-08. Score: 7

*Edit: 1 May 2021*

The following procedure uses the less accurate method from page 455 onward from the scanned sections of the book pictured below, from the original answer.

The procedure is a multistage process ideally suited to either a spreadsheet or programming code.

The equations use SI units.

***1. Calculate the saturated vapor pressure at the dry bulb temperature***

This is done using the equation:
$P''\_{ws} \ = \ 0.61078\ e\ ^{17.27T\_{dry}/(273.3+T\_{dry})} \ \ kPa$

Where $T\_{dry}$ is the dry bulb temperature.

***2. Calculate the saturated vapor pressure at the wet bulb temperature***

This is done using the equation:
$P'\_{ws} \ = \ 0.61078\ e\ ^{17.27T\_{wet}/(273.3+T\_{wet})} \ \ kPa$

Where $T\_{wet}$ is the wet bulb temperature.

***3. Calculate the moisture content of saturated air at the wet bulb temperature***

Use the equation: $r\_o \ = \ \frac{18.016 \ (1.0048)P'\_{ws}} {28.9664 \ (P\_{atm}-1.0048)P'\_{ws}} \ \ kg/kg$

Where $P\_{atm}$ is atmospheric pressure

***4. Calculate the enthalpy of water vapor pressure at the wet bulb temperature***

$H'\_{wo} \ = \ -0.00000662 \ t\_{wet}^3-0.000194 \ t\_{wet}^2+1.8375 \ t\_{wet}+2500.83 \ \ kJ/kg$

***5. Calculate the enthalpy of liquid water at the wet bulb temperature***

$H'\_{wl} \ = \ 0.0000063 \ t\_{wet}^3-0.000727 \ t\_{wet}^2+4.2058 \ t\_{wet}+0.03 \ \ kJ/kg$

***6. Calculate the enthalpy of water vapor pressure at the dry bulb temperature***

$H'\_{wi} \ = \ -0.00000662 \ t\_{dry}^3-0.000194 \ t\_{dry}^2+1.8375 \ t\_{dry}+2500.83 \ \ kJ/kg$

***7. Calculate the moisture content of saturated air at the wet bulb temperature***

$r \ = \ \frac{r\_o\*(H'\_{wo}-H'\_{wl})-(1.005 \ t\_{dry}-1.005 \ t\_{wet})}{(H'\_{wi}-H'\_{wl})} \ \ kg/kg$

***8. Calculate the vapor pressure***

$P\_w \ = \ \frac{r \ P\_{atm}} {1.0048 \ (18.016/28.9664+r)} \ \ kPa$

***9. Calculate the relative humidity***

$\phi \ = \ P\_w/P''\_{ws}$

---

***Previous Answer - scans from relevant pages from reference book***

I'm going to go old school with this one.

The following pictures are the relevant pages from: *Environmental Engineering in South African Mines*, The Mine Ventilation Society of South Africa, 1989, pp 451-455. They give the psychometric equations that are required to calculate relative humidity from wet & dry bulb temperatures.

[![enter image description here](https://i.sstatic.net/DfrY7.jpg)](https://i.sstatic.net/DfrY7.jpg)

[![enter image description here](https://i.sstatic.net/sKMCm.jpg)](https://i.sstatic.net/sKMCm.jpg)

[![enter image description here](https://i.sstatic.net/5Zupk.jpg)](https://i.sstatic.net/5Zupk.jpg)

[![enter image description here](https://i.sstatic.net/g4fNs.jpg)](https://i.sstatic.net/g4fNs.jpg)

[![enter image description here](https://i.sstatic.net/ZbbLp.jpg)](https://i.sstatic.net/ZbbLp.jpg)

For simplicity, I use the less accurate equations on p455, section 9.2.

As a slight diversion, the other way to measure [wet & dry bulb temperatures](http://science.waltermack.com/VirtualFieldTrip/whirling.html) is to use a [whirling hygrometer](https://www.aweimagazine.com/article/use-of-whirling-hygrometers-1137/). The wet bulb temperature is always read first because it will start to warm as soon as the hygrometer stops whirling.

[![enter image description here](https://i.sstatic.net/oTa44.gif)](https://i.sstatic.net/oTa44.gif)

> **Comments:**
> **username_0**: While screenshots of text are usually discouraged, this is the best possible answer for me at the moment, and I appreciate the speedy response! I'll take a look today and if nobody else does I'll add a summary answer based on what I've implemented, so that those who are visually impaired can have an answer as well. Thanks!  

---

