Chapter 19, Problem 5E

On a day when the air temperature is 85°F, the wet-bulb reading of a psychrometer is 70°F. Find each of the following: (a) relative humidity, (b) dew point, (c) maximum moisture capacity of the air, and (d) actual moisture content of the air.

To determine

The relative humidity.

Answer to Problem 5E

The relative humidity is $46\%$.

Explanation of Solution

Given info: The dry-bulb and wet-bulb readings of a psychrometer are $85°\text{F}$ and $70°\text{F}$ respectively.

Explanation:

Wet-bulb depression is the difference in the dry-bulb and wet-bulb reading.

The expression for the wet-bulb depression is as follows,

$\Delta T=\text{Dry bulb reading}-\text{Wet bulb reading}$

Here,

$\Delta T$ is the wet-bulb depression

Substitute $85°\text{F}$ for $\text{Dry bulb reading}$ and $70°\text{F}$ for $\text{Wet bulb reading}$.

$\begin{array}{c}\Delta T\text{ = }85°\text{F }-\text{ 70 °F}\\ \text{= 15 °F}\end{array}$

Refer table H.1 in Appendix H provided in the textbook to find the relative humidity.

The relative humidity of the air is $46\%$.

Conclusion:

Therefore, the relative humidity is $46\%$.

To determine

The dew point.

Answer to Problem 5E

The dew point of the air is $62°\text{F}$.

Explanation of Solution

Given info: The dry-bulb and wet-bulb readings of a psychrometer are $85°\text{F}$ and $70°\text{F}$ respectively.

Explanation:

Wet-bulb depression is the difference in the dry-bulb and wet-bulb reading.

The expression for the wet-bulb depression is as follows,

$\Delta T=\text{Dry bulb reading }-\text{ Wet bulb reading}$

Here,

$\Delta T$ is the wet-bulb depression

Substitute $70°\text{F}$ for $\text{Dry bulb reading}$ and $66°\text{F}$ for $\text{Wet bulb reading}$.

$\begin{array}{c}\Delta T\text{ = 70 °F }-\text{ 66 °F}\\ \text{= 4 °F}\end{array}$

Refer table H.2 in Appendix H provided in the textbook to find the dew point.

The dew point is $62°\text{F}$.

Conclusion:

The dew point of the air is $62°\text{F}$.

To determine

The maximum moisture capacity of the air.

Answer to Problem 5E

The maximum moisture capacity of the air is $12.7{\text{gr/ft}}^3$.

Explanation of Solution

Given info: The dry-bulb and wet-bulb readings of a psychrometer are $85°\text{F}$ and $70°\text{F}$ respectively.

Explanation:

Wet-bulb depression is the difference in the dry-bulb and wet-bulb reading.

The expression for the wet-bulb depression is as follows,

$\Delta T=\text{Dry bulb reading }-\text{ Wet bulb reading}$

Here,

$\Delta T$ is the wet-bulb depression

Substitute $70°\text{F}$ for $\text{Dry bulb reading}$ and $66°\text{F}$ for $\text{Wet bulb reading}$.

$\begin{array}{c}\Delta T\text{ = 70 °F }-\text{ 66 °F}\\ \text{= 4 °F}\end{array}$

Refer table H.1 in Appendix H provided in the textbook to find the maximum moisture capacity of the air.

The maximum moisture capacity of the air is $12.7{\text{gr/ft}}^3$.

Conclusion:

The maximum moisture capacity of the air is $12.7{\text{gr/ft}}^3$.

To determine

The actual moisture content of the air.

Answer to Problem 5E

The actual moisture content of the air is $5.8{\text{gr/ft}}^3$.

Explanation of Solution

Given info: The dry-bulb and wet-bulb readings of a psychrometer are $85°\text{F}$ and $70°\text{F}$ respectively.

Explanation:

The expression for the relative humidity is as follows,

$\%RH\text{ = }\left(\frac{AC}{MC}\right)\left(100\text{ \%}\right)$ (1)

Here,

$\%RH$ is the relative humidity in percentage

$AC$ is the actual moisture content of the air

$MC$ is the maximum moisture capacity of the air

Rearrange equation (1) to get an expression for the actual moisture content of the air.

$AC=\left(\frac{MC}{100\text{ \%}}\right)\left(\%RH\right)$

Substitute $12.7{\text{gr/ft}}^3$ for $MC$ and $46\%$ for $\%RH$.

$\begin{array}{c}AC=\left(\frac{12.7{\text{gr/ft}}^3}{100\text{ \%}}\right)\left(46\%\right)\\ =5.8{\text{gr/ft}}^3\end{array}$

The actual moisture content of the air is $5.8{\text{gr/ft}}^3$.

Conclusion:

The actual moisture content of the air is $5.8{\text{gr/ft}}^3$.