Chapter 19, Problem 6E

(a)

To determine

The relative humidity.

Answer to Problem 6E

The relative humidity is $65\%$.

Explanation of Solution

Given info: The dry-bulb and wet-bulb readings of a psychrometer are $90°\text{F}$ and $80°\text{F}$ 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 $90°\text{F}$ for $\text{Dry bulb reading}$ and $80°\text{F}$ for $\text{Wet bulb reading}$.

$\begin{array}{c}\Delta T\text{ = 90 }°\text{F }-\text{ 80 °F}\\ \text{= 10 °F}\end{array}$

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

The relative humidity of the air is $65\%$.

Conclusion:

Therefore, the relative humidity is $65\%$.

(b)

To determine

The dew point.

Answer to Problem 6E

The dew point of the air is $86°\text{F}$.

Explanation of Solution

Given info: The dry-bulb and wet-bulb readings of a psychrometer are $90°\text{F}$ and $80°\text{F}$ 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 $90°\text{F}$ for $\text{Dry bulb reading}$ and $80°\text{F}$ for $\text{Wet bulb reading}$.

$\begin{array}{c}\Delta T\text{ = 90 }°\text{F }-\text{ 80 °F}\\ \text{= 10 °F}\end{array}$

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

The dew point is $86°\text{F}$.

Conclusion:

The dew point of the air is $86°\text{F}$.

(c)

To determine

The maximum moisture capacity of the air.

Answer to Problem 6E

The maximum moisture capacity of the air is $14.8{\text{gr/ft}}^3$.

Explanation of Solution

Given info: The dry-bulb and wet-bulb readings of a psychrometer are $90°\text{F}$ and $80°\text{F}$ 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 $90°\text{F}$ for $\text{Dry bulb reading}$ and $80°\text{F}$ for $\text{Wet bulb reading}$.

$\begin{array}{c}\Delta T\text{ = 90 }°\text{F }-\text{ 80 °F}\\ \text{= 10 °F}\end{array}$

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 $14.8{\text{gr/ft}}^3$.

Conclusion:

The maximum moisture capacity of the air is $14.8{\text{gr/ft}}^3$.

(d)

To determine

The actual moisture content of the air.

Answer to Problem 6E

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 $90°\text{F}$ and $80°\text{F}$ 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 $14.8{\text{gr/ft}}^3$ for $MC$ and $65\%$ for $\%RH$.

$\begin{array}{c}AC=\left(\frac{14.8{\text{gr/ft}}^3}{100\text{ \%}}\right)\left(65\%\right)\\ =9.6{\text{gr/ft}}^3\end{array}$

The actual moisture content of the air is $9.6{\text{gr/ft}}^3$.

Conclusion:

The actual moisture content of the air is $9.6{\text{gr/ft}}^3$.