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Chapter 11: Problem 109

Use the psychrometric chart to find the missing property of \(\phi, \omega, T_{\text {wet }}, T_{\text {dry }}\) a. \(T_{\text {dry }}=25^{\circ} \mathrm{C}, \phi=80 \%\) b. \(T_{\text {dry }}=15^{\circ} \mathrm{C}, \phi=100 \%\) c. \(T_{\text {dry }}=20^{\circ} \mathrm{C}, \omega=0.010\) d. \(T_{\text {dry }}=25^{\circ} \mathrm{C}, T_{\text {wet }}=23^{\circ} \mathrm{C}\)

Short Answer

Expert verified
a. Read T_{ ext{wet}} and 蠅 from chart. b. T_{ ext{wet}} = 15^ ext{o}C , read 蠅 from chart. c. Read 蠁 from chart. d. Read 蠁 and 蠅 from chart.

Step by step solution

01

Understand the Psychrometric Chart

A psychrometric chart represents the physical and thermal properties of moist air. It shows various parameters like dry bulb temperature ( T_{ ext {dry }} ), wet bulb temperature ( T_{ ext {wet }} ), relative humidity ( ext{RH} or ext{蠁} ), and specific humidity or humidity ratio ( ext{蠅} ). By locating one or two known parameters, the chart can be used to find unknown properties.
02

Locate Given Data a on the Chart

For part (a), given that T_{ ext{dry}} = 25^ ext{o}C and ext{蠁} = 80 ext{%} , find the point on the psychrometric chart at these coordinates. Read the corresponding values for the wet bulb temperature ( T_{ ext{wet}} ) and the humidity ratio ( ext{蠅} ) using the intersecting contours.
03

Locate Given Data b on the Chart

For part (b), with T_{ ext{dry}} = 15^ ext{o}C and ext{蠁} = 100 ext{%} , locate the parameter on the saturation line. The wet bulb temperature is equal to the dry bulb temperature, and read the humidity ratio directly from the chart.
04

Locate Given Data c on the Chart

For part (c), given T_{ ext{dry}} = 20^ ext{o}C and ext{蠅} = 0.010 , find where the parameter intersects with the humidity ratio line ext{蠅} = 0.010 . Read the relative humidity ( ext{蠁} ) directly from the chart.
05

Locate Given Data d on the Chart

For part (d), with T_{ ext{dry}} = 25^ ext{o}C and T_{ ext{wet}} = 23^ ext{o}C , locate the curve on the chart representing these values. Read the relative humidity ( ext{蠁} ) and humidity ratio ( ext{蠅} ) directly from the chart intersections of these values.
06

Summarize the Results

After reading from the psychrometric chart: a. T_{ ext{wet}} and 蠅 for T_{ ext{dry}} = 25^ ext{o}C , 蠁 = 80 ext{%} are located. b. Relative humidity 蠁 = 100 ext{%} at T_{ ext{dry}} = 15^ ext{o}C means T_{ ext{wet}} = T_{ ext{dry}} . c. T_{ ext{wet}} and 蠁 for T_{ ext{dry}} = 20^ ext{o}C , 蠅 = 0.010 ext{kg/kg} are obtained. d. 蠁 and 蠅 for T_{ ext{dry}} = 25^ ext{o}C , T_{ ext{wet}} = 23^ ext{o}C are identified.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Dry Bulb Temperature
Dry bulb temperature (\(T_{\text{dry}}\)) is a fundamental measurement in psychrometry, the study of moist air. It is the temperature of air measured using a standard thermometer freely exposed to the air but shielded from radiation and moisture. This measurement does not take into account the presence of water vapor in the air.
Key points to remember about dry bulb temperature:
  • It is a direct measurement of the air's thermal energy or heat content.
  • Dry bulb temperature is used as a reference point on the psychrometric chart.
  • It helps in determining other measurements such as the wet bulb temperature, relative humidity, and specific humidity when combined with these parameters.
When applying this in exercises, like part (a), it is given as 25掳C, which helps locate the corresponding wet bulb temperature and humidity ratio using the psychrometric chart.
Wet Bulb Temperature
Wet bulb temperature (\(T_{\text{wet}}\)) provides insight into the humidity of the air. It is measured using a thermometer with a moistened wick or cloth around its bulb. This method involves letting air move across the wet bulb so that evaporation cools the thermometer.
Key characteristics of wet bulb temperature:
  • It is always equal to or less than the dry bulb temperature.
  • The wet bulb temperature is critical for calculating the air's enthalpy and for evaluating air-conditioning processes.
  • In a psychrometric chart, it is represented by contour lines running diagonally from left to right.
In part (d) of the exercise, it is given as 23掳C. When combined with a dry bulb temperature of 25掳C, the psychrometric chart helps determine the missing relative humidity and humidity ratio, highlighting its importance.
Relative Humidity
Relative humidity (\(\phi\)) is a key factor in determining the comfort level and moisture content of air. It is defined as the ratio of the current absolute humidity to the highest possible absolute humidity at that temperature. Relative humidity is expressed as a percentage and represents how moist the air is.
Things to know about relative humidity:
  • A higher percentage means that the air is more saturated with moisture.
  • Relative humidity is crucial for comfort and for various industrial processes.
  • On a psychrometric chart, it is shown as curves originating from the saturation line.
In the example problem (b), a relative humidity of 100% means that the air is fully saturated, and the wet bulb temperature equals the dry bulb temperature. Thus, these two temperatures assist in understanding the air's moisture level.
Humidity Ratio
Humidity ratio (\(\omega\)), also known as the specific humidity, quantifies the mass of water vapor per unit mass of dry air. It reflects the actual amount of moisture in the air.Key aspects about humidity ratio include:
  • It is usually expressed in kg of water vapor per kg of dry air (kg/kg).
  • A higher humidity ratio means more moisture in the air.
  • The humidity ratio line on a psychrometric chart is horizontal, making it easier to identify humidity changes.
For scenario (c) in the problem, where the dry bulb temperature is 20掳C and the humidity ratio is 0.010, the psychrometric chart is particularly useful for finding the unknown relative humidity and wet bulb temperature by following these horizontal lines.

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Most popular questions from this chapter

Moist air at \(31^{\circ} \mathrm{C}\) and \(50 \%\) relative humidity flows over a large surface of liquid water. Find the adi abatic saturation temperature by trial and error Hint: it is around \(22.5^{\circ} \mathrm{C}\).

A slightly oxygenated air mixture is \(69 \% \mathrm{~N}_{2}, 1 \%\) Ar, and \(30 \% \mathrm{O}_{2}\) on a mole basis. Assume a total pressure of \(101 \mathrm{kPa}\) and find the mass fraction of oxygen and its partial pressure.

I want to bring air at \(35^{\circ} \mathrm{C}, \Phi=40 \%\) to a state of \(25^{\circ} \mathrm{C}, \omega=0.015 .\) Do I need to add or subtract water?

A flow of \(2 \mathrm{~kg} / \mathrm{s}\) completely dry air at \(T_{1}, 100 \mathrm{kPa}\) is cooled down to \(10^{\circ} \mathrm{C}\) by spraying liquid water at \(10^{\circ} \mathrm{C}, 100 \mathrm{kPa}\) into it so that it becomes saturated moist air at \(10^{\circ} \mathrm{C}\). The process is steady state with no external heat transfer or work. Find the exit moist air humidity ratio and the flow rate of liquid water. Also find the dry air inlet temperature \(T_{1}\).

Use the formulas and the steam tables to find the missing property of \(\phi, \omega,\) and \(T_{\text {dry }} ;\) total pressure is \(100 \mathrm{kPa}\). Repeat the answers using the psychrometric chart. a. \(\phi=50 \%, \omega=0.010\) b. \(T_{\text {wet }}=15^{\circ} \mathrm{C}, \phi=50 \%\) c. \(T_{\text {dry }}=25^{\circ} \mathrm{C}, T_{\text {wet }}=21^{\circ} \mathrm{C}\)
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