/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 101 Atmospheric air at \(35^{\circ} ... [FREE SOLUTION] | 91Ó°ÊÓ

91Ó°ÊÓ

Atmospheric air at \(35^{\circ} \mathrm{C}\), relative humidity \(10 \%\), is too warm and also too dry. An air conditioner should deliver air at \(21^{\circ} \mathrm{C}\) and \(50 \%\) relative humidity at a rate of \(3600 \mathrm{~m}^{3} / \mathrm{h}\). Sketch a setup to accomplish this, and find any amount of liquid (at \(20^{\circ} \mathrm{C}\) ) that is needed or discarded and any heat transfer.

Short Answer

Expert verified
Cool air to 21°C and 50% RH by removing heat and add moisture via a humidifier.

Step by step solution

01

Understanding the problem

We need to cool and humidify air from an initial condition of 35°C and 10% relative humidity to a final condition of 21°C and 50% relative humidity, at a flow rate of 3600 m³/h. This involves removing some heat and possibly using water for humidification.
02

Analyzing Initial and Final Conditions

Determine the specific humidity, enthalpy, and other psychrometric properties of air at the initial condition of 35°C and 10% relative humidity and compare these to the final desired conditions of 21°C and 50% relative humidity. This will include using a psychrometric chart or calculations to find exact values.
03

Calculating Heat Removal

Calculate the amount of heat removed from the air to lower its temperature and change its humidity from the initial to final state. This involves calculating the change in enthalpy per unit mass, then multiplying by the mass flow rate derived from the volume flow rate and density of air.
04

Calculate Required Humidification

Find the difference in specific humidity (or moisture content) between the initial and final conditions. This will tell us how much water needs to be added to reach 50% relative humidity at 21°C.
05

Cooling Coil and Humidifier Setup

Design a setup where air first passes through a cooling coil to remove the necessary heat, followed by a humidifier to add the required moisture. This will ensure that air exits at the desired temperature and humidity.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91Ó°ÊÓ!

Key Concepts

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

Psychrometric Chart
The psychrometric chart is an essential tool for visualizing air properties and understanding air conditioning processes. This chart graphically represents the physical and thermal properties of moist air. It plots parameters such as temperature, relative humidity, enthalpy, and specific humidity.

To use a psychrometric chart effectively, pinpoint the initial and desired air conditions. For example, if you begin with air at 35°C and 10% relative humidity, locate this point on the chart. From there, you can trace the path to reach the final condition of 21°C and 50% relative humidity.

The psychrometric chart helps visualize the cooling and humidification process. You can better understand how heat removal and moisture addition impacts the air condition as you move through the chart. This tool assists in calculating necessary changes in specific humidity and heat energy required for a given process.
Specific Humidity Calculation
Specific humidity is the ratio of the mass of water vapor to the mass of dry air in a given air sample. To calculate specific humidity, you can use data from the psychrometric chart or apply an equation based on known parameters.

The formula: \[ \text{Specific Humidity (} \omega \text{)} = \frac{0.622 \times P_w}{P_{atm} - P_w} \]where - \(P_w\) is the partial pressure of water vapor- \(P_{atm}\) is the atmospheric pressure.

By using specific humidity calculations, you identify how much moisture content needs to be added or removed from the air. This calculation is crucial for designing systems that require precise adjustment of air moisture levels.
Cooling Coil Design
Cooling coil design involves creating a system to remove heat from the air, reducing its temperature to the desired level. The cooling coils are typically equipped within an air conditioning system to facilitate heat exchange.

For an effective design:
  • Determine the temperature difference between incoming and outgoing air.
  • Calculate the cooling load by determining the enthalpy change and multiplying by the mass flow rate.
  • Select appropriate materials and coil dimensions based on cooling requirements and space constraints.
This design ensures that the air reaches the target temperature, as calculated from specific enthalpy changes. Proper design results in a system that operates efficiently and meets desired ambient conditions.
Humidification Process
The humidification process is crucial when air needs to reach a specific moisture level, as in the case of achieving 50% relative humidity. This process generally involves adding water to air in a controlled manner.

To design this process:
  • Ascertain the specific humidity difference between the initial and final air conditions.
  • Calculate the quantity of water required to achieve this change through humidifiers.
  • Implement humidifiers to precisely regulate moisture addition.
Humidifiers can be evaporative, steam-based, or ultrasonic, each type offering distinct benefits. The humidification process ensures that air is neither too dry nor too humid for comfortable living conditions, meeting the requirements specified by target humidity levels.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Constant flows of pure argon and pure helium are mixed to produce a flow of mixture mole fractions \(0.25\) and \(0.75\), respectively. Explain how to meter the inlet flows to ensure the proper ratio, assuming inlet pressures are equal to the total exit pressure and all temperatures are the same.

A commercial laundry runs a dryer that has an exit flow of \(1 \mathrm{lbm} / \mathrm{s}\) moist air at \(120 \mathrm{~F}, 70 \%\) relative humidity. To reduce the heating cost a counter flow stack heat exchanger is used to heat a cold water line at \(50 \mathrm{~F}\) for the washers with the exit flow, as shown in Fig. P11.73. Assume the outgoing flow can be cooled to \(77 \mathrm{~F}\). Is there a missing flow in the figure? Find the rate of energy recovered by this heat exchanger and the amount of cold water that can be heated to \(86 \mathrm{~F}\).

Compressed dry air enters a molecular sieve at a high pressure, and out from the system comes one flow of pure oxygen at \(100 \mathrm{kPa}\) and another flow at \(150 \mathrm{kPa}\) with all the nitrogen and \(5 \%\) oxygen in it. Assume all temperatures are \(20^{\circ} \mathrm{C}\) and the process is reversible. Find the minimum required air inlet pressure.

Can moist air below the freezing point, say \(-5^{\circ} \mathrm{C}\), have a dew point?

Air to a gas turbine flows through a wetted matrix absorbing some water in an evaporative cooling process. The atmosphere is \(14.7\) psia, \(68 \mathrm{~F}, 60 \%\) relative humidity. Find how cold the air can become without external cooling and the \% reduction in specific volume.

See all solutions

Recommended explanations on Physics Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.