/*! 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 15 In an attempt to conserve water ... [FREE SOLUTION] | 91Ó°ÊÓ

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In an attempt to conserve water and to be awarded LEED (Leadership in Energy and Environmental Design) certification, a 20,000-liter cistem has been installed during construction of a new building. The cistem collects water from an HVAC (heating, ventilation, and air-conditioning) system designed to provide 2830 cubic meters of air per minute at \(22^{\circ} \mathrm{C}\) and \(50 \%\) relative humidity after converting it from ambient conditions \(\left(31^{\circ} \mathrm{C}, 70 \% \text { relative humidity }\right) .\) The collected condensate serves as the source of water for lawn maintenance. Estimate (a) the rate of intake of air at ambient conditions in cubic feet per minute and (b) the hours of operation required to fill the cistern.

Short Answer

Expert verified
(a) The rate of intake of air at ambient conditions is approximately 99841 cubic feet per minute. (b) It would take approximately 8.77 hours to fill the cistern.

Step by step solution

01

Conversion of Air Intake Rate

Given that the HVAC system provides 2830 cubic meters of air per minute. Now, convert this rate to cubic feet per minute. Using the conversion factor 1 cubic meter = 35.3147 cubic feet, the rate in cubic feet per minute can therefore be calculated as \(2830 \, m^3/min \times 35.3147 \, ft^3/m^3 = 99840.921 \, ft^3/min\).
02

Determine Moisture Content

The rate of condensation is directly related to the moisture content of the air. We know the HVAC system converts air from ambient conditions of \(31^{\circ} C\) and \(70 \%\) relative humidity to \(22^{\circ} C\) and \(50 \%\) relative humidity. Using psychrometric charts we know that at \(31^{\circ} C\) and \(70 \%\), the humidity ratio is about 0.0207 kg of moisture/kg of dry air, and at \(22^{\circ} C\) and \(50 \%\), the humidity ratio is about 0.0095 kg of moisture/kg of dry air. The difference is 0.0112 kg of moisture/kg of dry air.
03

Calculate Condensation Rate

The rate of condensation can be calculated using the humidity ratio difference, the density of air (about 1.2 kg/m3), and the volume flow rate of air. Therefore, the condensation rate would be \(2830 \, m^3/min \times 1.2 \, kg/m^3 \times 0.0112 \, kg/kg = 38 \, kg/min = 38 \, L/min\). This is because 1 kg of water is approximately equivalent to 1 L.
04

Calculate Time to Fill Cistern

To find out the hours of operation required to fill the cistern, divide the volume of the cistern by the rate of condensation i.e. \(20000 \, L / 38 \, L/min = 526.32 \, min = 8.77 \, hours\).

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Key Concepts

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

HVAC System
Heating, Ventilation, and Air-Conditioning (HVAC) systems are fundamental in maintaining comfortable and healthy indoor environments. They regulate temperature, humidity, and air quality in buildings. The HVAC system described in the exercise provides conditioned air with specific temperature and humidity levels. This process involves cooling the air, which, in return, condenses moisture out of the air.

An effective HVAC system not only ensures thermal comfort but also significantly impacts water conservation, especially when linked with innovative designs like integrated water collection for other uses, such as lawn maintenance. Understanding the operational flow rate, converted into familiar units like cubic feet per minute, allows for precise calculations essential in various engineering applications, including sustainability efforts and LEED certification goals.
Psychrometric Charts
A psychrometric chart is a valuable tool used in HVAC engineering to represent the physical and thermal properties of moist air. It visually depicts the humidity ratio, dry bulb temperature, wet bulb temperature, relative humidity, and enthalpy, among other relevant properties.

Using a psychrometric chart, engineers can calculate the condensation that occurs when air is conditioned from one state to another—like in our exercise from a higher to a lower humidity level. These charts simplify complex thermodynamic calculations into a readable graph, making assessment of air-conditioning processes more intuitive. By referring to this chart, the exercise demonstrates the direct relationship between the relative humidity, temperature, and the humidity ratio of air, crucial for accurate prediction of condensation rates.
Humidity Ratio
The humidity ratio, defined as the mass of water vapor per unit mass of dry air, is a critical concept in understanding moisture content in air. In chemical engineering education, grasping this concept is necessary for designing and operating HVAC systems efficiently. The exercise highlights the change in the humidity ratio between different states of air, effectively determining the amount of water that will condense out during the cooling process.

This value is essential not only for HVAC considerations but also for processes like drying, humidification, and predicting weather patterns. As demonstrated in the solution, calculating the difference in humidity ratio before and after air conditioning illustrates the water removed from the air, essential for assessing water conservation strategies in building projects.
LEED Certification
LEED (Leadership in Energy and Environmental Design) certification is a globally recognized symbol of sustainability achievement and leadership. It provides a framework for healthy, highly efficient, and cost-saving green buildings. The certification incentivizes innovation and recognizes best-in-class building strategies. LEED-certified buildings save energy, water, resources, generate less waste, and support human health.

In the context of the exercise, integrating an HVAC system with a cistern to collect condensate for reuse can contribute to earning LEED points for water efficiency. This holistic approach to building design and operation encompasses energy and water conservation, making significant strides towards sustainability – an increasingly important aspect of modern chemical engineering and architectural practices.

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Most popular questions from this chapter

The vapor pressure of an organic solvent is \(50 \mathrm{mm}\) Hg at \(25^{\circ} \mathrm{C}\) and \(200 \mathrm{mm} \mathrm{Hg}\) at \(45^{\circ} \mathrm{C}\). The solvent is the only species in a closed flask at \(35^{\circ} \mathrm{C}\) and is present in both liquid and vapor states. The volume of gas above the liquid is \(150 \mathrm{mL}\). (a) Estimate the amount of the solvent \((\mathrm{mol})\)contained in the gas phase. (b) What assumptions did you make? How would your answer change if the species dimerized (one molecule results from two molecules of the species combining)?

In-Hexane is used to extract oil from soybeans. (See Problem 6.24 .) The solid residue from the extraction unit, which contains 0.78 kg liquid hexane/kg dry solids, is contacted in a dryer with nitrogen that enters at \(85^{\circ} \mathrm{C}\). The solids leave the dryer containing \(0.05 \mathrm{kg}\) liquid hexane/kg dry solids, and the gas leaves the dryer at \(80^{\circ} \mathrm{C}\) and 1.0 atm with a relative saturation of \(70 \% .\) The gas is then fed to a condenser in which it is compressed to 5.0 atm and cooled to \(28^{\circ} \mathrm{C}\), enabling some of the hexane to be recovered as condensate.(a) Calculate the fractional recovery of hexane (kg condensed/kg fed in wet solids). (b) A proposal has been made to split the gas stream leaving the condenser, combining 90\% of it with fresh makeup nitrogen, heating the combined stream to \(85^{\circ} \mathrm{C},\) and recycling the heated stream to the dryer inlet. What fraction of the fresh nitrogen required in the process of Part (a) would be saved by introducing the recycle? What costs would be incurred by introducing the recycle?

You were recently hired as a process engineer by a pulp and paper manufacturing firm. Your new boss calls you in and tells you about a pulp dryer designed to reduce the moisture content of \(1500 \mathrm{kg} / \mathrm{min}\) of wet pulp from \(0.9 \mathrm{kg} \mathrm{H}_{2} \mathrm{O} / \mathrm{kg}\) dry pulp to \(0.15 \mathrm{wt} \% \mathrm{H}_{2} \mathrm{O}\). The design called for drawing atmospheric air at \(90 \%\) relative humidity, \(25^{\circ} \mathrm{C}, 760 \mathrm{mm}\) Hg into a blower that forces the air through a heater and into the dryer. When the operation was put into service, weather conditions were exactly as assumed in the design, and measurements showed that the air leaving the dryer was at \(80^{\circ} \mathrm{C}\) and a gauge pressure of \(10 \mathrm{mm}\) Hg. However, there was no way to check the operation of the blower to see if it was delivering the specified volumetric flow rate of air. Your boss wants to check that value and asks you to devise a method for doing so. You go back to your office, sketch the process, and determine that you can estimate the air flow rate from the given information if you also know the moisture content of the air leaving the dryer.(a) Propose a method to estimate the moisture content of the exit air. (b) Suppose your measurement is carried out and you learn that the exit air at \(10 \mathrm{mm}\) Hg gauge has a dew point of \(40^{\circ} \mathrm{C}\). Use that information and the mass of water removed from the wet pulp to determine the volumetric flow rate ( \(\mathrm{m}^{3} / \mathrm{min}\) ) of air entering the system.

The feed to a distillation column (sketched below) is a 45.0 mole\% \(n\) -pentane- 55.0 mole\% n-hexane liquid mixture. The vapor stream leaving the top of the column, which contains 98.0 mole\% pentane and the balance hexane, goes to a total condenser (which means all the vapor is condensed). Half of the liquid condensate is returned to the top of the column as reflux and the rest is withdrawn as overhead product (distillate) at a rate of \(85.0 \mathrm{kmol} / \mathrm{h}\). The distillate contains \(95.0 \%\) of the pentane fed to the column. The liquid stream leaving the bottom of the column goes to a reboiler. Part of the stream is vaporized; the vapor is returned to the bottom of the column as boilup, and the residual liquid is withdrawn as bottoms product.(a) Calculate the molar flow rate of the feed stream and the molar flow rate and composition of the bottoms product stream. (b) Estimate the temperature of the vapor entering the condenser, assuming that it is saturated (at its dew point) at an absolute pressure of 1 atm and that Raoult's law applies to both pentane and hexane. Then estimate the volumetric flow rates of the vapor stream leaving the column and of the liquid distillate product. State any assumptions you make. (c) Estimate the temperature of the reboiler and the composition of the vapor boilup, again assuming operation at 1 atm.(d) Calculate the minimum diameter of the pipe connecting the column and the condenser if the maximum allowable vapor velocity in the pipe is \(10 \mathrm{m} / \mathrm{s}\). Then list all the assumptions underlying the calculation of that number.

Recovery and processing of various oils are important elements of the agricultural and food industries. For example, soybean hulls are removed from the beans, which are then flaked and contacted with hexane. The hexane extracts soybean oil and leaves very little oil in the residual solids. The solids are dried at an elevated temperature, and the dried solids are used to feed livestock or further processed to extract soy protein. The gas stream leaving the dryer is at \(80^{\circ} \mathrm{C}\) 1 atm absolute, and 50\% relative saturation.(a) To recover hexane, the gas leaving the dryer is fed to a condenser, which operates at 1 atm absolute. The gas leaving the condenser contains 5.00 mole \(\%\) hexane, and the hexane condensate is recovered at a rate of \(1.50 \mathrm{kmol} / \mathrm{min}\). (b) In an altemative arrangement, the gas leaving the dryer is compressed to 10.0 atm and the temperature simultancously is increased so that the relative saturation remains at \(50 \% .\) The gas then is cooled at constant pressure to produce a stream containing 5.00 mole \(\%\) hexane. Calculate the final gas temperature and the ratio of volumetric flow rates of the gas streams leaving and entering the condenser. State any assumptions you make.(c) What would you need to know to determine which of processes (a) and (b) is more cost- effective?

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