/*! 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

A fuel gas containing methane and ethane is burned with air in a furnace, producing a stack gas at \(300^{\circ} \mathrm{C}\) and \(105 \mathrm{kPa}\) (absolute). You analyze the stack gas and find that it contains no unburned hydrocarbons, oxygen, or carbon monoxide. You also determine the dew-point temperature.(a) Estimate the range of possible dew-point temperatures by determining the dew points when the feed is either pure methane or pure ethane. (b) Estimate the fraction of the feed that is methane if the measured dew- point temperature is \(59.5^{\circ} \mathrm{C}\). (c) What range of measured dew point temperatures would lead to calculated methane mole fractions within 5\% of the value determined in Part (b)?

When fermentation units are operated with high aeration rates, significant amounts of water can be evaporated into the air passing through the fermentation broth. since fermentation can be adversely affected if water loss is significant, the air is humidified before being fed to the fermenter. Sterilized ambient air is combined with steam to form a saturated air-water mixture at 1 atm and \(90^{\circ} \mathrm{C}\). The mixture is cooled to the temperature of the fermenter \(\left(35^{\circ} \mathrm{C}\right),\) condensing some of the water, and the saturated air is fed to the bottom of the fermenter. For an air flow rate to the fermenter of \(10 \mathrm{L} / \mathrm{min}\) at \(35^{\circ} \mathrm{C}\) and \(1 \mathrm{atm},\) estimate the rate at which steam must be added to the sterilized air and the rate (kg/min) at which condensate is collected upon cooling the air-steam mixture.

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?

An aqueous waste stream leaving a process contains 10.0 wt\% sulfuric acid and 1 kg nitric acid per \(\mathrm{kg}\) sulfuric acid. The flow rate of sulfuric acid in the waste stream is \(1000 \mathrm{kg} / \mathrm{h}\). The acids are neutralized before being sent to a wastewater treatment facility by combining the waste stream with an aqueous slurry of solid calcium carbonate that contains 2 kg of recycled liquid per \(\mathrm{kg}\) solid calcium carbonate. (The source of the recycled liquid will be given later in the process description.) The following neutralization reactions occur in the reactor:$$\begin{array}{l} \mathrm{CaCO}_{3}+\mathrm{H}_{2} \mathrm{SO}_{4} \rightarrow \mathrm{CaSO}_{4}+\mathrm{H}_{2} \mathrm{O}+\mathrm{CO}_{2} \\ \mathrm{CaCO}_{3}+2 \mathrm{HNO}_{3} \rightarrow \mathrm{Ca}\left(\mathrm{NO}_{3}\right)_{2}+\mathrm{H}_{2} \mathrm{O}+\mathrm{CO}_{2} \end{array}$$,The sulfuric and nitric acids and calcium carbonate fed to the reactor are completely consumed. The carbon dioxide leaving the reactor is compressed to 30 atm absolute and \(40^{\circ} \mathrm{C}\) and sent elsewhere in the plant. The remaining reactor effluents are sent to a crystallizer operating at \(30^{\circ} \mathrm{C},\) at which temperature the solubility of calcium sulfate is \(2.0 \mathrm{g} \mathrm{CaSO}_{4} / 1000 \mathrm{g} \mathrm{H}_{2} \mathrm{O} .\) Calcium sulfate crystals form in the crystallizer and all other species remain in solution.The slurry leaving the crystallizer is filtered to produce (i) a filter cake containing \(96 \%\) calcium sulfate crystals and the remainder entrained saturated calcium sulfate solution, and (ii) a filtrate solution saturated with \(\mathrm{CaSO}_{4}\) at \(30^{\circ} \mathrm{C}\) that also contains dissolved calcium nitrate. The filtrate is split, with a portion being recycled to mix with the solid calcium carbonate to form the slurry fed to the reactor, and the remainder being sent to the wastewater treatment facility.(a) Draw and completely label a flowchart for this process. (b) Speculate on why the acids must be neutralized before being sent to the wastewater treatment facility.(c) Calculate the mass flow rates ( \(\mathrm{kg} / \mathrm{h}\) ) of the calcium carbonate fed to the process and of the filter cake; also determine the mass flow rates and compositions of the solution sent to the wastewater facility and of the recycle stream. (Caution: If you write a water balance around the reactor or the overall system, remember that water is a reaction product and not just an inert solvent.)(d) Calculate the volumetric flow rate ( \(L / h\) ) of the carbon dioxide leaving the process at 30 atm absolute and 40^0 C. Do not assume ideal-gas behavior. (e) The solubility of \(\mathrm{Ca}\left(\mathrm{NO}_{3}\right)_{2}\) at \(30^{\circ} \mathrm{C}\) is \(152.6 \mathrm{kg} \mathrm{Ca}\left(\mathrm{NO}_{3}\right)_{2}\) per \(100 \mathrm{kg} \mathrm{H}_{2} \mathrm{O}\). What is the maximum ratio of nitric acid to sulfuric acid in the feed that can be tolerated without encountering difficulties associated with contamination of the calcium sulfate by-product by \(\mathrm{Ca}\left(\mathrm{NO}_{3}\right)_{2} ?\)

Sodium bicarbonate is synthesized by reacting sodium carbonate with carbon dioxide and water at \(70^{\circ} \mathrm{C}\) and \(2.0 \mathrm{atm}\) gauge pressure: $$\mathrm{Na}_{2} \mathrm{CO}_{3}+\mathrm{CO}_{2}+\mathrm{H}_{2} \mathrm{O} \rightarrow 2 \mathrm{NaHCO}_{3}$$ An aqueous solution containing 7.00 wt\% sodium carbonate and a gas stream containing 70.0 mole\% \(\mathrm{CO}_{2}\) and the balance air are fed to the reactor. All of the sodium carbonate and some of the carbon dioxide in the feed react. The gas leaving the reactor, which contains the air and unreacted \(\mathrm{CO}_{2},\) is saturated with water vapor at the reactor conditions. A liquid-solid slurry of sodium bicarbonate crystals in a saturated aqueous solution containing \(2.4 \mathrm{wt} \%\) dissolved sodium bicarbonate and a negligible amount of dissolved \(\mathrm{CO}_{2}\) leaves the reactor and is pumped to a filter. The wet filter cake contains 86 wt\% sodium bicarbonate crystals and the balance saturated solution, and the filtrate also is saturated solution. The production rate of solid crystals is \(500 \mathrm{kg} / \mathrm{h}\).Suggestion: Although the problems to be given can be solved in terms of the product flow rate of \(500 \mathrm{kg} \mathrm{NaHCO}_{3}(\mathrm{s}) / \mathrm{h},\) it might be easier to assume a different basis and then scale the process to the desired production rate of crystals.(a) Calculate the composition (component mole fractions) and volumetric flow rate \(\left(\mathrm{m}^{3} / \mathrm{min}\right)\) of the gas stream leaving the reactor. (b) Calculate the feed rate of gas to the process in standard cubic meters/min \(\left[\mathrm{m}^{3}(\mathrm{STP}) / \mathrm{min}\right]\) (c) Calculate the flow rate \((\mathrm{kg} / \mathrm{h})\) of the liquid feed to the process. What more would you need to know to calculate the volumetric flow rate of this stream? (d) The filtrate was assumed to leave the filter as a saturated solution at \(70^{\circ} \mathrm{C}\). What would be the effect on your calculations if the temperature of the filtrate actually dropped to \(50^{\circ} \mathrm{C}\) as it passed through the filter? (e) The reactor pressure of 2 atm gauge was arrived at in an optimization study. What benefit do you suppose would result from increasing the pressure? What penalty would be associated with this increase? The term "Henry's law" should appear in your explanation. (Hint: The reaction occurs in the liquid phase and the \(\mathrm{CO}_{2}\) enters the reactor as a gas. What step must precede the reaction?)

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