) Room ventilation is an important area of environmental and architectural engineering for the application of fluid mechanics. Suppose there is a source S (mass per unit time) of air pollution in a room of volume V. Examples include carbon monoxide from cigarette smoke or an unvented kerosene heater, emissions from household cleaning products, and vapors given off by evaporation of volatile organic compounds from an open container. Let C represent the mass concentration (mass of contaminant per unit volume of air) and Q represent the volumetric flow rate of fresh air entering the room. If the room air is well mixed so that the concentration is uniform throughout the room, but varies with time, the differential equation for mass concentration in the room is: Where kw is an adsorption coefficient and As is the surface area of walls, floors, etc., that adsorb some of the contaminant. V.dC/dt = S-QC-Aw.As.C Write the primary dimensions of the first three additive terms in the equation, and verify that those terms are dimensionally homogeneous. Then determine the dimensions of kw. Use Cmax, the maximum allowable concentration of the pollutant, along with the other parameters V, S, kw, Q, and As to rewrite the equation in dimensionless form. Identify any established dimensionless groups that may appear. Use C* = C/Cmax and t*=Qt/V.

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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) Room ventilation is an important area of environmental and architectural engineering for the application of fluid mechanics. Suppose there is a source S (mass per unit time) of air pollution in a room of volume V. Examples include carbon monoxide from cigarette smoke or an unvented kerosene heater, emissions from household cleaning products, and vapors given off by evaporation of volatile organic compounds from an open container. Let C represent the mass concentration (mass of contaminant per unit volume of air) and Q represent the volumetric flow rate of fresh air entering the room. If the room air is well mixed so that the concentration is uniform throughout the room, but varies with time, the differential equation for mass concentration in the room is:

Where k_w is an adsorption coefficient and A_s is the surface area of walls, floors, etc., that adsorb some of the contaminant. V.dC/dt = S-QC-Aw.As.C

Write the primary dimensions of the first three additive terms in the equation, and verify that those terms are dimensionally homogeneous. Then determine the dimensions of k_w.
Use C_max, the maximum allowable concentration of the pollutant, along with the other parameters V, S, k_w, Q, and A_s to rewrite the equation in dimensionless form. Identify any established dimensionless groups that may appear. Use C^* = C/C_max and t^*=Qt/V.

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