Chapter 7, Problem 20P

An important application of fluid mechanics is the study of room ventilation. In particular, suppose there is a source S (mass per unit time) of air pollution in a room of volume V (Fig. P7-20). Examples include carbon monoxide from cigarette smoke or an unvented kerosene heater, gases like ammonia from household cleaning products, and vapors given off by evaporation of volatile organic compounds (VOCs) from an open container. We let c represent the mass concentration (mass of contaminant per unit volume of air). $\stackrel{\dot{}}{V}$ is the volume flow rate of fresh air entering the room. If the room air is well mixed so that the mass concentration c is uniform throughout the room, but varies with time, the differential equation for mass concentration in the room as a function of time is

   $V\frac{dc}{dt}=S-\stackrel{\dot{}}{V}c-c{A}_s{k}_w$

where $k_w$ is an adsorption coefficient and $A_s$ is the surface area of walls, floor, furniture, etc., that adsorb some of the contaminant. What the primary dimensions of the first three terms in the equation (including the term on the left side), and verify that those term are dimensionally homogeneous. Then determine the dimensions of $k_w$ . Show all your work.