Chapter 7, Problem 30P

Consider ventilation of a well-mixed room as in Fig. P7-21. The differential equation for mass concentration in the room as a function of time is given in Prob. 7-21 and is repeated here for convenience,
$V\frac{dc}{dt}=S-\stackrel{\dot{}}{V}c-c{A}_s{k}_w$There are three characteristic parameters in such a situation: L, a characteristic length scale of the room (assume $L=V^{1/3}$); $\stackrel{\dot{}}{V}$, the volume flow rate of fresh air into the room, and $c_{\text{limit}}$ , the maximum mass concentration that is not harmful. (a) Using these three characteristic parameters, define dimensionless forms of all time variables in the equation. (Hint: For example, define $c*=c/c_{\text{limit}}$.) (b) Rewrite the equation in dimensionless form and identify any established dimensionless groups that may appear.