33. Calculate the overall efficiency of \( \mathrm{N} \) compartments in a baghouse operated in parallel, if the volumetric flowrates and inlet concentrations to each compartment are \( \mathrm{q}_{1} ; \mathrm{q}_{2} \ldots . \mathrm{q}_{\mathrm{N}} \) and \( \mathrm{C}_{1}, \mathrm{C}_{2}, \ldots, \mathrm{C}_{\mathrm{N}} \), respectively, and the corresponding efficiencies are \( E_{1}, E_{2}, \ldots, E_{N} \). Also, express the result in terms of the q's, the \( E^{\prime} \) 's, and the C's. Calculate the overall efficiency of a baghouse consisting of three compartments treating \( 9000 \mathrm{ft}^{3} / \mathrm{min} \) of gas with an inlet loading of \( 4 \mathrm{gr} / \mathrm{ft}^{3} \). The first and third compartments operate at a fractional efficiency of 0.995 while the second compartment operates at a fractional efficiency of 0.990 . What is the overall efficiency of the baghouse if the flow and inlet concentration are evenly distributed? Also calculate the efficiency if the following flow distribution exists:
\begin{tabular}{lclc}
\hline Compartment & \( q(\mathrm{acfm}) \) & \( c\left(\mathrm{gr} / \mathrm{ft}^{3}\right) \) & \( E \) \\
\hline 1 & 2500 & 3.8 & 0.995 \\
2 & 4000 & 4.25 & 0.990 \\
3 & 2500 & 3.8 & 0.995 \\
\hline
\end{tabular}