The "stack effect" due to a difference in temperature between the inside and outside of a cooling room is often cited as the major reason for air infiltration. In this context, $\Delta \mathrm{P}$ is positive at the lowest section of a cooler and is negative at the highest section, with a zone, called the neutral zone, at approximately the center of the room where the $\Delta \mathrm{P}$ is zero. If the area of the openings at the lowest sections where $\Delta \mathrm{P}$ is positive equals the area of the openings in the highest sections where $\Delta \mathrm{P}$ is negative, air will enter at the top and escape at the openings in the bottom at the same volumetric rate of flow (assuming no pressure change inside the room). If the room allows air leakage at the rate of $2 \%$ of the room volume per minute at a $\Delta \mathrm{P}$ of $0.5 \mathrm{in}$. wg ( $124 \mathrm{~Pa})$, determine the rate of air infiltration that can be expected in a room that is $2 \mathrm{~m}(6.56 \mathrm{ft})$ high to the neutral zone if the interior of the room is at $-20^{\circ} \mathrm{C}$ $\left(-4^{\circ} \mathrm{F}\right)$ and ambient temperature is $30^{\circ} \mathrm{C}\left(86^{\circ} \mathrm{F}\right)$. The rate of gas flow through the cracks is proportional to the square root of $\Delta \mathrm{P}$. Assume air is an ideal gas. $\Delta \mathrm{P}$ due to a column of air of height $h$ at different temperatures $=g\left(\rho_1-\rho_2\right) h$, where $\rho_1$ and $\rho_2$ are the densities of the columns of air.