$1-$a$)$ The pressure loss along duct section $\backslash ($ R$\_\{1\}\backslash )$ is $60$ Pa when the volume flow rate is $\backslash (2\backslash$mathrm$\{$~m$\}^\{3\}/\backslash$mathrm$\{$s$\}\backslash ).$ Similarly, the pressure loss along duct section $\backslash ($ R$\_\{2\}\backslash )$ is $270$ Pa when the volume flow rate is $\backslash (3\backslash$mathrm$\{$~m$\}^\{3\}/\backslash$mathrm$\{$s$\}\backslash ).$ The supply and exhaust fan have identical characteristics, which are provided in the table below. Your task is to determine the pressure in the interactive classroom and the corresponding volume flow rate of the supply air.

$(9$ marks$)$

$1-$b$)$ Based on a site investigation, it has been determined that there is an air loss from the interactive classroom due to exfiltration through an aperture. This aperture causes a pressure loss of $55$ Pa when the volume flow rate is $\backslash (0\mathrm{.}5\backslash$mathrm$\{$~m$\}^\{3\}/\backslash$mathrm$\{$s$\}\backslash ).$ Your task is to sketch the equivalent network for the entire system and calculate the pressure in the interactive classroom, as well as the volume flow rates of the supply and exhaust air.

$(11$ marks$)$

$1-$c$)$ How does the pressure loss in the ventilation system affect the volume flow rates of the supply and exhaust air in a large interactive classroom? Considering the changes in pressure loss and volume flow rate in duct sections $\backslash (\backslash$mathrm$\{$R$\}\_\{1\}\backslash )$ and $\backslash (\backslash$mathrm$\{$R$\}\_\{2\}\backslash ),$ as well as the increased pressure loss due to the aperture, how might these changes impact the overall ventilation efficiency of the interactive classroom? What strategies could be implemented to mitigate any potential negative effects?