Question $1$

An air$-$conditioning system serving an interactive classroom is shown in Figure Q$1$a and the equivalent fan$-$duct network is shown in Figure Q$1$b$.$ The design supply air flow rate is $2\mathrm{.}5\frac{m^3}{s},$ including an amount of outdoor air of $0\mathrm{.}5\frac{m^3}{s}.$ The supply and return fans are of the same model and size, and their performance characteristics at $720$ rpm can be represented by the following equation:

$P_t=500-18\mathrm{.}6V^2$

$(P_t$: fan total pressure, $Pa$;$V$: airflow rate,$\frac{m^3}{s})$

Upon completion of installation, the system has to be commissioned to obtain the design air flow rates whilst maintaining the interactive classroom at a positive pressure of $20$ Pa $.$

$1-$a$)$ Keeping the return air damper fully open, $R_1$ and $R_2$ are tuned by adjusting the volume control dampers so that the design amounts of outdoor air intake and recirculation air can be obtained. Calculate the required resistance for $R_1$ and $R_2($taking $R_1$ and $R_2).$

$(3$ marks$)$

$1-$b$)$ Calculate the required fan total pressure and speed for the supply fan in order to achieve the design supply airflow rate and room pressure. Determine that the required return fan speed is larger or smaller than the supply fan speed?

$(17$ marks$)$

$1-$c$)$ How would the resistance of the outdoor air intake and exhaust air ductwork affect the operation of the system with economy cycle for energy saving?

$(5$ marks$)$