The tunnel was driven through a hill at a gradient of one in seven. The length of the tunnel on plan is $530m.$ Tunnel is $1\mathrm{.}80m$ wide and $2\mathrm{.}0m$ high and constant air temperature in the tunnel is $21C.$ The surface temperature in the area varies between $0C$ and $($in winter$)$ and $35C($in summer$).$ Average barometric pressure is measured as $101\mathrm{.}25$kPa.

Hint: Consider vertical projection of tunnel as a Depth $($D$).$

a$.$ What is the resistance of the tunnel $)=(0\mathrm{.}039?$

b$.$ What is the max and min airflow to be expected in the tunnel due to NVP$?$

The tunnel is enlarged to $4m$ wide by $3m$ high and shotcrete lined throughout it $0\mathrm{.}0032).$ The ventilation engineer decides that $65\frac{m^3}{sec}$ airflow is required in the tunnel and acquired a $($exhaust$)$ fan with a $55\%$ efficiency and installed it at point B$.$

c$.$ What is the power requirement of the fan in winter and in summer?