PROBLEM $6.(20$ POINTS$)$

The layout of a ductwork system is shown below. The centrifugal fan takes air at atmospheric pressure and supplies it through two branches which discharge to atmosphere.

Using the data provided below and duct friction charts, calculate the total air flow rate handled by the fan and the flow rates from the two outlets:

a$.$ When the damper is fully open.

b$.$ When both outlets are delivering equal flow rates after adjustment of the damper.

Data:

Velocity pressure factors:

Bend; $0\mathrm{.}3$

Branch : flow to main: $0\mathrm{.}2($applied to downstream velocity pressure$)$ flow to branch: $0\mathrm{.}5($ applied to velocity pressure in off$-$take$)$

Discharge grill: $0\mathrm{.}4$

Expander: $0\mathrm{.}25($applied to maximum velocity$)$

Damper $($fully open$)$: $0\mathrm{.}2$

Fan characteristic: $P_t=200-12V^2(V$ is volumetric flow$)$