Need help to find average velocity and pressure drop in duct

[mchi6aa2]

Homework Statement

1. the average velocity of the air to meet the required volume flow rate,
2. the pressure a fan needs to produce to overcome the frictional losses in the duct,

2. Relevant Information

Duct size - 600 mm x 600 mm which operates at 3 Pa/m.
The air path is 87 meters from intake to discharge including allowances for grilles, bends and dampers.
The pressure drops per meter are for the required volume flow rate of 5000 l/s. Average velocities in the duct can be calculated by considering the volume flow rate and cross sectional area of the ducts.

Please help. Thanks

Danny

 

[mchi6aa2]

Thats the way I did. I am not sure is it right or wrong:

First , Head required to overcome friction Losses and to maintain
velocity head is to be calculated.

Q= 5000 l/s = 5 m³ /s , A= 0.6 * 0.6 = 0.36 m² , Av . Velocity = Q/A =13.88 m/s

Velocity head = V²/2g = 9.83 m of air coloumn ,
frictional head to overcome by the fan = 3*87=267 Pa

Fan pressure = 1.145 * 9.83 * 9.8 KPa + 267 Pa = 110.63 KPaFan power required = PQ = 110.63 * 5 = 555 Kw