(a) A duct for an air conditioning system has a rectangular cross section of 1.8 ft × 8 in. The duct is fabricated from galvanized iron. Determine the Reynolds number for a flow rate of air of 5400 cfm at 100 °F and atmospheric pressure (g=0.0709 lbf/ft3 u=1.8×10-4ft2/s and m=3.96×10-7lbf. s/ft2) (9 points)

Reynolds number = 654350.92

Explanation:

Given data:

Cross section of  rectangular cross section = 1.8ft * 8 in  ( 8 in = 2/3 ft )

Flow rate of air = 5400 cfm = 90 ft^3 / sec

v ( kinematic viscosity of air ) = 1.8*10^-4 ft^2/s

Reynolds number

Re = VDn / v

Dn ( hydraulic diameter ) = 4A / P

where A = area, P = perimeter

a = 1.8 ft  ( length )

b = 2/3 ft ( width )

hence Dn =  =  =   0.9729 ft

V ( velocity of air flow ) =  = = 121.064 ft/sec

back to Reynolds equation

Re = VDn / v  -------------- equation 1

V = 121.064 ft/sec

Dn = 0.9729 ft

v = 1.8*10^-4 ft^2/s

insert the given values into equation 1

Re = (121.064 * 0.9729 ) / 1.8*10^-4

     = 654350.92

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