Answer:
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 = [tex]\frac{4(ab)}{2(a+b)}[/tex] = [tex]\frac{4(1.8*0.6667}{2(1.8+0.6667)}[/tex] = 0.9729 ft
V ( velocity of air flow ) = [tex]\frac{Q}{\pi /4 * Dn^2 }[/tex] = [tex]\frac{90}{\pi /4 * 0.9729^2 }[/tex] = 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
