To cool a given room it is necessary to provide 4 ft³/s of air through an 8-inches diameter pipe, for this Entrance length in this pipe = 17.7 ft
Q = 4ft³/s
Diameter = D = 8 inches
Entrance length in this pipe = [tex]l_{e}[/tex] = ?
By using flow rate formula:
V = Q/A
V= Q/ π/4*D²
= 4ft³/s / π/4 (8/12 ft)²
V= 11.5 ft/s
Thus, with ν = 1.57 x 10⁻⁴ft²/s (value from table)
Re = VD/ν
Re = 11.5 ft/s (8/12 ft)/1.57x10⁻⁴ft²/s
Re = 48,800 > 4000 (based on the criteria)
so, the flow is turbulent
Hence,
[tex]l_{e} / D[/tex] = [tex]4.4 R_{e}^{1/6}[/tex]
[tex]l_{e}[/tex] = 4.4 (48,800)[tex]^{1/6}[/tex] (8/12)
[tex]l_{e}[/tex] = 17.7 ft
Entrance Length of an 8-inch diameter pipe = 17.7 ft
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