Answer :
Answer:
The distance from the entrance at which the flow becomes fully developed (entrance lenght) is:
[tex]L_{E}=1.752 m[/tex]
Explanation:
First, we need to know if the flow is laminar or turbulent using the equation for the Reynolds number in a circular tube, which is:
[tex]Re=\frac{VD}{v}[/tex] (Equation 1)
We know that for
[tex]Re\leq 2300[/tex], the flow is laminar
[tex]2300\leq Re\leq 1x10^{5}[/tex], the flow is turbulent
Then, tanking into account that for air at 20 kPa and 5°C, kinematic viscosity [tex](v)[/tex] is [tex]1.252x10^{-5} \frac{m^{2}}{s}[/tex] (taken from Table A-9, Cengel's book), we use the equation 1 ,
[tex]Re=\frac{(1.5 m/s)(0.015m)}{1.252x10^{-5}m^{2}/s}=1797.12[/tex]
And, we can conclude that the flow is laminar. Then, we can use the relationship between the entrance length [tex](L_{E})[/tex], which is the distance from the entrance at wich the flow becomes fully developed, and diameter for a laminar flow in a circular tube, which is:
[tex]\frac{L_{E}}{D}=0.065Re[/tex]
And we obtain,
[tex]L_{E}=0.065ReD\\L_{E}=0.065(1797.12)(0.015 m)\\L_{E}=1.752m[/tex]