Air at 20 kPa and 5 °C enters a 1.5 cm diameter tube at a uniform velocity of 1.5 m/s. The tube walls are maintained at a uniform temperature of 45 °C. Estimate the distance from the entrance at which the flow becomes fully developed.

The distance from the entrance at which the flow becomes fully developed (entrance lenght) is:

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:

         (Equation 1)

We know that for

,   the flow is laminar

,    the flow is turbulent

Then, tanking into account that for air at 20 kPa and 5°C, kinematic viscosity is (taken from Table A-9, Cengel's book), we use the equation 1 ,

And, we can conclude that the flow is laminar. Then, we can use the relationship between the entrance length , 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:

And we obtain,

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explanation: