Question

Consider air flowing at 10m/s (p=1.2kg/m^3,v=1.47*10^-5 m^2/s) on a flat plate having a length 1m and a width of .5m respectively then the length upto which the flow of air will be laminar?

Answer 1

The flow is laminar up to  length = 0.735 meter after that it becomes turbulent.

Given:

Air flowing at 10 m/s

$\rho$=1.2 kg/m³

Kinematic viscosity=1.47× $10^-^5$  m²/s

Flat plate having a length 1m and a width of .5m respectively.

To find:

The length up to which the flow of air will be laminar.

Concept used:

For laminar flow over a flat plat Reynolds number = 5×$10^5$

Reynolds number = $\frac{ v L}{\nu}$

Where v = velocity of flow

           L = characteristic length

Explanation:

Reynolds number =     $\frac{ v L}{\nu}$ =  $\frac{ 10\times 1}{1.47 \times 10^-^5}$  = 6.8× $10^5$      

On the front portion, the boundary layer is laminar and on the rear, it is turbulent.

For laminar flow over a flat plat Reynolds number ≤ 5×$10^5$

                                    $\frac{ v L}{\nu}$  ≤ 5×$10^5$

                               $\frac{ 10\times L}{1.47 \times 10^-^5}$ ≤ 5×$10^5$

Length = 0.735 meter.

The flow is laminar up to  length = 0.735 meter after that it becomes turbulent from the leading edge.

To learn more...

1)Whether boundary layer changes from laminar to turbulent? If so determine distance at which the laminar boundary layer existing at the leading-edge transforms into turbulent boundary layer.

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2)Explain different layer of boundary layer​.

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