Question

A smooth two-dimensional flat plate is exposed to a wind velocity of 70 km per hour. If the laminar boundary layer exists up to a value of R_ex equal to 3 × 10⁵ and kinematics viscosity of air = 1.49 × 10^-5 m²/sec, what would be the maximum distance up to which laminar boundary persists?
1. 0.063 m
2. 0.115 m
3. 0.229 m
4. 3.78 m
5.

Answer 1

Correct Answer - Option 3 : 0.229 m

Concept:

The Reynolds number for flow over plate can be given as:

\({R_e} = \frac{{\rho UX}}{\mu }\)

Where

X is the distance from the leading edge.

U is the free mean velocity.

μ is the dynamic viscosity of fluid flowing.

ρ is the density of fluid flowing.

If Reynolds number is less than or equal to critical Reynold’s number then boundary layer formed over flat plate is laminar i.e.Re ≤ ReCr­

Calculation:

Given:

U = 70 km per hour, kinematic viscosity (ν) = 1.49 × 10-5 m2/sec

Rex = 3 × 105

Let ‘x’ is the distance from the leading edge up to which the Boundary layer formed is laminar,

\({{\mathop{\rm R}\nolimits} _{ex}} = \frac{{\rho Vx}}{\mu } = \frac{{Vx}}{\upsilon }\)

\(3 \times {10^5} = \frac{{\frac{{70}}{{3.6}} \;\times\; x}}{{1.49\; \times \;{{10}^{ - 5}}}}\)

x = 0.229 m