Air flow at 15 m/s past a thin flat plate. Estimate the distance x from the leading edge at which the boundary layer thickness will be (a) 10 cm and (b) 1 mm. Use a transition Reynolds number of 5 x 105.

a) x = 5.7791 m ( this a turbulent flow )

b) x = 0.04 m ( this is a Laminar flow )

Explanation:

For Air, take

p = 1.2 kg/m³ and u = 1.8×10⁻⁵ kg/m³

So for A , x = 10 cm

Guess turbulent flow;

(Sturb / x) = (0.16 / (p∪x / u)^1/7)

we substitute

(0.1/x = 0.16) / ( 1.2 × 15 × x / 1.8×10⁻⁵)^1/7

x = 5.7791 m

CHECK

Re = (1.2 × 15 × 5.7791) / 1.8×10⁻⁵ = 5.779×10⁶

Therefore this a turbulent flow

for B, x = 1mm

Guess Laminar flow

(S-laminar / x) = ( 5 / (Reₓ)^1/2)

x = (Stutb)²p∪ / 23u

x = ((0.001)² × 1.2 × 15) / (25 × 1.8×10⁻⁵)

x = 0.04 m

CHECK

Re = (1.2 × 15 × 0.04) / (1.8×10⁻⁵)

= 40000

Therefore  this is a Laminar flow

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answer:

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Explanation: