Consider the laminar flow of water over a flat plate of length 1 m. If the boundary layer thickness at a distance of 0.25 m from the leading edge of t

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Consider the laminar flow of water over a flat plate of length 1 m. If the boundary layer thickness at a distance of 0.25 m from the leading edge of the plate is 8 mm, the boundary layer thickness (in mm), at a distance of 0.75 m, is _______

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Explanation:

For laminar flow over a flat plate

Blausius equation is:

$\begin{array}{l} \frac{\delta }{x} = \frac{5}{{{{\left( {{R_{{e_x}}}} \right)}^{\frac{1}{2}}}}}\\ \Rightarrow \frac{\delta }{x} = \frac{5}{{{{\left( {\frac{{\rho Vx}}{\mu }} \right)}^{\frac{1}{2}}}}} \end{array}$

$\Rightarrow \frac{\delta }{x} = \frac{{constant}}{{\sqrt x }}$ {∴ δ, v & μ are constant}

$\begin{array}{l} \Rightarrow \frac{\delta }{{\sqrt x }} = constant\\ \Rightarrow \frac{{{\delta _1}}}{{\sqrt {{x_1}} }} = \frac{{{\delta _2}}}{{\sqrt {{x_2}} }}\\ \Rightarrow {\delta _2} = \sqrt {\frac{{{x_2}}}{{{x_1}}}} {\delta _1}\\ \Rightarrow {\delta _2} = \sqrt {\frac{{0.75}}{{0.25}}} \times 8 \end{array}$

⇒ δ2 = 13.86 mm