# An incompressible fluid flows over a flat plate with zero pressure gradient. The boundary layer thickness is 1 mm at a location where the Reynolds num

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An incompressible fluid flows over a flat plate with zero pressure gradient. The boundary layer thickness is 1 mm at a location where the Reynolds number is 1000. If the velocity of the fluid alone is increased by a factor of 4, then the boundary layer thickness at the same location, in mm will be
1. 4
2. 2
3. 0.5
4. 0.25

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Correct Answer - Option 3 : 0.5

Concept:

According to the Blasius equation, for a laminar flow

Boundary layer thickness (δ) can be calculated by:

$\delta = \frac{{5x}}{{\sqrt {R{e_x}} }}$

where Rex = Reynold's number = $\frac{{\rho Vx}}{\mu }$ {V = Velocity}

$\therefore \delta \propto \frac{1}{V}$

Calculation:

Given:

δ1 = 1 mm, V2 = 4V1

$As,\,\delta \propto \frac{1}{V}$

$\frac{{{\delta _1}}}{{{\delta _2}}} = \sqrt {\frac{{{V_2}}}{{{V_1}}}}$

$\frac{1}{{{\delta _2}}} = \sqrt {\frac{4}{1}} = 2$

δ2 = 0.5 mm