GATE Papers >> Mechanical >> 2018 >> Question No 132

Question No. 132 Mechanical | GATE 2018

The viscous laminar flow of air over a flat plate results in the formation of a boundary layer. The boundary layer thickness at the end of the plate of length L is $ \delta_L $. When the plate length is increased to twice its original length, the percentage change in laminar boundary layer thickness at the end of the plate (with respect to $ \delta_L $) is ________ (correct to two decimal places).

Answer : 41.30 to 41.50

Solution of Question No 132 of GATE 2018 Mechanical Paper

From Blasius equation 

We known;

$ \begin{array}{l}\frac{\mathrm\delta}{\mathrm x}=\frac5{\sqrt{{\mathrm{Re}}_\mathrm x}}\\\mathrm\delta=\frac{5\mathrm x}{\sqrt{\displaystyle\frac{\mathrm{PVx}}{\mathrm\mu}}}\\\mathrm\delta\;\mathrm\alpha\;\;\sqrt{\mathrm x}\\\therefore\frac{{\mathrm\delta}_{2\mathrm L}}{{\mathrm\delta}_\mathrm L}=\frac{\sqrt{2\mathrm L}}{\sqrt{\mathrm L}}=\sqrt2\end{array} $

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