GATE 2023 MT – Question 33
A liquid of density 900 kg m$^{-3}$ flows over a flat plate at free-stream velocity 0.1 m s$^{-1}$. Its laminar boundary-layer thickness 0.2 m from the leading edge is 0.007 m. Its viscosity is ______ centipoise (two decimal places). Given: 1 centipoise $=10^{-3}$ kg m$^{-1}$ s$^{-1}$.
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Correct answer: 0.84 to 0.92
Explanation
For a laminar flat-plate boundary layer, $\delta\approx5x/\sqrt{\mathrm{Re}_x}$.
Thus $\mathrm{Re}_x=(5\times0.2/0.007)^2=20408.16$. Using $\mu=\rho Ux/\mathrm{Re}_x$ gives $\mu=900(0.1)(0.2)/20408.16=0.000882$ Pa·s, or **0.88 cP**.