GATE 2019 ME (ME1) – Question 55
Two immiscible incompressible viscous fluids of equal density occupy the shown 2 m gap between infinite horizontal plates. Bottom plate is fixed; top moves right at 3 m/s. For Newtonian, steady, fully developed laminar flow with zero pressure gradients, $d^2u/dy^2=0$ in each layer. Each layer is 1 m thick; lower viscosity is twice upper viscosity. Find interface velocity (m/s), to two decimal places.
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Correct answer: .98 to 1.02
Explanation
Both velocity profiles are linear. Shear continuity requires $\mu_1(3-u)=\mu_2u$. Since $\mu_2=2\mu_1$, $3-u=2u$ and **$u=1.00$ m/s**.