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Two immiscible, incompressible, viscous fluids having same densities but different viscosities are contained between two infinite horizontal parallel plates. 2 m apart as shown below. The bottom plate is fixed and the upper plate move to the right with a constant velocity of 3 m/s. With the assumptions of Newtonian fluid steady, and fully developed laminar flow with zero pressure gradient in all directions, the momentum equations simplify to
d²u = 0 dy²
If the dynamic viscosity of the lower fluid, μ2 is twice that of the input fluid, μ1, then the velocity at the interface (round off to two decimal places) is_____m/s.
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- 1 m/s
- 2 m/s
- - 1 m/s
- - 2 m/s
Correct Option: A
μ² = 2μ1
V2 = 3 m/s
Shear stress value at intermediate plate will be
| τ = | = | h | h |
Since μ2 = 2μ1
∴ 2V1 = V1 – V1
⇒ V2 = V1 +2V1
V2 = 3V1 [V2 = 3 m/s]
&rARr; 3 = 3V1
| ⇒V1 = | = 1 m/s | 3 |
