Section: Fluid Mechanics | Marks: 2
Figure shows two parallel plates (upper plate at π₯= π and lower one at π₯= βπ) of length L (aligned in π§ direction) and infinite width (in π¦ direction, normal to the plane of the figure). Two immiscible, incompressible liquids are flowing steadily in the π§ direction through the thin passage between the plates under the influence of horizontal pressure gradient (π0 βππΏ) L β . During the flow, the passage is always half-filled with denser fluid I (viscosity ππΌ) at the bottom and rest is occupied by lighter fluid II (viscosity ππΌπΌ; ππΌπΌ< ππΌ). Considering exactly planar interface between the fluids and no instabilities in the flow, the shear stress, ππ₯π§ is expressed as: ππ₯π§= (π0 βππΏ)π L [(π₯ π) β1 2 (ππΌβππΌπΌ ππΌ+ ππΌπΌ)] Which one of the following options correctly identifies the location of the point having maximum velocity of the flow?
- A. Above the interface
- B. Below the interface
- C. At the interface
- D. At the top plate
Answer: A. Above the interface