Hele-Shaw flow is used to experimentally visualize potential flow because the flow of a viscous fluid between two closely spaced parallel plates is mathematically analogous to
- ATurbulent flow in a pipe.
- BInviscid, irrotational flow in 2D.Correct
- CCompressible supersonic flow.
- DBoundary layer separation.
Solution
Concept
Hele-Shaw cell analogy to 2D potential flow
Formula
\nabla2 p = 0
Step-by-step solution
1. Hele-Shaw flow describes the slow, creeping laminar flow of a viscous fluid between two flat plates separated by a tiny gap. 2. For creeping flow (Re << 1), inertial forces are negligible, and velocity is directly proportional to the local pressure gradient. 3. Applying continuity leads to Laplace's equation for pressure: \nabla2 p = 0. 4. Because 2D potential flow satisfies \nabla2 φ = 0, the streamline patterns are mathematically identical to inviscid, irrotational 2D flow. Answer: B
Explanation
Hele-Shaw flow represents the creeping, laminar flow of a viscous fluid through a very narrow gap between two parallel plates. Because inertial effects are negligible and depth-averaged velocity is proportional to the pressure gradient, the pressure satisfies Laplace's equation (\nabla2 p = 0), making the flow pattern mathematically identical to 2D inviscid, irrotational potential flow.
Why the other options are wrong
A) Hele-Shaw flow is creeping laminar flow, completely unlike high-Reynolds-number turbulent pipe flow. C) It is an incompressible liquid flow, not compressible supersonic flow. D) Inertial forces are negligible, so boundary layer separation does not occur.
Shortcut
Hele-Shaw cell = Creeping viscous flow \equiv 2D inviscid, irrotational potential flow.
Common mistake
Assuming viscous laminar flow cannot represent inviscid potential flow, missing the mathematical identity of Laplace equations.
Correct answer: B) Inviscid, irrotational flow in 2D.