In fluid dynamics, d'Alembert's paradox refers to which one of the following?
Show Hint
- Deviation of drag from \(D \propto v^2\) at very low speeds
- Deviation of drag from \(D \propto v^2\) at high subsonic speeds
- Prediction of zero drag by potential flow theory
- Presence of shocks in transonic flows
The Correct Option is C
Solution and Explanation
In 1752, d'Alembert used potential flow theory (flow that is inviscid, incompressible and irrotational) to find the net force on a body moving at constant speed through a fluid.
The result he got was that the drag force comes out to be exactly zero, no matter what shape the body has.
Step 2: Compare this result with real flow.
In a real fluid, a body moving through it always feels a drag force, because of viscosity and the boundary layer that forms on its surface.
So potential flow theory (which ignores viscosity) predicts zero drag, while every real body actually has drag. This contradiction between theory and reality is the paradox.
Step 3: Why the other options are wrong.
Options (A) and (B) talk about the drag law \(D \propto v^2\) breaking down at very low or high subsonic speeds. That is a separate topic (deviation of the drag coefficient with Reynolds number or Mach number), not d'Alembert's paradox.
Option (D) refers to shock waves in transonic flow, which is a compressibility effect and has nothing to do with the inviscid drag prediction.
Final Answer:
d'Alembert's paradox is the prediction of zero drag by potential (inviscid, irrotational) flow theory, which does not match real, viscous flow. \[ \boxed{\text{Option (C)}} \]
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