Question

The drag force on a non-lifting smooth body immersed in an incompressible, irrotational, uniform flow is ______.

• A. zero
• B. finite and greater than zero
• C. infinite
• D. finite and less than zero

Hint:

Recall what ideal, inviscid potential flow theory predicts for the fore and aft pressure symmetry on a smooth body.

Answer 1

The Correct Option is A

This question is describing ideal potential flow around a smooth, non-lifting body, and asks what drag that theory predicts.

1. zero: in an incompressible, irrotational, uniform (inviscid) flow, the pressure distribution computed around a closed smooth body comes out perfectly symmetric fore and aft, so the net pressure force in the flow direction cancels to nothing. With no viscosity there is also no skin friction drag. This is the correct choice, known as d'Alembert's paradox.
2. finite and greater than zero: this is what happens in a real viscous flow, where skin friction and pressure asymmetry from boundary layer separation both add drag, but that mechanism is switched off in the ideal flow this question describes.
3. infinite: nothing in potential flow theory produces an unbounded force on a smooth body, so this option has no basis.
4. finite and less than zero: a negative drag would mean the flow pushes the body forward on its own, which does not happen for a body held in a steady uniform stream.

So the drag on a non-lifting smooth body in ideal flow works out to zero, option A, the classic d'Alembert paradox result.