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

Step 1: State the assumptions in play.
The flow is incompressible and irrotational, so it can be described by a velocity potential, and the body is smooth and non-lifting, so no circulation is generated around it.

Step 2: Use symmetry of the potential flow solution.
For a closed smooth body in a uniform stream, the potential flow solution builds up a pressure field that is symmetric between the front and back of the body, since the flow that decelerates approaching the nose reaccelerates by the same amount leaving the tail. Integrating this symmetric pressure over the body surface gives equal and opposite contributions fore and aft, so the net force along the flow direction is zero.

Step 3: Check the other possible drag source.
Drag can also come from viscous skin friction, but the flow here is treated as inviscid (no viscosity term appears), so there is no shear stress on the surface either.

Final Answer:
With both pressure drag and friction drag equal to zero, the total drag predicted by ideal flow theory is zero, which is d'Alembert's paradox. \[ \boxed{D = 0} \]