D'Alembert's paradox

The d' Alembert's paradox is a statement in fluid mechanics, which can be derived from the conservation of energy (see below). The paradox was first formulated in 1752 by Jean Baptiste le Rond d' Alembert.

It states that an arbitrarily shaped, opaque body experiences in an infinite, smooth and steady Parallelanströmung no resistance, so no force in the direction of flow when the condition is satisfied that the body caused by the disturbance of the flow at a large distance from the body decays. Forces perpendicular to the inflow direction (dynamic lift as the wing ) are not ruled out, so that for example an infinite horizontal gliding without energy expenditure would be possible.

A source, ie a body, flowing out of the liquid, even experiencing a propulsion, ie a force which is directed opposite to the flow. Conversely, experiencing a depression, a force in the direction of flow.

The statement of the paradox of d' Alembert is paradoxical in the sense that it contradicts our everyday experience, since in real flows are generally neither the frictional forces nor the disturbance of the flow can be completely neglected by the body, so that the conditions of the statement are not met are.

The reasoning with the law of energy goes as follows: When a force component would be required in the direction of the uniform motion of the body to maintain the movement, so would the force constant mechanical work on the liquid (or gas) done. The power may, however, from the ideal liquid ( or the gas ) can not be received because there is no friction losses which would allow conversion to heat, even variations in the kinetic energy of the fluid (due to the assumed stationarity, that everywhere constant flow rates ). According to the energy conservation law, therefore, the force component in the direction of motion must be zero.