English Title

Clarifications into fluid resistance


Leonhard Euler

Enestrom Number


Fuss Index


Original Language


Archive Notes

According to Jacobi, a treatise with this title was read to the Berlin Academy on April 8, 1756. According to St. Petersburg Academy records, it was presented to that Academy on January 13, 1757.

Content Summary

This paper is notable for Euler's remarks on the cavitation that arises from the negative pressure that occurs in incompressible fluids. He shows that "the common rule of resistance rests on the false hypothesis of the analogy to impact solids." Euler also tries to apply hydrodynamics, especially the Bernoulli equation for stream-lines, to the problem of resistance, perhaps uniting the physical discussion of resistance, the stepwise integration method, and an attempt at formulating the general equations of a plane steady flow. He also attempts to characterize the possible stream-line patterns for a perfect incompressible fluid in plane steady flow, not necessarily a potential flow. According to Truesdell, this result remained for many decades the "only non-trivial exact solution of the hydrodynamical equations that could be given a reasonably simple interpretation." (Based on Clifford Truesdell's introduction to Opera Omnia Series II, Volume 12.)

Published as

Journal article

Published Date


Written Date


Original Source Citation

Novi Commentarii academiae scientiarum Petropolitanae, Volume 8, pp. 197-229.

Opera Omnia Citation

Series 2, Volume 12, pp.215-243.

Record Created


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Mathematics Commons