# Paul Richard Heinrich Blasius

Paul Richard Heinrich Blasius
Born 9 August 1883
Berlin, Brandenburg, Prussia, Imperial Germany
Died 24 April 1970 (aged 86)
Hamburg, West Germany
Citizenship German
Nationality German
Fields Fluid mechanics and mechanical engineering
Alma mater University of Göttingen
Thesis Boundary layers in liquids with low friction (1907)
Known for Blasius boundary layer
Blasius theorem

Paul Richard Heinrich Blasius (9 August 1883 – 24 April 1970) was a German fluid dynamics physicist.

He was one of the first students of Prandtl who provided a mathematical basis for boundary-layer drag but also showed as early as 1911 that the resistance to flow through smooth pipes could be expressed in terms of the Reynolds number for both laminar and turbulent flow. After six years in science he changed to Ingenieurschule Hamburg (today: University of Applied Sciences Hamburg) and became a Professor. On 1 April 1962 Heinrich Blasius celebrated his 50th anniversary and was active in teaching until he died on 24 April 1970.

One of his most notable contributions involves a description of the steady two-dimensional boundary-layer that forms on a semi-infinite plate that is held parallel to a constant unidirectional flow ${\displaystyle U}$.

## Blasius' theorem

For a steady fluid flow with complex potential ${\displaystyle w(z)}$ around a fixed body enclosed by a contour ${\displaystyle C}$, the net force on the body due to fluid motion is given by [1]

${\displaystyle F_{x}-\mathrm {i} F_{y}={\frac {\mathrm {i} \rho }{2}}\oint _{C}\left({\frac {\mathrm {d} w}{\mathrm {d} z}}\right)^{2}\,\mathrm {d} z}$

where ${\displaystyle \rho }$ is the constant fluid density. This is a contour integral which may be computed by using Cauchy's residue theorem.

## Correlations

First law of Blasius for turbulent Fanning friction factor:

${\displaystyle f/2=0.039Re^{-0.25}\,}$

Second law of Blasius for turbulent Fanning friction factor:

${\displaystyle f/2=0.023Re^{-0.22}\,}$

Law of Blasius for friction coefficient in turbulent pipe flow:

${\displaystyle \lambda =0.3164Re^{-0.25}\,}$

## Notes

1. ^ Acheson, D.J., "Elementary Fluid Dynamics", Chapter 4

## References

• Hager, W.H., "Blasius: A life in research and education," Experiments in Fluids, 34: 566–571 (2003)
• Blasius, H., "Das Aehnlichkeitsgesetz bei Reibungsvorgängen in Flüssigkeiten", Mitteilungen über Forschungsarbeiten auf dem Gebiete des Ingenieurwesens, vol.134, VDI-Verlag Berlin (1913)