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The calibration of the Stanton tube as a skin-friction meter

  • L. Trilling
  • R. J. Häkkinen

Summary

The available calibrations of a wide variety of Stanton tubes as wall skinfriction meters in a boundary layer, made between 1920 and 1954, are gathered and presented systematically. A dimensional analysis argument indicates that the tube pressure reading P is related to the skin friction τ w by a law of the form
$$ \frac{{P{\varrho _w}{h^2}}} {{{\mu _{{w^2}}}}} = f\left( {\frac{{{\tau _w}{\varrho _w}{h^2}}} {{{\mu _{{w^2}}}}},\frac{h} {\delta },M} \right) $$
(A)
where ϱ w , μ w are the density and viscosity at the wall, h is a characteristic height of the tube, and δ is the boundary layer thickness.

If \( \frac{{{\tau _w}{\varrho _w}{h^2}}} {{{\mu _{{w^2}}}}} \ll 1\), Taylor’s measurements and Stokes flow theory indicate that P is proportional to τ w .

If \( 10 < \frac{{{\tau _w}{\varrho _w}{h^2}}} {{{\mu _{{w^2}}}}} < {10^3}\) and if h is so small that the Stanton tube is embedded in the linear region of the boundary layer profile (h is of sublayer thickness order), the available data and a boundary layer perturbation theory developed by the authors suggest that P ~ τ w 5/3.

If \( \frac{{{\tau _w}{\varrho _w}{h^2}}} {{{\mu _{{w^2}}}}} > {10^3}\) the tube appears to stick out of the linear profile region and the form of f depends on the particular profile under study.

At supersonic freestream Mach numbers, appreciably higher pressures are observed than at low speeds, for the same values of \( \frac{{{\tau _w}{\varrho _w}{h^2}}} {{{\mu _{{w^2}}}}}\) , although the mechanism of this effect is not yet fully understood.

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References

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Copyright information

© Springer Fachmedien Wiesbaden 1955

Authors and Affiliations

  • L. Trilling
    • 1
  • R. J. Häkkinen
    • 1
  1. 1.Massachusetts Institute of TechnologyCambridgeUSA

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