Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-25T20:24:56.313Z Has data issue: false hasContentIssue false
  • English
  • Français

The Determination of Turbulent Skin Friction by Means of Pitot Tubes

Published online by Cambridge University Press:  28 July 2016

J. H. Preston
J. H. Preston*
Affiliation:
Cambridge University Aeronautics Laboratory
Get access Rights & Permissions [Opens in a new window]

Summary

A simple method of determining local turbulent skin friction on a smooth surface has been developed which utilises a round pitot tube resting on the surface. Assuming the existence of a region near the surface in which conditions are functions only of the skin friction, the relevant physical constants of the fluid and a suitable length, a universal non-dimensional relation is obtained for the difference between the total pressure recorded by the tube and the static pressure at the wall, in terms of the skin friction. This relation, on this assumption, is independent of the pressure gradient. The truth and form of the relation were first established, to a considerable degree of accuracy, in a pipe using four geometrically similar round pitot tubes—the diameter being taken as representative length. These four pitot tubes were then used to determine the local skin friction coefficient at three stations on a wind tunnel wall, under varying conditions of pressure gradient. At each station, within the limits of experimental accuracy, the deduced skin friction coefficient was found to be the same for each pitot tube, thus confirming the basic assumption and leaving little doubt as to the correctness of the skin friction so found. Pitot traverses were then made in the pipe and in the boundary layer on the wind tunnel wall. The results were plotted in two non-dimensional forms on the basis already suggested and they fell close together in a region whose outer limit represented the breakdown of the basic assumption, but close to the wall the results spread out, due to the unknown displacement of the effective centre of a pitot tube near a wall. This again provides further evidence of the existence of a region of local dynamical similarity and of the correctness of the skin friction deduced from measurements with round pitot tubes on the wind tunnel wall. The extent of the region in which the local dynamical similarity may be expected to hold appears to vary from about 1/5 to 1/20 of the boundary-layer thickness for conditions remote from, and close to, separation respectively.

Type
Research Article
Information
The Aeronautical Journal , Volume 58 , Issue 518 , February 1954 , pp. 109 - 121
Copyright
Copyright © Royal Aeronautical Society 1954

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Squire, H. B. and Young, A. D. (1937). The Calculation of the, Profile Drag of Aerofoils. R. & M. 1838. November 1937.Google Scholar
2. Kempf, G. (1929). Werft, Reederei, Hafen, 10. 1929.Google Scholar
3. Dhawan, S. (1951). Direct Measurements of Skin Friction. N.A.C.A. T.N. 2567.Google Scholar
4. von Kármán, T. (1934). Turbulence and Skin Friction. Journal of the Aeronautical Sciences, 1. 1934.CrossRefGoogle Scholar
5. Fage, A. and Falkner, V. M. (1930). An Experimental Determination of the Intensity of Friction on the Surface of an Aerofoil. R. & M. 1315. April 1930. Proc. Roy. Soc. A., Vol. 129, p. 378. 1930. (See als. R. & M. 1852, 1938, A. Fage.)Google Scholar
6. Ludwieg, H. (1950). Instrument for Measuring the Wall Shearing Stress of Turbulent Boundary Layers. (Trans.) N.A.C.A. T.M. 1284. 1950.Google Scholar
7. Ludwieg, H. and Tillmann, W. (1950). Investigations of the Wall Shearing Stress in Turbulent Boundary Layers. (Trans.) N.A.C.A. T.M. 1285. 1950.Google Scholar
8. Spence, D. A. (1951). The Growth of Turbulent Boundary Layers. Communicated by P.D.S.R.(A.), Ministry of Supply. A.R.C. 14.162—F.M. 1585. 19th July 1951.Google Scholar
9. Maskell, E. C. (1951). Approximate Calculation of the Turbulent Boundary Layer in Two-dimensional Incompressible Flow. R.A.E. Report No. Aero. 2443. A.R.C. 14,654—F.M. 1664. November 1951.Google Scholar
10. Zaat, J. A. (1951). Revised Methods for Calculation of Laminar and Turbulent Boundary Layers. N.L.L. Report. (Amsterdam.) 1951.Google Scholar
11. Schubauer, G. B. and Klebanoff, P. S. (1950). Investigation of Separation of the Turbulent Boundary Layer. N.A.C.A. T.N. 2133. 1950.Google Scholar
12. Kempf, G. and — Karhan, (1951). Surface Friction of Ships. Jarbuch der Schiffbautecknischen Gesellschaft. 1951.Google Scholar
13. Stephens, A. V. and Haslam, J. A. G. (1938). Flight Experiments on Boundary Layer Transition in Relation to Profile Drag. R. & M. 1800. August 1938.Google Scholar
14. Young, A. D. and Maas, J. N. (1937). The Behaviour of a Pitot Tube in a Transverse Total-pressure Gradient. R. & M. 1770. 1937.Google Scholar
15. Preston, J. H. (1950). The Three-quarter Radius Pitot Tube Flow Meter. The Engineer. 27th October 1950.Google Scholar
16. Spence, D. A. (1953). Cambridge Ph.D. Thesis. 1953. (To be published.. Google Scholar