A general equation for the velocity distribution in steady, incompressible, two-dimensional, turbulent flow is constructed by correction of the logarithmic velocity profile for the independent effects of pressure gradients and of surface roughness. Predicted characteristics of pipe flows, flat plate flows, and diffusing flows over smooth surfaces are found to be in good agreement with empirical data at high Reynolds numbers. Pipe flow data are used to evaluate surface roughness effects, and hence to describe flat plate flows and diffusing flows over rough surfaces.
Get full access to this article
View all access options for this article.
References
1.
MellorG. L.‘The effects of pressure gradients on turbulent flow near smooth wall’, J. Fluid Mech.196624, (Pt 2), 255.
2.
SpaldingD. B.PatankarS. V.Heat and mass transfer in boundary layers1967 (Morgan-Grampian, London).
3.
MillikanC. B.‘A critical discussion of the turbulent flows in channels and circular tubes’, Proc. 5th Int. Congr. Appl. Mech., Cambridge, Mass. 1938, 386.
4.
HinzeJ. O.Turbulence1959 (McGraw-Hill, New York).
5.
ColesD.‘The law of the wake in the turbulent boundary layer’, J. Fluid Mech.19561, 191.
6.
SpaldingD. B.‘A unified theory of friction, heat transfer, and mass transfer in the turbulent boundary layer and wall jet’, A.R.C. C.P.829, 1965.
NikuradseJ.‘Strömungsgesetze in rauhen Rohren’, VDI ForschHft No. 361, 1933; ‘Laws of flow in rough pipes’, Tech. Mem. nat. adv. Comm. Aero., Wash. No. 1292, 1950.
10.
SchlichtingH. (translated by KestinJ.). Boundary layer theory, fourth edition1960 (McGraw-Hill, New York).
11.
ClauserF. H.‘Turbulent boundary layers in adverse pressure gradients’, J. aero. Sci.195421, (No. 2), 91.
12.
LauferJ.‘The structure of turbulence in fully developed pipe flow’, Tech. Rep. nat. adv. Comm. Aero., Wash. No. 1174, 1954.
13.
LauferJ.‘Investigation of turbulent flow in a two-dimensional channel’, Tech. Rep. nat. adv. Comm. Aero., Wash. No. 1033, 1951.
14.
PrandtlL.‘Zur turbulenten Strömung in Rohren und längs Platten’, Rep. Aerod. Versuchsanst, Göttingen1932 (4th series).
15.
HamaF. R.Trans. Soc. nav. Archit. mar. Engrs, N. Y.195462, 333 (cited by J. O. Hinze, reference (4)).
16.
PrestonJ. H.‘The minimum Reynolds number for a turbulent boundary layer and the selection of a transition device’, J. Fluid Mech.19583, (Pt 4), 373.
17.
BradshawP.FerrissD. H.AtwellN. P.‘Calculation of boundary layer development using the turbulent energy equation’, J. Fluid Mech.196728, (Pt 3), 593.
18.
SchubauerG. B.KlebanoffP. S.‘Investigation of separation of the turbulent boundary layer’, Tech. Note nat. adv. Comm. Aero., Wash. No. 2133, 1950.
19.
NewmanB. G.‘Some contributions to the study of the turbulent boundary layer’, Aust. Dept Supply Rep. No. AOA-53, 1951.
20.
HeadM. R.‘Entrainment in the turbulent boundary layer’, Rep. mem. A.R.C. No. 3152, 1960.
21.
WieghardtK.TillmannW.‘Zur turbulenten Reibungsschicht bei Druckanstieg’, UM 6617 (cited by H. Schlichting, reference (10)).
22.
NicollW. B.EscudierM. P.‘Empirical relationships between the shape factors H32 and H12 for uniform density turbulent boundary layers and wall jets’, AIAA Journal19664 (No. 5).
23.
LudwiegH.TillmannW.‘Investigations of the wall shearing stress in turbulent boundary layers’, Tech. Mem. nat. adv. Comm. Aero., Wash. No. 1285, 1950.
24.
StratfordB. S.‘The prediction of separation of the turbulent boundary layer’, J. Fluid Mech.19595, (Pt 1), 1.
25.
StratfordB. S.‘An experimental flow with zero skin friction throughout its region of pressure rise’, J. Fluid Mech.19595, (Pt 1), 17.
26.
TownsendA. A.‘The development of turbulent boundary layers with negligible wall stress’, J. Fluid Mech.19608, (Pt 1), 143.
27.
LockwoodF. C.‘Equilibrium–turbulent boundary layer prediction for a proposed Prandtl mixing length distribution’, Jl. mech. Engng Sci.196810, (No. 5), 426.
28.
BradshawP.GaleaP. V.‘Step-induced separation of a turbulent boundary layer in incompressible flow’, J. Fluid Mech.196727, (Pt 1), 111.
