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Research Papers: Fundamental Issues and Canonical Flows

# Experimental Investigation Into the Relationship Between the Roughness Height in Use With Nikuradse or Colebrook Roughness Functions and the Internal Wall Roughness Profile for Commercial Steel Pipes

[+] Author and Article Information
K. K. Botros

Fluid Dynamics Department,
Centre for Applied Research,
NOVA Chemicals,
2928-16 Street NE,
e-mail: kamal.botros@novachem.com

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received October 24, 2015; final manuscript received January 18, 2016; published online April 22, 2016. Assoc. Editor: Mark F. Tachie.

J. Fluids Eng 138(8), 081202 (Apr 22, 2016) (8 pages) Paper No: FE-15-1763; doi: 10.1115/1.4032601 History: Received October 24, 2015; Revised January 18, 2016

## Abstract

The relationships between the sand grain roughness height (ks) in use with Nikuradse or Colebrook correlations for the roughness function (RF) and the internal pipe wall roughness element described by the root-mean-square (RMS) of the roughness profile (Rq) for turbulent flow in pipes are experimentally examined. Flow tests were conducted on a total of 13 commercial steel pipes of two sizes: 168.3 mm and 114.3 mm outer diameter (OD). The aim was to provide further insight into relationship between ks and Rq, for use with either RF correlations. The tests were conducted on high-pressure pipeline quality natural gas in the range of Reynolds number (based on pipe internal diameter) of 9 × 106–16 × 106. For commercial carbon steel pipes, the relationship between ks and Rq was found in the form $ks=1.306 Rq+0.078 Rq2$ and $ks=2.294 Rq$ (both ks and Rq in μm), for use with Colebrook and Nikuradse RF correlations, respectively. These correlations cover a wide range of Rq from 2.7 μm to 12.5 μm which is typically found in commercial carbon steel pipes. For stainless steel (SS) pipes, preliminary results indicate that other surface roughness profile parameters need to be employed to better define the values of ks for these types of commercial steel pipes.

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## References

Colebrook, C. F. , 1939, “ Turbulent Flow in Pipes, With Particular Reference to the Transitional Region Between Smooth and Rough Wall Laws,” J. Inst. Civ. Eng., 3, pp. 133–156.
Langelandsvik, L. I. , Kunkel, J. K. , and Smits, A. J. , 2008, “ Flow in a Commercial Steel Pipe,” J. Fluid Mech., 595, pp. 323–339.
ASME B46.1, 2009, “ Surface Texture, Surface Roughness, Waviness, and Lay,” American National Standard, ASME, New York.
ISO 4287, 1997, “ Geometrical Product Specifications—Surface Texture: Profile Method—Terms, Definitions and Surface Texture Parameters,” Standard by International Organization for Standardization, Geneva, Switzerland.
Shockling, M. A. , Allen, J. J. , and Smits, A. J. , 2006, “ Roughness Effects in Turbulent Pipe Flow,” J. Fluid Mech., 564, pp. 267–285.
McKeon, B. J. , Zagarola, M. V. , and Smits, A. J. , 2005, “ A New Friction Factor Relationship for Fully Developed Pipe Flow,” J. Fluid Mech., 538, pp. 429–443.
McKeon, B. J. , Swanson, C. J. , Zagarola, M. V. , Donnelly, R. J. , and Smits, A. J. , 2004, “ Friction Factors for Smooth Pipe Flow,” J. Fluid Mech., 511, pp. 41–44.
Bradshaw, P. , 2000, “ A Note on Critical Roughness Height and Transitional Roughness,” Phys. Fluids, 12(6), pp. 1611–1614.
Kunkel, G. J. , Allen, J. J. , and Smits, A. J. , 2007, “ Further Support for Townsend's Reynolds Number Similarity Hypothesis in High Reynolds Number Rough-Wall Pipe Flow,” Phys. Fluids, 19(5), p. 055109.
Nikuradse, J. , 1933, Laws of Flow in Rough Pipes, VDI Forschungsheft, p. 361 [NACA TM 1292, November 1950].
Hama, F. R. , 1954, “ Boundary-Layer Characteristics for Smooth and Rough Surfaces,” Trans. Soc. Naval Archit. Mar. Eng., 62, pp. 333–358.
McKeon, B. J. , Li, J. , Jiang, W. , Morrison, J. F. , and Smits, A. J. , 2004, “ Further Observations on the Mean Velocity Distribution in Fully Developed Pipe Flow,” J. Fluid Mech., 501, pp. 135–147.
Colebrook, C. F. , and White, C. M. , 1937, “ Experiments With Fluid Friction in Roughened Pipes,” Proc. R. Soc. London A, 161(906), pp. 367–378.
Afzal, N. , 2007, “ Friction Factor Directly From Transitional Roughness in a Turbulent Pipe Flow,” ASME J. Fluids Eng., 129(10), pp. 1255–1267.
Granville, P. S. , 1987, “ Three Indirect Methods for the Drag Characteristics of Arbitrary Rough Surfaces on Flat Plate,” J. Ship Res., 31(1), pp. 70–77.
Zagarola, M. V. , and Smits, A. J. , 1998, “ Mean-Flow Scaling of Turbulent Pipe Flow,” J. Fluid Mech., 373, pp. 33–79.
Perry, A. E. , and Abell, C. J. , 1977, “ Asymptotic Similarity of Turbulence Structures in Smooth and Rough Walled Pipes,” J. Fluid Mech., 79(04), pp. 785–799.
Ligrani, P. M. , and Moffat, R. J. , 1986, “ Structure of Transitionally Rough and Fully Rough Turbulent Boundary Layers,” J. Fluid Mech., 162, pp. 69–98.
Moody, L. F. , 1944, “ Friction Factors for Pipe Flow,” Trans. ASME, 66, pp. 671–684.
Karnik, U. , Bowles, E. , and Sloet, G. , 2000, “ Maintaining Facility Measurement Integrity: Efforts in Canada, USA and The Netherlands,” ASME Paper No. FEDSM2000-11105.
Karnik, U. , Studzinski, W. , Geerligs, J. , and Kowch, R. , 1999, “ Scale Up of the NOVA Flow Conditioner,” Fourth International Symposium on Fluid Flow Measurement, Denver, CO.
Karnik, U. , 1995, “ A Compact Orifice Meter/Flow Conditioner Package,” Third International Symposium on Fluid Flow Measurement, San Antonio, TX, Mar. 20–22.
Schultz, M. P. , and Flack, K. A. , 2007, “ The Rough-Wall Turbulent Boundary Layer From the Hydraulically Smooth to the Fully Rough Regime,” J. Fluid Mech., 580, pp. 381–405.
Flack, K. A. , Schultz, M. P. , and Rose, W. B. , 2012, “ The Onset of Roughness Effects in the Transitionally Rough Regime,” Int. J. Heat Fluid Flow, 35, pp. 160–167.
Flack, K. A. , and Schultz, M. P. , 2010, “ Review of Hydraulic Roughness Scales in the Fully Rough Regime,” ASME J. Fluids Eng., 132(4), p. 041203.
Duan, Z. , Yovanovich, M. M. , and Muzychka, Y. S. , 2012, “ Pressure Drop for Fully Developed Turbulent Flow in Circular and Noncircular Ducts,” ASME J. Fluids Eng., 134(6), p. 061201.

## Figures

Fig. 1

Nikuradse and Colebrook RFs versus roughness Reynolds number (ks+)

Fig. 2

Schematic of the test setup for the 114.3 mm OD pipes (top) and the 168.3 mm OD pipes (bottom). The test section is the part between the two indicated differential pressure measurement ports shown with two circles and marked A (upstream) and B (downstream). All dimensions are in millimeter.

Fig. 3

Measured roughness parameters of the 13 pipes tested in the present work—error bars represent ±95% confidence intervals

Fig. 4

Plot of friction factor versus Re for the example pipe #1 test data

Fig. 5

Experimental results of the RF, ΔU+, superimposed on Colebrook and Nikuradse RF (labels indicate pipe #)

Fig. 6

Results of the measured friction factor (λ) and corresponding Colebrook curves passing through each data point of the 13 tested pipes

Fig. 7

Results of the experimentally extracted Colebrook equivalent sand grain roughness (ks) versus surface roughness characteristics parameter (Rq), based on the present test data on the 11 commercial steel pipes, and comparison with Langelandsvik et al. [2] and Shockling et al. [5] data points

Fig. 8

Results of the experimentally extracted Nikuradse equivalent sand grain roughness (ks) versus surface roughness characteristics parameter (Rq) based on the present test data on 11 commercial steel pipes

Fig. 9

Results of the experimentally extracted Colebrook equivalent sand grain roughness (ks) versus surface roughness characteristics parameter (Rq), based on the present test data on the two SS pipes #6 and #13

Fig. 10

Comparison between the roughness elements of pipe #6 (SS) to pipe #11 (carbon steel); both have the same Rq but pipe #6 has much lower RSm than pipe #11

## Errata

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