This article describes the reproduction and extended analysis of Reynolds’ color-band experiment. Reynolds found two critical Reynolds numbers (Rc) in pipe flows: Rc1 of 12,830 from laminar to turbulent flow and Rc2 of 2030 from turbulent to laminar flow. Since no clear relationship has been established between them, we studied how the entrance shape affects Rc. Thus, for the first time, a hysteresis graph can be drawn by connecting the two curves of Rc1 and Rc2 such that the two Rc values lie on separate branches of the hysteresis plot.

1.
Kerswell
,
R. R.
, 2005, “
Recent Progress in Understanding the Transition to Turbulence in a Pipe
,”
Nonlinearity
0951-7715,
18
, pp.
R17
R44
.
2.
Eckhardt
,
B.
,
Schneider
,
T. M.
,
Hof
,
B.
, and
Westerweel
,
J.
, 2007, “
Turbulence Transition in Pipe Flow
,”
Annu. Rev. Fluid Mech.
0066-4189,
39
, pp.
447
468
.
3.
Reynolds
,
O.
, 1883, “
An Experimental Investigation of the Circumstances Which Determine Whether the Motion of Water Shall be Direct or Sinuous, and of the Law of Resistance in Parallel Channels
,”
Philos. Trans. R. Soc. London
0370-2316,
174
, pp.
935
982
.
4.
White
,
F. M.
, 1991,
Viscous Fluid Flow
,
2nd ed.
,
McGraw-Hill
,
New York
, pp.
369
370
.
5.
Drazin
,
P. G.
, 2002,
Introduction to Hydrodynamic Stability
,
Cambridge University Press
,
Cambridge, England
, p.
5
.
6.
Eliahou
,
S.
,
Tumin
,
A.
, and
Wygnanski
,
A.
, 1998, “
Laminar-Turbulent Transition in Poiseuille Pipe Flow Subjected to Periodic Perturbation Emanating From the Wall
,”
J. Fluid Mech.
0022-1120,
361
, pp.
333
349
.
7.
Chen
,
R.-Y.
, 1973, “
Flow in the Entrance Region at Low Reynolds Numbers
,”
ASME J. Fluids Eng.
0098-2202,
95
, pp.
153
158
.
8.
Lamb
,
H.
, 1975,
Hydrodynamics
,
6th ed.
,
Cambridge University Press
,
London
, p.
664
.
9.
Ekman
,
V. W.
, 1910, “
On the Change From Steady to Turbulent Motion of Liquids
,”
Ark. Mat., Astron. Fys.
0365-4133,
6
(
12
), pp.
1
16
.
10.
Van Dyke
,
M.
, 1982,
An Album of Fluid Motion
,
Parabolic
,
Stanford
, p.
61
.
11.
Darbyshire
,
A. G.
, and
Mullin
,
T.
, 1995, “
Transition to Turbulence in Constant-Mass-Flux Pipe Flow
,”
J. Fluid Mech.
0022-1120,
289
, pp.
83
114
.
12.
Prandtl
,
L.
, and
Tietjens
,
O. G.
, 1957,
Applied Hydro- and Aeromechanics
,
Dover
,
New York
, p.
35
.
13.
ASHRAE Handbook Committee
, 1997,
ASHRAE Handbook of Fundamentals
,
ASHRAE
,
Atlanta
, p.
32.32
.
14.
Granger
,
R. A.
, 1995,
Fluid Mechanics
,
Dover
,
New York
, pp.
484
and
511
512
.
15.
White
,
F. M.
, 1999,
Fluid Mechanics
,
4th ed.
,
McGraw-Hill
,
New York
, p.
372
.
16.
Barnes
,
H. T.
, and
Coker
,
E. G.
, 1904, “
The Flow of Water Through Pipes: Experiments on Stream-Line Motion and the Measurement of Critical Velocity
,”
Proc. R. Soc. London, Ser. A
0950-1207,
74
, pp.
341
356
.
17.
Stanton
,
T. E.
, and
Pannell
,
J. R.
, 1914, “
Similarity of Motion in Relation to the Surface Friction of Fluids
,”
Philos. Trans. R. Soc. London, Ser. A
0962-8428,
214
, pp.
199
224
.
18.
Binnie
,
A. M.
, 1945, “
A Double-Refraction Method of Detecting Turbulence in Liquids
,”
Proc. Phys. Soc. London
0370-1328,
57
, pp.
390
402
.
19.
Senecal
,
V. E.
, and
Rothfus
,
R. R.
, 1953, “
Transition Flow of Fluids in Smooth Tubes
,”
Chem. Eng. Prog.
0360-7275,
49
(
10
), pp.
533
538
.
20.
Kanda
,
H.
, and
Oshima
,
K.
, 1987, “
Numerical Study of the Entrance Flow and Its Transition in a Circular Pipe (2)
,”
Proceedings of the Symposium on the Mechanics for Space Flight 1986
, Report No. SP5,
Instiution of Space and Astronautical Science
,
Tokyo
, pp.
47
76
.
21.
Tanekoda
,
S.
, 1988,
Fluid Dynamics by Learning From Flow Images
,
Asakura
,
Tokyo
, p.
165
, in Japanese.
22.
Fox
,
R. W.
, and
McDonald
,
A. T.
, 1994,
Introduction to Fluid Mechanics
,
Wiley
,
New York
, pp.
336
337
.
23.
Kanda
,
H.
, and
Yanagiya
,
T.
, 2005, “
Experimental Conditions for Minimum Critical Reynolds Number in Pipe Flow
,”
Proceedings of the ASME International Mechanical Engineering Congress and Exposition
,
Orlando
, Paper No. IMECE2005-80637.
24.
Leite
,
R. J.
, 1959, “
An Experimental Investigation of the Stability of Poiseuille Flow
,”
J. Fluid Mech.
0022-1120,
5
, pp.
81
96
.
25.
Rubin
,
Y.
,
Wygnanski
,
I. J.
, and
Haritonidis
,
J. H.
, 1979, “
Further Observations on Transition in a Pipe
,”
Proceedings of the IUTAM Symposium on Laminar-Turbulent Transition
,
Stuttgart
, pp.
17
26
.
26.
Reshotko
,
E.
, 1958, “
Experimental Study of the Stability of Pipe Flow. I. Establishment of an Axially Symmetric Poiseuille Flow
,” Jet Propulsion Laboratory, Pasadena, Progress Report No. 20-364.
27.
Kanda
,
H.
, “
Calculation of Minimum Critical Reynolds Number in Pipe Flows
,”
Proceedings of the 21th CFD Symposium
, JSFM, Paper No. D3-2.
You do not currently have access to this content.