We study both experimentally and theoretically the classical problem of the circular hydraulic jump. By means of elementary hydrodynamics we investigate the scaling laws governing the position of the hydraulic jump and compare our predictions with experimental data. The results of our simple model are in good agreement with the experiments and with more elaborate approaches. The problem can be effectively used for educational purposes, being appropriate both for experimental investigations and for theoretical application of many fluid mechanics concepts.
REFERENCES
1.
D. J. Acheson, “Hydraulic jumps and shock waves,” in Elementary Fluid Dynamics (Oxford, U.P., New York, 1990), pp. 100–104.
2.
S. Whitaker, “Hydraulic jump,” in Introduction to Fluid Mechanics (Prentice–Hall, Englewood Cliffs, NJ, 1968), pp. 382–385.
3.
Lord
Rayleigh
, “On the theory of long waves and bores
,” Proc. R. Soc. London, Ser. A
90
, 324
–328
(1914
).4.
R. G.
Olsson
and E. T.
Turkdogan
, “Radial spread of a liquid stream on a horizontal plate
,” Nature (London)
211
(5051), 831
–816
(1966
).5.
S.
Ishigai
, S.
Nakanishi
, M.
Mizuno
, and T.
Imamura
, “Heat transfer of the impinging round water jet in the interference zone of film flow along the wall
,” Bull. JSME
20
(139
), 85
–92
(1977
).6.
A. A. M.
Khalifa
and J. A.
McCorquodale
, “Radial hydraulic jump
,” J. Hydraulics Division, ASCE
105
, No HY9 (Sept. 1979
).7.
A. D. D.
Craik
, R. C.
Latham
, M. J.
Fawkes
, and P. W. F.
Gribbon
, “The circular hydraulic jump
,” J. Fluid Mech.
112
, 347
–362
(1981
).8.
X.
Liu
and J. H. V.
Lienhard
, “The hydraulic jump in circular jet impingement and in other thin liquid films
,” Exp. Fluids
15
(2
), 108
–116
(1993
).9.
B.
Siwon
, “Experimental investigations of the liquid film by a gas-liquid spray jet impinging onto a flat surface
,” Int. Comm. Heat Mass Transfer
20
(5
), 665
–677
(1993
).10.
C.
Ellegaard
, A. E.
Hansen
, A.
Haaning
, and T.
Bohr
, “Experimental results on flow separation and transitions in the Circular Hydraulic Jump
,” Phys. Scr.
T67
, 105
–110
(1996
).11.
C.
Ellegaard
, A. E.
Hansen
, A.
Haaning
, T.
Bohr
, J. L.
Hansen
, and S.
Watanabe
, “Creating corners in kitchen sinks
,” Nature (London)
392
(6678
), 767
–768
(1998
).12.
T.
Bohr
, C.
Ellegaard
, A. E.
Hansen
, and A.
Haaning
, “Hydraulic jumps, flow separation and wave breaking: An experimental study
,” Physica B
228
, 1
–10
(1996
).13.
S. H.
Hansen
, S.
Horlück
, D.
Zauner
, P.
Dimon
, C.
Ellegaard
, and S. C.
Creagh
, “Geometric orbits of surface waves from a circular hydraulic jump
,” Phys. Rev. E
55
(6
), 7048
–7061
(1997
).14.
M. Kurihara, “Report of the Research Institute for Fluid Engineering, Kyusyu Imperial University,” Vol. 3 (2), 11–33 (1946).
15.
A. A. M.
Khalifa
and J. A.
McCorquodal
, “Simulation of the radial hydraulic jump
,” J. Hydraul. Res.
30
(2
), 149
–163
(1992
).16.
R. I.
Bowles
and F. T.
Smith
, “The standing hydraulic jump: Theory, computations and comparisons with experiments
,” J. Fluid Mech.
242
, 145
–168
(1992
).17.
Yu. A.
Buyevich
and V. A.
Ustinov
, “Hydrodynamic conditions of transfer processes through a radial jet spreading over a flat surface
,” Int. J. Heat Mass Transf.
37
(1
), 165
–173
(1994
).18.
Yu. A.
Buyevich
, V. N.
Mankevich
, and V. A.
Ustinov
, “Spreading flow of an axis-symmetric laminar jet over a horizontal obstacle
,” J. Eng. Phys.
64
(1
), 31
–37
(1993
).19.
T.
Bohr
, P.
Dimon
, and V.
Putkaradze
, “Shallow-water approach to the circular hydraulic jumps
,” J. Fluid Mech.
254
, 635
–648
(1993
).20.
T.
Bohr
, V.
Putkaradze
, and S.
Watanabe
, “Averaging Theory for the Structure of Hydraulic Jumps and Separation in Laminar free-Surface Flows
,” Phys. Rev. Lett.
79
(6
), 1038
–1041
(1997
).21.
F. J.
Higuera
, “The hydraulic jump in a viscous laminar flow
,” J. Fluid Mech.
274
, 69
–92
(1994
).22.
F. J.
Higuera
, “The circular hydraulic jump
,” Phys. Fluids
9
(5
), 1476
–1478
(1997
).23.
I.
Tani
, “Water jump in the boundary layer
,” J. Phys. Soc. Jpn.
4
, 212
–215
(1949
).24.
E. J.
Watson
, “The radial spread of a liquid jet over a horizontal plane
,” J. Fluid Mech.
20
(3
), 481
–499
(1964
).25.
V. E.
Nakaryakov
, B. G.
Pokusaev
, and E. N.
Troyan
, “Impingement of an axisymmetric liquid jet on a barrier
,” Int. J. Heat Mass Transf.
21
(9
), 1175
–1184
(1977
).26.
R. P.
Godwin
, “The hydraulic jump (‘shocks’ and viscous flow in the kitchen sink)
,” Am. J. Phys.
61
(9
), 829
–832
(1993
).27.
B. L.
Blackford
, “The hydraulic jump in radially spreading flow: A new model and new experimental data
,” Am. J. Phys.
64
(2
), 164
–169
(1996
).28.
D. J. Acheson, “Boundary layers,” in Elementary Fluid Dynamics (Oxford U.P., New York, 1990), Chap. 8.
29.
L. D. Landau and E. M. Lifsitz, Fluid Mechanics (Butterworth–Heinemann Ltd., Jordan Hill, Oxford, 1987), 2nd ed., Chap. 2, Sec. 23 (flow in diverging and converging channels), p. 80.
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1999
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