Abstract
The topics which may be deduced about the nature of a flowing fluid without referring to the dynamics of continuum are explored in this chapter. First, the flow lines embracing streamlines, pathlines, and streaklines are discussed. These flow lines are not only useful for flow visualization, but also supply means by which solutions to governing equations of flow problems may be interpreted physically. Second, the concepts of circulation and vorticity are introduced, with their full usefulness becoming apparent in discussing the balance equations of fluid motion. Streamline and vorticity lead to the concepts of stream tube and stream filament, and vortex tube and vortex filament, respectively. Discussions on the kinematics of stream and vortex filaments are provided at the end, which consists part of the Helmholtz equations. The other part, i.e., the dynamics of vorticity, will be discussed in Sect. 8.1.
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Notes
- 1.
The velocity vector is locally tangent to the contour.
- 2.
The present analysis forms part of the Helmholtz theorems of vorticity . Hermann Ludwig Ferdinand von Helmholtz, 1821–1894, a German physicist, with contributions to several scientific fields. The largest German association of research institutions, the Helmholtz Association, is named after him.
Further Reading
R.S. Brodkey, The Phenomena of Fluid Motions (Dover, New York, 1967)
Y.A. Cengel, J.M. Cimbala, Fluid Mechanics: Fundamentals and Applications, 3rd edn. (McGraw-Hill, New York, 2014)
S. Chandrasekhar, Hydrodynamic and Hydromagnetic Stability (Dover, New York, 1961)
I.G. Currie, Fundamental Mechanics of Fluids, 2nd edn. (McGraw-Hill, Singapore, 1993)
D.F. Elger, B.C. Williams, C.T. Crowe, J.A. Roberson, Engineering Fluid Mechanics, 10th edn. (Wiley, Singapore, 2014)
R.W. Fox, P.J. Pritchard, A.T. McDonald, Introduction to Fluid Mechanics, 7th edn. (Wiley, New York, 2009)
K. Hutter, Y. Wang, Fluid and Thermodynamics. Volume 1: Basic Fluid Mechanics (Springer, Berlin, 2016)
H. Lamb, Hydrodynamics, 6th edn. (Dover, New York, 1945)
B.R. Munson, D.F. Young, T.H. Okiishi, Fundamentals of Fluid Mechanics, 3rd edn. (Wiley, New York, 1990)
R.H.F. Pao, Fluid Mechanics (Wiley, New York, 1961)
A.J. Smith, A Physical Introduction to Fluid Mechanics (Wiley, New York, 2000)
C.S. Yih, Fluid Mechanics: A Concise Introduction to the Theory (McGraw-Hill, New York, 1969)
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Fang, C. (2019). Flow Kinematics. In: An Introduction to Fluid Mechanics. Springer Textbooks in Earth Sciences, Geography and Environment. Springer, Cham. https://doi.org/10.1007/978-3-319-91821-1_4
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DOI: https://doi.org/10.1007/978-3-319-91821-1_4
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