Abstract
The hydrodynamic principles that deal with the mechanics of fluid flow and the derivations are based on three conservation principles: Mass, momentum and energy. In this chapter, these are initially discussed from the viewpoint of classical hydrodynamics and then with reference to their application in open channel flow. The continuity equation ensures the conservation of mass. The specific force equation is based on the momentum principle and calls for force balance. The specific energy equation is based on the energy principle and calls for energy balance. These important principles related to open channel flow are discussed and applications are explained. The additional features of this chapter are the introduction to the boundary layer theory, flow in a curved channel, hydrodynamic drag and lift on a particle and Stokes law.
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- 1.
Convective acceleration is the acceleration of fluid due to space at a given time, while the local acceleration is the acceleration of fluid due to time at a given spatial location.
- 2.
Alternatively, a downward slope is steep if it exceeds the critical slope S c (that is the slope at which the normal depth of flow is critical depth). Hence, S 0 > S c. Similarly, mild slope can be explained.
- 3.
The mass flux through BC can be obtained as ρ(\( u\hat{i} + w\hat{k}\))·(−d\( \delta\hat{i} \) + d\( x\hat{k} \)) = ρ(−udδ + wdx).
- 4.
Hydraulic jump occurs when there is a rapid change in flow depth resulting from a low stage (supercritical) to a high stage (subcritical) with an abrupt rise in free surface elevation. It is therefore a local phenomenon due to a transition from a supercritical flow to a subcritical flow.
References
Bélanger JB (1828) Essai sur la solution numérique de quelques problèmes relatifs au mouvement permanent des eaux courantes. Carilian-Goeury, Paris
Blasius H (1912) Das aehnlichkeitsgesetz bei reibungsvorgangen. Zeitschrift des Vereines Deutscher Ingenieure 56:639–643
Blasius H (1913) Das aehnlichkeitsgesetz bei reibungsvorgängen in flüssigkeiten. Mitteilungen über Forschungsarbeiten auf dem Gebiete des Ingenieurwesens 131:1–41
Chaudhry MH (2008) Open-channel flow. Springer, New York
Chow VT (1959) Open channel hydraulics. McGraw-Hill Book Company, New York
de Saint-Venant B (1871) Theorie du mouvement non permanent des eaux, avec application aux crues de rivieras et a l’introduction des marces dans leur lit. Comptes Rendus de l’Academic des Sciences, vol 73, Paris, pp 147–154, 237–240
Dey S (2000) Chebyshev solution as aid in computing GVF by standard step method. J Irrig Drainage Eng 126(4):271–274
Jaeger C (1957) Engineering fluid mechanics. Saint Martin’s Press, New York
Jansen P, van Bendegom L, van den Berg J, de Vries M, Zanen A (1979) Principles of river engineering. Pitman, London
Kikkawa H, Ikeda S, Kitagawa A (1976) Flow and bed topography in curved open channels. J Hydraul Div 102(9):1327–1342
Odgaard AJ (1989) River-meander model. I: development. J Hydraul Eng 115(11):1433–1450
Prandtl L (1904) Über flüssigkeitsbewegung bei sehr kleiner reibung. Verhandlungen des III. Internationalen Mathematiker Kongress, Heidelberg, pp 484–491
Rozovskii IL (1957) Flow of water in bends in open channels. Academy of Sciences of the Ukrainian Soviet Socialist Republic, Kiev
Rubinow SI, Keller JB (1961) The transverse force on a spinning sphere moving in a viscous fluid. J Fluid Mech 11:447–459
Saffman PG (1965) The lift on a small sphere in a slow shear flow. J Fluid Mech 22:385–400
Saffman PG (1968) Corrigendum, the lift on a small sphere in a slow shear flow. J Fluid Mech 31:624
Stokes GG (1851) On the effect of the internal friction of fluids on the motion of pendulums. Trans Cambridge Philos Soc 9:80–85
Streeter VL (1948) Fluid dynamics. McGraw-Hill Book Company, New York
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Dey, S. (2014). Hydrodynamic Principles. In: Fluvial Hydrodynamics. GeoPlanet: Earth and Planetary Sciences. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-19062-9_2
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