Abstract
The knowledge about the characteristics of fluids at rest is referred to as fluid statics, or alternatively as hydrostatics, which is derived from the fact that the disciplines are used frequently for water at rest. The pressure of a still fluid in the gravitational field experiences a spatial variation, and the pressure distribution over the surface of a solid body with finite volume results in a net force acting on the body. This net force is termed differently as the hydrostatic or buoyant force in different circumstances, which are discussed in separate sections of this chapter. Specifically, the pressure distribution in a still fluid is discussed, followed by the estimations on the hydrostatic forces on a plane and a curved surface. Formation of the free surface of a still fluid with relations to the surface tension and capillary effect is presented. Buoyancy and stability analysis of a floating and submerged bodies in a still fluid are introduced by using the relative positions between the centers of gravity and buoyancy. Last, due to the same Cauchy stress state as that of a still fluid, the pressure variation of a fluid in rigid body motion is discussed.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsNotes
- 1.
The gravitational acceleration g is considered a constant.
- 2.
The value of m is \(9.8\,^\circ \hbox {C/km}\) for completely dry air. It takes the value of \(6.5\,^\circ \hbox {C/km}\) if the water vapor in the air does not condense to liquid water during ascending, while the value of \(m=5.5\,^\circ \hbox {C/km}\) is used when condensation takes place.
- 3.
Although air is a gas mixture consisting of nearly 78% nitrogen, nearly 21% oxygen and less than 1% minor gases and water vapor, it is a simple compressible substance in the macroscopic point of view.
- 4.
The calculation is conducted by that the density of seawater is 1000 \(\hbox {kg/m}^3\), \(g=9.8\) \(\hbox {m/s}^2\), \(m=9.8\,^\circ \hbox {C/km}\), \(T_0=25\,^\circ \hbox {C}\), and \(R=0.287\) kJ/kg-K.
- 5.
Data quoted from: The U.S. Standard Atmosphere (1976), Washington, D.C., U.S. Government Printing Office, 1976.
- 6.
However, an equilibrium state cannot be maintained if \((\mathcal {C}_{23}-\mathcal {C}_{13})\gg \mathcal {C}_{12}\), in which fluid 1 coats the whole wall, e.g. petrol in metal containers.
- 7.
The analysis is termed jump conditions in continuum mechanics.
- 8.
Archimedes of Syracuse, c. 287–212 BC., a Greek polymath, who is regarded as one of the leading scientists in classical antiquity. The original statement of Archimedes’ principle reads: “A body in a fluid experiences an apparent reduction in weight equal to the weight of the displaced fluid.”
Further Reading
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)
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)
B.R. Munson, D.F. Young, T.H. Okiishi, Fundamentals of Fluid Mechanics, 3rd edn. (Wiley, New York, 1990)
P. Oswald, Rheophysics: The Deformation and Flow of Matter (Cambridge University Press, Cambridge, 2009)
R.H.F. Pao, Fluid Mechanics (Wiley, New York, 1961)
L. Prandtl, O.G. Tietjens, Fundamentals of Hydro- and Aeromechanics (Dover, New York, 1934)
L. Prandtl, O.G. Tietjens, Applied Hydro- and Aeromechanics (Dover, New York, 1934)
A.J. Smith, A Physical Introduction to Fluid Mechanics (Wiley, New York, 2000)
J. Spurk, Fluid Mechanics (Springer, Berlin, 1997)
C.S. Yih, Fluid Mechanics: A Concise Introduction to The Theory (McGraw-Hill, New York, 1969)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2019 Springer International Publishing AG
About this chapter
Cite this chapter
Fang, C. (2019). Hydrostatics. 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_3
Download citation
DOI: https://doi.org/10.1007/978-3-319-91821-1_3
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-91820-4
Online ISBN: 978-3-319-91821-1
eBook Packages: Earth and Environmental ScienceEarth and Environmental Science (R0)