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2015•Oxford University Press eBooksRequires access

Conservation Laws

E. Guyon, Jean‐Pierre Hulin, Luc Petit, Catalin D Mitescu

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Abstract

This chapter deals with the conservation laws for mass, momentum and energy in a moving fluid. Combining the equations of motion and of the conservation of mass for general fluids leads to the equation for the conservation of momentum: applying it to a suitably chosen “control volume” within the fluid” allows one to analyze the exchange of momentum in the flows. The equation of conservation of energy can be written in the form of Bernoulli’s equation and is then applied to a number of classical examples (Pitot tube, Venturi effect, etc.). Finally, a few more complex problems are studied: they illustrate how one can analyze quantitatively a number of flows by means of conservation laws, without requiring a complete determination of the velocity field of the fluid.

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What this paper is about

This chapter deals with the conservation laws for mass, momentum and energy in a moving fluid. Combining the equations of motion and of the conservation of mass for general fluids leads to the equation for the conservation of momentum: applying it to a suitably chosen “control volume” within the fluid” allows one to analyze the exchange of momentum in the flows. The equation of conservation of energy can be written in the form of Bernoulli’s equation and is then applied to a number of classical examples (Pitot tube, Venturi effect, etc.). Finally, a few more complex problems are studied: they illustrate how one can analyze quantitatively a number of flows by means of conservation laws, without requiring a complete determination of the velocity field of the fluid.

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Available abstract

This chapter deals with the conservation laws for mass, momentum and energy in a moving fluid. Combining the equations of motion and of the conservation of mass for general fluids leads to the equation for the conservation of momentum: applying it to a suitably chosen “control volume” within the fluid” allows one to analyze the exchange of momentum in the flows. The equation of conservation of energy can be written in the form of Bernoulli’s equation and is then applied to a number of classical examples (Pitot tube, Venturi effect, etc.). Finally, a few more complex problems are studied: they illustrate how one can analyze quantitatively a number of flows by means of conservation laws, without requiring a complete determination of the velocity field of the fluid.

Key concepts: Conservation law, Conservation of mass, Acoustic theory, Bernoulli's principle, Energy conservation, Venturi effect, Momentum (technical analysis), Classical mechanics

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