Law of Conservation Draft for Information Only
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Law of Conservation
Law of Conservation
Based on linear acoustic, assuming the
crosssection area equals to A and no mass is entering or leaving the system due to the acoustic
disturbance, the wave propagation can be represented by following figure: where, at ambient environment and at acoustic disturbance state: and,
where,
properties of acoustic disturbance:
where,
properties at wavefront: Continuity Equation, 1D
For a control volume, from the principle of conservation of mass, the instantaneous rate of change of
mass in a control volume equals to the net mass flux flow into or out
of the control volume, therefore: The relationship between density and velocity is defined Euler's Equation of Inviscid Motion, 1D
For a control volume, from principle of momentum conservation, the
instantaneous rate of change of net momentum of a control
volume equals to the net applied force and the net momentum change due to the
momentum flux flow into or out of the control volume. The applied force in
this case is pressure only and no other forces, no gravity, no viscous force
etc., then: Since both U_{total} , ρ_{total} are a function of time, imply: Therefore, because of conservation of mass, the equation is: As the medium fluid is assumed to be inviscid, the assumption of inviscid flow is valid for sound propagation and the euler's equation of motion can be applied. The additional relationship between pressure and velocity is defined Energy Equation, 1D
For a control volume, from principle of energy conservation, rate of change of
energy equal to rate of heat added and the net rate of energy flow into or out
of the control volume minus the rate of work done. By neglecting heat energy
and external work, and potential energy then: The additional relationship between Enthalpy and velocity is defined. ©sideway ID: 100900019 Last Updated: 17/9/2010 Revision: 1 Ref: References
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