Conservation of Energy
The conservation of energy law follows from the ?rst law of thermodynamics for a moving system
(3.2.12)
where is the rate at which heat is added to the system, the rate at which the system works on
its surroundings, and e is the total energy per unit mass. For a particle of mass dm the contributions to
the speci?c energy e are the internal energy u, the kinetic energy V2/2, and the potential energy, which
in the case of gravity, the only body force we shall consider, is gz, where z is the vertical displacement
opposite to the direction of gravity. (We assume no energy transfer owing to chemical reaction as well
Differential Relations for Fluid Motion
In the previous section the conservation laws were derived in integral form. These forms are useful in
calculating, generally using a control volume analysis, gross features of a ?ow. Such analyses usually
require some a priori knowledge or assumptions about the ?ow. In any case, an approach based on
integral conservation laws cannot be used to determine the point-by-point variation of the dependent
variables, such as velocity, pressure, temperature, etc. To do this requires the use of the differential forms
of the conservation laws, which are presented below.
Mass Conservation–Continuity Equation
Applying Gauss?s theorem (the divergence theorem) to Equation (3.2.3) we obtain
المادة المعروضة اعلاه هي مدخل الى المحاضرة المرفوعة بواسطة استاذ(ة) المادة . وقد تبدو لك غير متكاملة . حيث يضع استاذ المادة في بعض الاحيان فقط الجزء الاول من المحاضرة من اجل الاطلاع على ما ستقوم بتحميله لاحقا . في نظام التعليم الالكتروني نوفر هذه الخدمة لكي نبقيك على اطلاع حول محتوى الملف الذي ستقوم بتحميله .
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