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# Bernoulli’s equation

الكلية كلية الهندسة     القسم  الهندسة البيئية     المرحلة 2
أستاذ المادة نسرين جاسم حسين المنصوري       10/12/2014 09:50:26
his article is about Bernoulli s principle and Bernoulli s equation in fluid dynamics. For Bernoulli s theorem in probability, see law of large numbers. For an unrelated topic in ordinary differential equations, see Bernoulli differential equation.

A flow of air into a venturi meter. The kinetic energy increases at the expense of the fluid pressure, as shown by the difference in height of the two columns of water.
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In fluid dynamics, Bernoulli s principle states that for an inviscid flow of a nonconducting fluid, an increase in the speed of the fluid occurs simultaneously with a decrease in pressure or a decrease in the fluid s potential energy. The principle is named after Daniel Bernoulli who published it in his book Hydrodynamica in 1738.

Bernoulli s principle can be applied to various types of fluid flow, resulting in what is loosely denoted as Bernoulli s equation. In fact, there are different forms of the Bernoulli equation for different types of flow. The simple form of Bernoulli s principle is valid for incompressible flows (e.g. most liquid flows) and also for compressible flows (e.g. gases) moving at low Mach numbers (usually less than 0.3). More advanced forms may in some cases be applied to compressible flows at higher Mach numbers (see the derivations of the Bernoulli equation).

Bernoulli s principle can be derived from the principle of conservation of energy. This states that, in a steady flow, the sum of all forms of energy in a fluid along a streamline is the same at all points on that streamline. This requires that the sum of kinetic energy, potential energy and internal energy remains constant. Thus an increase in the speed of the fluid – implying an increase in both its dynamic pressure and kinetic energy – occurs with a simultaneous decrease in (the sum of) its static pressure, potential energy and internal energy. If the fluid is flowing out of a reservoir, the sum of all forms of energy is the same on all streamlines because in a reservoir the energy per unit volume (the sum of pressure and gravitational potential ? g h) is the same everywhere.

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 .