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# Bernoulli Equation and Applications

الكلية كلية الهندسة     القسم  الهندسة البيئية     المرحلة 3
أستاذ المادة عدي عدنان جهاد الخيكاني       05/10/2012 11:56:36
INTRODUCTION
In chapter five flow of ideal fluids was discussed. The main idea was the study of flow pattern. The determination of equal flow paths and equal potential lines was discussed. No attempt was made to determine the numerical value of these quantities. In this chapter the method of determination of the various energy levels at different locations in the flow is discussed. In this process first the various forms of energy in the fluid
are identified. Applying the law of conservation of energy the velocity, pressure and potential at various locations in the flow are calculated. Initially the study is limited to ideal flow. However the modifications required to apply the analysis to real fluid flows are identified. The material discussed in this chapter are applicable to many real life fluid flow problems. The laws presented are the basis for the design of fluid flow systems.
Energy consideration in fluid flow:
Consider a small element of fluid in flow field. The energy in the element as it moves in the flow field is conserved. This principle of conservation of energy is used in the determination of flow parameters like pressure, velocity and potential energy at various locations in a flow. The concept is used in the analysis of flow of ideal as well as real fluids. Energy can neither be created nor destroyed. It is possible that one form of energy is converted to another form. The total energy of a fluid element is thus conserved under usual flow conditions. If a stream line is considered, it can be stated that the total energy of a fluid element at any location on the stream line has the same magnitude.
FORMS OF ENERGY ENCOUNTERED IN FLUID FLOW
Energy associated with a fluid element may exist in several forms. These are listed here and the method of calculation of their numerical values is also indicated.
Kinetic Energy
This is the energy due to the motion of the element as a whole. If the velocity is V, then the kinetic energy for m kg is given by
KE =mV2/2go Nm
The unit in the SI system will be Nm also called Joule (J)
The learner should be familiar with both forms of the equation and should be able to choose and use the proper equation as the situation demands. When different forms of the energy of a fluid element is summed up to obtain the total energy, all forms should be in the same unit.
Potential Energy
This energy is due to the position of the element in the gravitational field. While a zero value for KE is possible, the value of potential energy is relative to a chosen datum. The value of potential energy is given by

PE = m Z g/go Nm

Where m is the mass of the element in kg, Z is the distance from the datum along the gravitational direction, in m. The unit will be (kg m m/s2) × (Ns2/kgm) i.e., Nm. The specific potential energy (per kg) is obtained by dividing equation 6.1.3 by the mass of the element. PE = Z g/g0 Nm/kg
This gives the physical quantity of energy associated with 1 kg due to the position of the fluid element in the gravitational field above the datum. As in the case of the kinetic energy, the value of PE also is expressed as head of fluid, Z.

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 .