Fluid Dynamics : Lecture-3                                                                                                                    Print this page
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7. Bernouilli's  Theorem:

             The swiss physicist Daniel Bernoulli (1700-1787) derived an expression relating pressure, velocity and height of the fluid. It is a fundamental expression in fluid dynamics.

             Bernoulli's equation is a product of general work energy theorem in fluid flow. According to this theorem, the work done by the resultant force acting on a system is equal to the change in kinetic energy of the system.

            For the derivation of Bernoulli's theorem, the fluid flow is considered as ideal with following conditions. The fluid flow should be steady, incompressible, irrotational and non-viscous. Consider the flow of fluid through a portion of pipe as shown in Fig. 9.

            The left side horizontal portion of the pipe is at an elevation of  y1 and at the right side its elevation is y2. Let   A1 and A2 be the area of cross sections of the pipe at the left and right end respectively.

 

Fig. 9: Portion of the fluid moving from one end to other end
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