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Learn how Bernoulli's equation is derived from Euler's equation of motion, the role of energy conservation, and the key assumptions affecting its applicability in fluid dynamics.
Bernoulli's equation can be derived from Euler's equation of motion by integrating Newton's 2nd law along a streamline with gravitational and pressure forces as the only forces acting on a fluid element. The equation represents a form of the conservation of energy principle where the total energy along a streamline remains constant.
By considering a fluid undergoing steady flow and applying energy methods, Bernoulli's equation relates pressure, density, and speed of the flow at different points. It is essential to note the assumptions made, such as the constant density, conservation of mass, and steady flow conditions, that limit the use of this form of the equation.
The derivation of Bernoulli's Equation involves an elegant application of the Work-Energy Theorem, showcasing how energy transformations between potential and kinetic energy influence fluid flow behavior.
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