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Eulers Equation of Motion amp Bernoullis EQs derivation mechanicalengineering civilengineering
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Download PDF notes link click here https://drive.google.com/file/d/1kZP_... • • • Euler's Equation of Motion in classical Mechanics extends Newton's laws of motion for point particles to rigid body motion. Leonhard Euler developed them around 50 years after Isaac Newton developed his laws. Fluid dynamics is a highly quantitative discipline that necessitates close attention to the physical interpretations of differential equations. • Euler's equation of motion is among the simplest to apply of all the equations used in fluid dynamics, especially in the ranges where a fluid's viscosity and compressibility are minimal. Since they can yield intuitive results and are simpler to work with than the complete Navier-Stokes equations for compressible fluids, Euler's equation of motion in fluid dynamics is typically used as the foundation for CFD classes. In this sophisticated area of mathematics, Leonhard Euler and the complex numbers used in these Euler equation components often work with both exponential and differential equations to create various fluid and fluid element requirements. • Derive Euler's Equation of Motion • We shall simply consider gravity and pressure forces in Euler's equation of motion. Other factors will be ignored. • Assumptions: • As stated here, the following presumptions are the foundation for Euler's equation of motion. • The fluid has no viscosity. Frictional losses won't exist at all. • The substance is uniform and incompressible. • The fluid moves steadily, continuously, and in a streamline. • The section's fluid flow velocity is consistent. • Only the forces of gravity and pressure will be considered. • Imagine a fluid moving from point A to point B, and consider a very small cylindrical portion of this fluid flow with length dS and cross-sectional area dA, as shown in the figure below. • Consider the forces on the cylinder: Pressure force PdA, in the direction of fluid flow.
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