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Shan K
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Will anyone give me the derivations for continuty equation of fluid and euler's equation of fluid motion .
First we will talk about the time rate of change of mass in the volume. We define the following:The time rate of change of mass in a control volume, [itex]\mathscr{V}[/itex] plus the net outward flux of mass through its surface, [itex]A[/itex] is identically equal to zero.
Using the same method as before to define each term, we can say thatThe time rate of change of momentum in [itex]\mathscr{V}[/itex] plus the net outward momentum flux through [itex]A[/itex] equals the net force on the fluid.
I can't understand why the mass flux is p(rho)v
I also can't understand why you had taken a minus sign when you calculated the force due to pressure on dA in the second derivation
Next, the outward momentum flux term can be addressed as follows:
The Continuity equation of Fluid is a fundamental equation in fluid dynamics that expresses the conservation of mass for a fluid. It states that the rate of change of mass in a given volume of fluid is equal to the net flow of mass into or out of the volume.
The Continuity equation of Fluid is derived from the principle of conservation of mass, which states that mass is neither created nor destroyed. By considering a small volume of fluid and applying this principle, we can arrive at the Continuity equation.
Euler's Equation of Fluid Motion is a fundamental equation in fluid dynamics that describes the motion of an inviscid (non-viscous) fluid. It combines the concepts of conservation of mass, conservation of momentum, and conservation of energy to describe the acceleration of a fluid element.
Euler's Equation of Fluid Motion is derived from Newton's Second Law of Motion, which states that the net force acting on an object is equal to its mass times its acceleration. By considering a small element of fluid and applying this law, we can arrive at Euler's Equation.
The main assumptions made in deriving the Continuity equation and Euler's Equation are that the fluid is incompressible (i.e. its density does not change), inviscid (i.e. it has no internal friction), and the flow is steady (i.e. it does not change with time). Additionally, Euler's Equation assumes that the flow is irrotational (i.e. the fluid particles do not rotate as they move). These assumptions allow for simplified mathematical descriptions of fluid flow and are appropriate for many real-world applications.