7. The Navier-Stokes Equation
The chapter discusses the Navier-Stokes equations, which are fundamental in computational fluid dynamics, addressing complex fluid flow problems. It covers the derivation of these equations, emphasizing their application in incompressible isothermal flows using Cartesian and cylindrical coordinate systems. The discussion also extends to the assumptions behind Newtonian and non-Newtonian fluids, as well as their implications in fluid mechanics.
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Sections
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What we have learnt
- The Navier-Stokes equations are derived from the principles of momentum conservation and density continuity.
- The equations describe how the velocity, pressure, and density of fluid flow interact under various conditions.
- Understanding Newtonian and non-Newtonian fluids is essential in applying the Navier-Stokes equations effectively in real-world scenarios.
Key Concepts
- -- NavierStokes Equations
- A set of non-linear partial differential equations that describe the motion of fluid substances.
- -- Newtonian Fluid
- A fluid that exhibits a linear relationship between shear stress and shear strain rate.
- -- Incompressible Flow
- A flow in which the fluid density remains constant throughout the fluid domain.
- -- Isothermal Flow
- A flow in which the temperature of the fluid remains constant within its domain.
- -- Boundary Conditions
- The conditions specified at the boundaries of the fluid flow region that allow for the determination of the flow field.
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