At the end of this seminar, the reader should be able to able to derive Basic Governing Equations for Compressible/Incompressible equations which include continuity equation, Momentum equation and Energy equation.
- A System is defined as an arbitrary quantity of mass of fixed identity. Everything external to system is called its surrounding and the system is separated from its surroundings by boundaries.
- A control volume is a mathematical abstraction employed in the process of creating mathematical models of physical processes. In an inertial frame of reference, it is a fixed volume in space through which the fluid flows. The surface enclosing the control volume is referred to as control surface.
- In continuum assumption, Fluid is considered as continuous such that fluid properties are continuous functions of spatial coordinates.
- MASS CONSERVATION: Mass of a system is conserved i.e it can neither be created nor destroyed.
- The rate of change of momentum equals the sum of the forces on a fluid particle. (Newton 's second law of motion)
- First Law of Thermodynamics:The increase in the internal energy of a system is equal to the amount of energy added by heating the system, minus the amount lost as a result of the work done by the system on its surroundings.
- Divergence of a Vector:Let x, y, z be a system of Cartesian coordinates on a 3-dimensional space, and let i, j, k be the corresponding unit vectors.
The divergence of a continuously differentiable vector field F = F1 i + F2 j + F3 k is defined as
- Substantive (Total) Derivative:
Reynold Transport theorem: The Reynolds transport theorem refers to any extensive property, N, of the fluid in a particular control volume. It is expressed in terms of a substantive derivative on the left-hand side.
Back ground Study material
- Pressure force and equilibrium of a fluid (Reference 2)
- Reynold transport theorem (Reference 3)
- Conservation of Mass (Reference 4)
- The Linear Momentum Equation (Reference 5)
- The energy equation (Reference 6)
- Fluid Mechanics by FRANK M WHITE page 225-249
- Fluid Mechanics by FRANK M WHITE page 65
- Fluid Mechanics by FRANK M WHITE page 139
- Fluid Mechanics by FRANK M WHITE page 147
- Fluid Mechanics by FRANK M WHITE page 153
- Fluid Mechanics by FRANK M WHITE page 172
- Viscous Flow by FRANK M White page 69
- An introduction to Computational Fluid Dynamic; The Finite Volume Approach by HK Vesteeg & W Malalasekera Chapter2