3. Mass Conservation Equation- I
The chapter discusses the differential analysis of fluid flow, emphasizing the transition from integral to differential approaches in fluid mechanics. It introduces the fundamental principles behind mass conservation and momentum equations and elaborates on the concept of partial differential equations as they relate to fluid dynamics. Key derivations include the application of Reynolds transport theorem and Gauss's divergence theorem, which are vital for understanding mass conservation in fluid systems.
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What we have learnt
- Differential analysis provides a more detailed understanding of fluid dynamics compared to integral analysis.
- Mass conservation is governed by equations derived from Reynolds transport theorem and Gauss's divergence theorem.
- Four coupled partial differential equations can be derived to describe mass and momentum in fluid flow.
Key Concepts
- -- Integral Approach
- A method of analyzing fluid flow by considering control volumes to estimate gross characteristics of force and mass conservation.
- -- Differential Approach
- An analysis method focusing on point-specific properties in the fluid flow domain to derive equations for pressure, velocity, and density.
- -- Mass Conservation Equation
- A fundamental equation in fluid mechanics that relates the rate of change of mass in a control volume to the mass inflow and outflow rates.
- -- Reynolds Transport Theorem
- A theorem that relates the time rate of change of a quantity in a control volume to the flux of that quantity through the control surface.
- -- Gauss's Divergence Theorem
- A statement that allows the conversion of volume integrals of a vector field's divergence into surface integrals over the boundary of that volume.
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