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Derivation Continuity Equation for Cartesian Coordinates Video Lecture | Topper Handwritten Notes & Videos for GATE ME - Mechanical Engineering

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FAQs on Derivation Continuity Equation for Cartesian Coordinates Video Lecture - Topper Handwritten Notes & Videos for GATE ME - Mechanical Engineering

1. What is the derivation of the continuity equation in Cartesian coordinates?
Ans. The derivation of the continuity equation in Cartesian coordinates involves considering a control volume in a fluid flow system and applying the principles of conservation of mass. By applying the divergence theorem and simplifying the equation, we can derive the continuity equation, which states that the rate of change of mass within a control volume is equal to the net mass flux across its boundaries.
2. How is the continuity equation applied in fluid mechanics?
Ans. The continuity equation is a fundamental equation in fluid mechanics that is used to analyze fluid flow. It is applied by considering a control volume and examining the mass balance within that volume. By applying the continuity equation, we can determine how the fluid velocity and density change within the system, helping us understand the behavior of the fluid flow.
3. What are the assumptions made in the derivation of the continuity equation?
Ans. The derivation of the continuity equation relies on several assumptions, including the assumption of incompressibility of the fluid, which means that the density of the fluid remains constant throughout the flow. Additionally, it assumes that the flow is steady, meaning that the velocity of the fluid does not change with time. These assumptions simplify the derivation and allow for the application of the continuity equation in various fluid flow problems.
4. Can the continuity equation be applied to compressible fluids?
Ans. The continuity equation, as derived for incompressible fluids, cannot be directly applied to compressible fluids. In compressible flow, the density of the fluid varies significantly, and the assumption of constant density no longer holds. However, a modified form of the continuity equation can be derived for compressible fluids, taking into account the changes in density and fluid properties.
5. What are some practical applications of the continuity equation in engineering?
Ans. The continuity equation is widely used in various engineering fields and has practical applications in fluid dynamics and hydraulics. It is used to analyze and design pipelines, pumps, and other fluid transport systems. It is also utilized in the analysis of air flow in ventilation systems, aerodynamics of vehicles, and the design of water distribution networks. By applying the continuity equation, engineers can optimize the efficiency and performance of these systems.
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