Which one of the following is the conservation law from which the equa

Which one of the following is the conservation law from which the equation of continuity for fluid flow is derived?

[amp_mcq option1=”Conservation of momentum” option2=”Conservation of volume” option3=”Conservation of mass” option4=”Conservation of energy” correct=”option3″]

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UPSC Geoscientist – 2022

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The equation of continuity for fluid flow is a direct consequence of the conservation of mass principle. It states that mass is conserved within a flowing fluid system, meaning it is neither created nor destroyed.

In a steady flow of a fluid, the equation of continuity relates the fluid density, flow speed, and cross-sectional area of the flow channel. For any given section of a fluid flow, the rate at which mass enters that section must equal the rate at which mass leaves, assuming no sources or sinks within the section. This principle is a statement of mass conservation applied to fluid dynamics.

For an incompressible fluid (where density ρ is constant), the continuity equation simplifies to A₁v₁ = A₂v₂, meaning the product of the cross-sectional area and the fluid velocity is constant along a streamline. This reflects that if the area decreases, the velocity must increase to maintain a constant mass flow rate. Other conservation laws (momentum and energy) are fundamental to deriving other equations in fluid dynamics, such as the Navier-Stokes equations and Bernoulli’s equation, respectively.

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