A fluid flows steadily through a pipe whose cross-sectional area varies from one section to another. Which fundamental conservation law leads to the equation of continuity for this flow?
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Question

A fluid flows steadily through a pipe whose cross-sectional area varies from one section to another. Which fundamental conservation law leads to the equation of continuity for this flow?

G1 Physics · Accepted Answer

The equation of continuity expresses the requirement that mass cannot accumulate indefinitely at any section of a pipe during steady flow. For steady flow, mass flow rate entering a section = mass flow rate leaving that section. Therefore, ρ₁A₁v₁ = ρ₂A₂v₂. For an incompressible liquid, ρ₁ = ρ₂, so the relation becomes A₁v₁ = A₂v₂. Hence the equation of continuity follows from conservation of mass. Correct option: C.