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The equation of continuity $A_1 v_1 = A_2 v_2$ is conservation of mass for incompressible, steady flow through a tube of varying cross-section. The product $Av = Q$ (volume flow rate, m$^3$/s) is constant throughout the tube.

Physical meaning: fluid speeds up in narrow sections and slows down in wide sections. This is why water from a hose speeds up when you partially block the nozzle — the same volume must pass through a smaller area in the same time.

For compressible fluids (gases at high speeds), the mass flow rate $\rho Av$ is conserved instead. For JEE, most problems involve incompressible fluids where volume flow rate is constant.

The continuity equation is always the first step in Bernoulli problems involving varying pipe diameters — use it to relate velocities at two points, then apply Bernoulli to find pressure differences.