Explain the continuity equation and its practical applications.

The continuity equation states that for steady flow, mass flow rate remains constant throughout a flow system: ρ₁A₁V₁ = ρ₂A₂V₂. For incompressible flow, this simplifies to A₁V₁ = A₂V₂, meaning velocity increases when cross-sectional area decreases and vice versa. Practical applications include designing nozzles and diffusers, calculating flow velocities in variable-area ducts, sizing pipes for required flow rates, and analyzing venturi meters and flow measurement devices.