Video narration
How do Reynolds transport theorem and the Navier-Stokes equation fit together when water flows through a pipe? You follow moving fluid particles, but analyze a fixed pipe section-a control volume-where momentum crosses. Reynolds transport theorem makes that switch, converting a moving-system balance into a control-volume balance. Apply it to momentum conservation, then add Newton's law and a stress model: Navier-Stokes is the local momentum equation. The theorem is the bridge, turning a fixed pipe-section balance into Navier-Stokes.