Bold v is the velocity vector; vx and vy are its Cartesian components; v₁ and v₂ are uniform section speeds; vavg is area-mean speed; ρ is density; Q is volume flow; ṁ is mass flow; M is mass stored; n is the outward unit normal. All control volumes are fixed in space during a measurement. Changing their placement resets a trial.

Conceptual sequence follows the accompanying “Discovering Conservation of Mass” assignment and Welty, Wicks, Wilson & Rorrer, Fundamentals of Momentum, Heat, and Mass Transfer, 5th edition, Chapter 4, “Conservation of Mass: Control-Volume Approach,” pp. 34–39. Publisher companion site (later edition). Checked against the supplied WeltyWicksWilson.pdf. Investigation 7 uses the differential form in Chapter 9 §9.1, where the differential continuity equation is developed.

These are kinematic measurement models, not solutions of the momentum or energy equations. Unequal imposed fluxes in a rigid, fully filled incompressible duct cannot describe a steady physical flow; the predicted change in mass makes that incompatibility visible. Tank overflow and dry-out stop a trial. No external libraries or network connection are required.