# Faster water means a narrower stream > Using the familiar example of water flowing from a faucet to illustrate the principles of fluid dynamics, particularly in a one-dimensional model. This common observation, where the stream of water becomes visibly narrower as it falls, is a direct consequence of the continuity principle and mass conservation in steady, non-turbulent flow. As gravity accelerates the water, its velocity ($$v$$) increases. To maintain a constant mass flow rate (current, $$j$$), the linear density ($$\rho\_{\ell}$$) must decrease. This current can be mathematically modelled as the product of linear density and velocity ($$j=\rho\_{\ell} v$$). The mathematical analysis confirms this decrease, showing that $$\frac{d \rho\_{\ell}}{d x}<0$$, meaning the linear density decreases as the distance ($$x$$) fallen increases. Because water is treated as having a fixed volume density, the decrease in linear density requires that the cross-sectional area of the water stream must decrease. A crucial insight offered by this example is the realization that fundamental flow principles can be analyzed effectively using a one-dimensional system focusing on linear density, rather than necessarily a three-dimensional volume. ### :paperclips:IllustraDemo {% embed url="" %} ### :paperclips:IllustraDemo hub {% embed url="" %}