Flow visualization is especially useful in experimental [[Fluid|fluid]] mechanics. Flow visualization also provides a tangible understanding of flows. Four common flow visualizations are as follows: - **Streaklines**: The set of points that particles have passed through after passing through a fixed point. Streaklines can not intersect. - **Pathlines**: Traces the path of a single particle in the flow. $\dfrac{dx_p}{dt}=u(x,y,z,t)$ $\dfrac{dy_p}{dt}=v(x,y,z,t)$ $\dfrac{dz_p}{dt}=w(x,y,z,t)$ - **Timelines**: A line of particles that may change shape due to flow over time. Can be thought of as a set of pathlines. - **Streamlines**: Curve which is always tangent to the [[Velocity|velocity]] of the particle. Fluid can not flow across a streamline by definition. In 3D: $\dfrac{dx}{u}=\dfrac{dy}{v}=\dfrac{dz}{w}$ In 2D: $\dfrac{dy}{dx}=\dfrac{v}{u}$