- **Streaklines** connect all the fluid particles that have passed through a certain point in space - $t_{0}$ varies while $t$ stays the same $ \vec{u}=\frac{d\vec{r}}{dt}=\vec{r}(t=t_{0})=\vec{r}_{0} $ - **Streamlines** are family of curves whose tangent vectors constitute the velocity vector field of the flow. Tangent to the velocity vectors - You can never have any flow across (normal to) the streamline - Streamline going to the center of the air foil is called a "**stagnation streamline**", occurs at the stagnation point where velocity goes to zero - Streamlines are measured physically using "particle image velocimetry" $ \vec{u}=\vec{u}(x,y,z,t) $ $ \frac{dy}{dx}=\frac{u_{y}}{u_{x}}\to \frac{dx}{u_{x}}=\frac{dy}{u_{y}}=\frac{dz}{u_{z}} $ - **Pathlines** show where a single fluid particle moves as a function of time (e.g long exposure photography) - Unlike streaklines, $t$ varies rather than $t_{0}$ - Steady: $\frac{\partial}{\partial t}(\dots)=0,$ not a function of time - For steady flow, path/streak/streamlines are identical - Flow dimension: # of spatial dimensions required to describe the flow - 1D: $\vec{u}=\vec{u}(t,x)$ or $\vec{u}=\vec{u}(x)$ - 3D: $\vec{u}=\vec{u}(r,\theta,z,t)$ or $\vec{u}=\vec{u}(r,\theta,z)$ - Uniform: no variation in a particular dimension > - Laminar flow: fluid flows as layers, little mixing between them > - Turbulent flow: random, chaotic vortices/eddies of varied sizes, good mixing > - Transitional flow: has elements of both laminar/turbulent, switches between them