# Definition Flow field $\vec{V}=\left(V_1,\,V_2\right)$ that is: 1. Steady $ \frac{\partial\vec{V}}{\partial t}=0 $ 2. Incompressible $ \nabla\cdot\vec{V}=0\rightarrow \frac{\partial V_1}{\partial x}+\frac{\partial V_2}{\partial y}=0 $ 3. Irrotational $ \nabla\times\vec{V}=0\rightarrow \frac{\partial V_2}{\partial x}+\frac{\partial V_1}{\partial y}=0 $ These conditions are satisfied automatically if $\vec{V}=\nabla\varphi$ for a real-valued potential $\varphi$ that satisfies [[Laplace's equation]] $\nabla^2\varphi=0$ #