Steady and Unsteady Flows

Given a velocity field description of a fluid $\mathbf{V}=\mathbf{V}(x,y,z,t)$ we can say that steady and unsteady flows can be characterized:

• Steady flow: $\mathbf{V}=\mathbf{V}(x,y,z)$
• Unsteady flow: $\mathbf{V}=\mathbf{V}(x,y,z,t)$

Essentially, the steady flows don’t vary with time, so we don’t need to parametrize with time. They can just be defined based on $\mathbf{V}$ at a certain position $\mathbf{V}=\mathbf{V}(x_0,y_0,z_0)$.

• $\mathbf{V}(x_0,y_0,z_0,t_1)=\mathbf{V}(x_0,y_0,z_0,t_2)$ would be a steady flow
• $\mathbf{V}(x_0,y_0,z_0,t_1)\ne \mathbf{V}(x_0,y_0,z_0,t_2)$ would be a steady flow