The boundary layer equations describe the behavior of fluid flow within this thin layer. One of the fundamental equations governing the boundary layer is the boundary layer momentum equation, also known as the boundary layer equation or the boundary layer velocity profile equation. The simplified form of the boundary layer equation for an incompressible, steady flow along a flat plate can be expressed as:

Where:

• $u(y)$ is the velocity profile within the boundary layer at a distance $y$ from the surface,
• $U$ is the freestream velocity far away from the surface,
• $f(\eta )$ is the dimensionless velocity profile function, which depends on the dimensionless distance from the wall.