I am studying how to determine the aerodynamic force on solid bodies in a fluid. This is using the Vortex Particle Method.
In order to determine aerodynamic forces on solid bodies embedded in a fluid, the pressure distribution is needed. Considering the no-slip boundary condition, the Navier-Stokes equations in a stationary frame of reference reduce to $\nabla p = \mu \nabla^2u$, where $\mu = ν\rho$ is the laminar viscosity. Replacing the velocity by the vorticity: $\omega = \nabla \times u$, gives
$$\nabla p = -\mu \nabla \times \omega.\tag{4.51}$$
To obtain the pressure, this expression can be integrated along the surface as $$\nabla p \cdot t_0 = −\mu \nabla\omega\cdot n_0\tag{4.52}$$
where $t_0$ is the surface unit tangential vector.
I cannot understand the transition from equation 4.51 to 4.52. How come the $\nabla\times\omega$ magically changes to $\nabla\omega\cdot n_0$?
I would sincerely appreciate any help.