A fluid touching a solid surface is often modeled as having the same velocity as that surface. At a stationary wall, that means zero fluid velocity right at the wall. This is the no-slip condition.
Key idea
No-slip describes the velocity at the boundary. It does not say that the entire fluid is stationary.
Understand the idea
In a viscous fluid, adjacent layers exchange momentum. When a pressure difference drives flow through a pipe, the stationary wall restrains the nearby fluid. Farther from the wall, the fluid can move faster. The velocity gradient is associated with viscous shear stress.
Engineering example
For a straight circular pipe with stationary walls, the axial velocity is zero at the radius R. In fully developed laminar flow, the maximum occurs on the centreline. A numerical model should impose the intended wall condition and resolve the nearby gradients adequately.
Checkpoint
Does no-slip imply zero wall shear stress?
No. A zero velocity at the wall can coexist with a nonzero velocity gradient. For a Newtonian fluid in this simple shear setting, shear stress is proportional to dynamic viscosity times the velocity gradient.
Where the assumption needs care
No-slip is a useful macroscopic continuum model for many ordinary liquid and gas flows. Rarefied gases and some micro-scale or specially treated interfaces may require different boundary models.
Next step
Now connect what happens at a boundary to the mass flowing through a cross-section.