If the fluid flows through a pipe with equal areas at different sections (a1 = a2 = a3), the velocity of the fluid will be the same at all those sections. This is known as the principle of continuity or the equation of continuity.
According to the principle of continuity, the mass flow rate of an incompressible fluid remains constant along a pipe. The mass flow rate is given by the product of the density (ρ), velocity (v), and cross-sectional area (A) of the pipe:
ρ1 * A1 * v1 = ρ2 * A2 * v2 = ρ3 * A3 * v3
Since the areas (a1 = a2 = a3), the velocities (v1 = v2 = v3) will be the same. In other words, the fluid will have a uniform velocity at any cross-sectional area of the pipe.