Equation of Continuity

Definition

The Equation of Continuity is a fundamental principle in fluid dynamics that expresses the conservation of mass within a fluid flow.

It is based on the principle that the mass entering a given section of a fluid flow must equal the mass leaving that section, assuming there is no mass added or lost within the section.

Mathematical Form

The Equation of Continuity is mathematically represented as follows:

\[ A_1 \cdot v_1 = A_2 \cdot v_2 \]

where:

• \(A_1\) and \(A_2\) are the cross-sectional areas of the pipe or tube at two different points,
• \(v_1\) and \(v_2\) are the corresponding fluid velocities at those points.

Interpretation

The equation implies that as the cross-sectional area of a pipe decreases, the fluid velocity must increase to maintain the same mass flow rate, and vice versa.