Which statement correctly describes the continuity condition at a junction in a pipe network?

• A. The sum of pressures equals the sum of velocities
• B. The sum of diameters is constant
• C. The sum of inflows equals the sum of outflows
• D. The sum of velocity heads equals zero

Answer: (C)

Continuity at a junction is about conservation of mass. For an incompressible fluid, the amount of fluid flowing into a junction per unit time must equal the amount flowing out. Since the flow rate Q is the product of area and velocity (Q = A v), the sum of all inflows must balance the sum of all outflows, regardless of how the pipes join or split. That is why the statement describing the inflows equaling the outflows best captures the continuity condition. The other ideas mix different quantities—pressure with velocity, diameters without regard to flow rate—or refer to velocity heads, which do not in general cancel at a junction without considering energy losses or changes in elevation and pipe characteristics.