State the continuity equation for incompressible flow in a network and how it applies at junctions.

State the continuity equation for incompressible flow in a network and how it applies at junctions.

• A. The energy conservation principle applies to all flows at a junction.
• B. The momentum balance is the only requirement at a junction.
• C. Mass conservation: Σinflow Q = Σoutflow Q; at junctions, sum of incoming flows equals sum of outgoing flows.
• D. Density changes significantly in incompressible flow.

Answer: (C)

At the heart of this concept is conservation of mass. For incompressible flow, density stays constant, so what matters is that fluid mass entering any junction must equal fluid mass leaving it. In practice, that means the sum of the volumetric flow rates going into a junction equals the sum of the volumetric flow rates going out. This is the continuity condition at network junctions: all incoming flows must balance all outgoing flows at steady state, with no accumulation of fluid at the node. That’s why the statement that mass conservation holds—sum of inflow Q equals sum of outflow Q—is the correct description. The other ideas aren’t the continuity condition: energy conservation and momentum balance describe different aspects of fluid behavior, and incompressible flow does not imply density changes.

At the heart of this concept is conservation of mass. For incompressible flow, density stays constant, so what matters is that fluid mass entering any junction must equal fluid mass leaving it. In practice, that means the sum of the volumetric flow rates going into a junction equals the sum of the volumetric flow rates going out. This is the continuity condition at network junctions: all incoming flows must balance all outgoing flows at steady state, with no accumulation of fluid at the node.

That’s why the statement that mass conservation holds—sum of inflow Q equals sum of outflow Q—is the correct description. The other ideas aren’t the continuity condition: energy conservation and momentum balance describe different aspects of fluid behavior, and incompressible flow does not imply density changes.