In a pipe network with a loop, which fundamental equations must be satisfied to solve for the branch flows?

• A. Conservation of mass at junctions and energy conservation around loops
• B. Momentum conservation along each branch
• C. Pressure continuity at all nodes
• D. Bernoulli's equation applied to every point

Answer: (C)

The key idea is balancing flow and energy in a looped pipe network. To determine branch flows, you use continuity at every junction: the sum of flows entering a node must equal the sum leaving it. Along each independent loop, the total head losses around the loop must add to zero. Together with a pipe-headloss relationship (such as Darcy–Weisbach) for each branch, these two principles form the equations you solve for the unknown flows and node pressures.

Why this matters: continuity enforces mass conservation—water isn’t created or destroyed at junctions—while the loop energy balance ensures the same hydraulic head is consistent around any closed path, accounting for losses. Pressure continuity at nodes is an inherent feature of the node-pressure model, but without the mass-balance and loop-energy equations, it doesn’t by itself fix how much flow goes through each branch. Bernoulli’s equation applied all along every point isn’t appropriate in real networks with losses and nonuniform conditions, so it isn’t the fundamental tool used to solve for branch flows.