Compare node analysis and loop (Hardy Cross) methods for pipe networks.

• A. Node analysis solves by applying loop conditions; Hardy Cross uses node continuity.
• B. Node analysis solves by applying continuity and energy across nodes; Hardy Cross iteratively adjusts loop flows.
• C. Hardy Cross yields exact solution in a single step.
• D. Node analysis is only used for open channels.

Answer: (B)

The main idea is that these two methods approach the network from different angles: node analysis uses conservation at the nodes, while the Hardy Cross loop method balances energy around loops through iterative corrections.

In node analysis, you treat the network as a set of nodes connected by pipes. The unknowns are the hydraulic heads at the nodes (and from those you get the pipe flows). At each node, mass conservation (continuity) must hold: the sum of flows into the node equals the sum of flows out. The flow in each pipe is related to the heads at its ends through a head-loss equation (from Darcy–Weisbach or Hazen–Williams), so you end up with a system of nonlinear equations in the node heads that you solve simultaneously. Once the node heads are known, every pipe flow follows from the head-loss relations.

The Hardy Cross method, by contrast, works with loops. You start with an initial guess of the flows around each loop and compute the head losses around the loops. If the loop is not balanced (the algebraic sum of head losses around the loop isn’t zero), you apply a correction to the loop flow. You repeat this process for all loops, iterating until the corrections become small and the energy balance around every loop is satisfied. It’s an iterative procedure, not a one-step exact solution.

That’s why the correct description is: node analysis solves by applying continuity and energy considerations across nodes, and Hardy Cross iteratively adjusts loop flows to satisfy energy balance around loops. The other statements don’t fit the fundamentals—node analysis isn’t about loop conditions, Hardy Cross isn’t exact in a single step, and node analysis isn’t restricted to open channels.