Which statement best describes how node analysis and Hardy Cross differ in pipe-network practice?

• A. Node analysis uses only energy balance; Hardy Cross uses mass balance.
• B. Hardy Cross yields exact solution in one step.
• C. Node analysis applies to pressure networks; Hardy Cross applies to temperature fields.
• D. Hardy Cross uses iterative adjustment of loop flows to satisfy energy losses and continuity; node analysis solves by applying continuity and energy at nodes.

Answer: (D)

The main idea is that these two methods approach the network from different angles and use different unknowns. Node analysis treats the network in terms of node pressures (heads) and uses continuity at each node together with the energy (head) losses in each pipe to form a set of equations that are solved simultaneously. In other words, you apply mass balance at the nodes and the energy relationships along the connections, and solve for the node heads (and from them the pipe flows).

Hardy Cross, on the other hand, is a loop-based, iterative method. You start with an initial guess of loop (cycle) flows and then repeatedly adjust those loop flows so that the energy losses around each loop disappear (the loop head loss sums go to zero), while the flow distribution still satisfies continuity. This is inherently an iterative approach to reach a consistent set of loop flows.

So, the statement that Hardy Cross uses iterative loop-flow adjustments to satisfy energy losses and continuity, while node analysis solves by applying continuity and energy at nodes, captures the essential difference between the two methods. The other choices mix up the roles (energy vs mass balance) or misstate the nature of the methods (one-step exact solution) or their application (temperature fields), which doesn’t align with how these techniques are used in pipe-network practice.