Which statement expresses energy conservation around a loop in pipe flow problems?

• A. Darcy-Weisbach head losses sum to zero around a loop
• B. Momentum theorem around a node
• C. Bernoulli's equation cannot be applied to viscous flow
• D. Continuity equation alone determines flows

Answer: (A)

Energy conservation around a loop in pipe flow is reflected in the fact that the algebraic sum of head changes around a closed path must be zero for steady, incompressible flow with no external energy sources. In practice, each pipe segment has a friction head loss described by the Darcy-Weisbach equation, and when you go around the loop in a consistent direction, these losses must balance so you return to the same energy level at the starting point. If a pump or turbine is present, its head gain would appear as a positive term and balance the losses around the loop. This is why expressing energy conservation as the sum of head losses around a loop equaling zero best captures the concept. Bernoulli’s equation can still be used for viscous flow when losses are included as a head-loss term; continuity alone does not determine flows, since it only enforces mass conservation, and momentum balance around a node is a different consideration.