What are minor losses in pipe flow and how are they calculated?

Minor losses (local losses) occur at fittings, valves, bends, expansions, and contractions due to flow separation and turbulence. They are calculated using loss coefficients (K-factors): h_L = K × V²/2g. Typical K-values: 90° elbow (0.3-0.9), gate valve fully open (0.2), globe valve (6-10), sudden expansion ((1-A₁/A₂)²), sudden contraction (0.5), entrance sharp-edged (0.5), exit (1.0). For long pipelines, minor losses are typically 5-10% of friction losses, but in compact systems with many fittings, they can dominate total losses.