Explain the momentum equation and its application to calculate forces on pipe bends.

The linear momentum equation states: ΣF = d(mV)/dt = ṁ(V_out - V_in), where ṁ is mass flow rate. For steady flow through a control volume, forces include pressure forces, weight, and reaction forces from solid boundaries. For a pipe bend: F_x = P₁A₁ - P₂A₂cosθ + ṁ(V₁ - V₂cosθ) and F_y = P₂A₂sinθ + ṁV₂sinθ. These forces must be resisted by pipe supports or anchors. Applications include: designing pipe anchors and supports, calculating thrust blocks for bends, analyzing jet forces on turbine blades, and sizing reaction forces in nozzles.