Force on a pipe fitting or support from the steady-state linear momentum equation. Handles bends, elbows, reducers, and nozzles.
Fluid Mechanics II · SpecializedFitting type / bend angle:
Unit applies to both D₁ and D₂.
Unit applies to both P₁ and P₂. Use gauge pressures.
Steady-state linear momentum equation:
Inlet in +x direction, outlet at angle θ from +x axis (CCW positive).
Component equations (force of pipe ON fluid):
Force on the fitting (reaction):
Quick results for equal-diameter pipes (V₁ = V₂ = V):
| Case | Fx | Fy |
|---|---|---|
| θ = 0° (straight, P₂ = 0) | P₁A₁ | 0 |
| θ = 90° (elbow, P₂ = 0) | ṁV + P₁A₁ | −ṁV |
| θ = 180° (U-bend, P₂ = 0) | 2ṁV + P₁A₁ | 0 |
Where: