.TRANSFORM.Fluid.FittingsAndResistances.Elbow

Information

Minor-loss resistance for a smooth circular pipe bend (elbow). The pressure loss is computed as

dp = K*m_flow^2/(2*rho*A^2)

where A is the pipe cross-sectional area and the resistance coefficient K is given by the Rennels & Hudson (2012) smooth-bend correlation (K_smoothBend), combining an arc-friction term, the primary turning loss, and a secondary-flow (Dean-vortex) term. The Darcy friction factor used in the friction terms is evaluated from the existing single-phase 2-region correlation, so wall roughness and the laminar/turbulent transition (Re_lam, Re_turb) are honoured.

Geometry

• dimension – pipe inner diameter D.
• radius – bend radius of curvature rc measured to the pipe centerline; the relative bend radius is rc/D.
• angle – deflection (turning) angle; defaults to 90°.

Notes / range of validity

The correlation is referenced to the (constant) pipe velocity head and applies to circular cross-sections. It is a turbulent-flow minor-loss correlation; at very low Reynolds number the friction contribution dominates and the model remains well-behaved (the friction factor uses an internal Reynolds-number floor). Flow reversal is supported: the loss always opposes the flow direction.

References

Rennels, D. C. & Hudson, H. M. Pipe Flow: A Practical and Comprehensive Guide. John Wiley & Sons (2012).

Cross-check implementation: Bell, C. fluids (open-source), fluids.fittings.bend_rounded(method="Rennels").