.TRANSFORM.Fluid.ClosureRelations.PressureLoss.Functions.Bends.K_smoothBend

Information

Resistance coefficient K for a smooth circular pipe bend (elbow) per Rennels & Hudson (2012). The coefficient is referenced to the velocity head in the pipe cross-section (constant diameter through the bend), i.e. it is used as dp = K*m_flow^2/(2*rho*A^2) with A the pipe cross-sectional area.

The correlation combines an arc-friction term, the primary turning loss, and a secondary-flow (Dean-vortex) term. It reduces toward the straight-pipe friction loss as the deflection angle approaches zero and is valid for arbitrary turning angle and relative bend radius rc/D.

References

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

Interface

function K_smoothBend
  extends TRANSFORM.Icons.Function;
  input SI.Length dimension "Pipe (hydraulic) diameter";
  input SI.Length radius "Bend radius of curvature (to the pipe centerline)";
  input SI.Angle angle "Bend deflection (turning) angle";
  input SI.ReynoldsNumber Re "Reynolds number";
  input SI.Length roughness = 0 "Average height of surface asperities";
  input SI.ReynoldsNumber Re_lam = 2300 "Laminar transition Reynolds number";
  input SI.ReynoldsNumber Re_turb = 4000 "Turbulent transition Reynolds number";
  output Units.NonDim K "Resistance coefficient";
end K_smoothBend;