BEND_ROUNDED

Computes the loss coefficient for a rounded elbow from pipe diameter, bend angle, and curvature using one of several engineering correlations.

Depending on method, the model incorporates geometry ratios such as r_c/D and may include Reynolds-number effects to account for friction and secondary-flow behavior.

The returned value is a dimensionless coefficient K used in minor-loss pressure-drop calculations.

Excel Usage

=BEND_ROUNDED(Di, angle, rc, Re, bend_method)

Di (float, required): Inside diameter of pipe [m]
angle (float, required): Angle of bend [degrees]
rc (float, required): Radius of curvature of the bend [m]
Re (float, optional, default: 100000): Reynolds number of the pipe flow [-]
bend_method (str, optional, default: “Rennels”): Calculation method

Returns (float): Loss coefficient K for the rounded bend [-]

Example 1: 90 degree bend with Rennels method

Inputs:

Di	angle	rc	Re
0.1	90	0.15	100000

Excel formula:

=BEND_ROUNDED(0.1, 90, 0.15, 100000)

Expected output:

0.225316

Example 2: 45 degree bend

Inputs:

Di	angle	rc	Re
0.1	45	0.15	100000

Excel formula:

=BEND_ROUNDED(0.1, 45, 0.15, 100000)

Expected output:

0.155242

Example 3: 90 degree bend with Crane method

Inputs:

Di	angle	rc	Re	bend_method
0.1	90	0.15	100000	Crane

Excel formula:

=BEND_ROUNDED(0.1, 90, 0.15, 100000, "Crane")

Expected output:

0.229023

Example 4: 90 degree bend with Swamee method

Inputs:

Di	angle	rc	Re	bend_method
0.1	90	0.15	100000	Swamee

Excel formula:

=BEND_ROUNDED(0.1, 90, 0.15, 100000, "Swamee")

Expected output:

0.371729

Python Code

Show Code

from fluids.fittings import bend_rounded as fluids_bend_rounded

def bend_rounded(Di, angle, rc, Re=100000, bend_method='Rennels'):
    """
    Calculate the loss coefficient (K) for a rounded pipe bend (elbow) using various methods.

    See: https://fluids.readthedocs.io/fluids.fittings.html#fluids.fittings.bend_rounded

    This example function is provided as-is without any representation of accuracy.

    Args:
        Di (float): Inside diameter of pipe [m]
        angle (float): Angle of bend [degrees]
        rc (float): Radius of curvature of the bend [m]
        Re (float, optional): Reynolds number of the pipe flow [-] Default is 100000.
        bend_method (str, optional): Calculation method Valid options: Rennels, Miller, Crane, Ito, Swamee. Default is 'Rennels'.

    Returns:
        float: Loss coefficient K for the rounded bend [-]
    """
    try:
      try:
        Di = float(Di)
        angle = float(angle)
        rc = float(rc)
        Re = float(Re)
      except (ValueError, TypeError):
        return "Error: Di, angle, rc, and Re must be numbers."

      if Di <= 0:
        return "Error: Di must be positive."
      if angle <= 0 or angle > 180:
        return "Error: Angle must be between 0 and 180 degrees."
      if rc <= 0:
        return "Error: Rc must be positive."
      if Re <= 0:
        return "Error: Re must be positive."

      kwargs = {'Di': Di, 'angle': angle, 'Re': Re, 'method': bend_method}
      if bend_method == 'Crane':
          kwargs['bend_diameters'] = rc / Di
      else:
          kwargs['rc'] = rc

      result = fluids_bend_rounded(**kwargs)
      return float(result)
    except Exception as e:
      return f"Error: {str(e)}"

Online Calculator

Di *

Inside diameter of pipe [m]

angle *

Angle of bend [degrees]

rc *

Radius of curvature of the bend [m]

Reynolds number of the pipe flow [-]

bend_method

Calculation method