BEND_MITER

Computes the local loss coefficient for a single-joint miter bend in a pipe using published empirical correlations selected by method.

For the Rennels method, the loss scales with bend angle and follows a sine-based relation of the form K = 0.42\sin(\alpha/2) + 2.56\sin^3(\alpha/2), where \alpha is the bend angle in degrees.

The result is a dimensionless resistance coefficient suitable for pressure-drop calculations in piping networks.

Excel Usage

=BEND_MITER(angle, Di, Re, miter_method)

angle (float, required): Angle of miter bend [degrees]
Di (float, optional, default: null): Inside diameter of pipe (required for Miller and Blevins methods) [m]
Re (float, optional, default: null): Reynolds number of the pipe flow (required for Miller method) [-]
miter_method (str, optional, default: “Rennels”): Calculation method

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

Example 1: 90 degree miter bend

Inputs:

angle
90

Excel formula:

=BEND_MITER(90)

Expected output:

1.20208

Example 2: 45 degree miter bend

Inputs:

angle
45

Excel formula:

=BEND_MITER(45)

Expected output:

0.304196

Example 3: 45 degree miter bend with Miller method

Inputs:

angle	Di	Re	miter_method
45	0.6	1000000	Miller

Excel formula:

=BEND_MITER(45, 0.6, 1000000, "Miller")

Expected output:

0.285421

Example 4: 150 degree miter bend

Inputs:

angle
150

Excel formula:

=BEND_MITER(150)

Expected output:

2.71281

Python Code

Show Code

from fluids.fittings import bend_miter as fluids_bend_miter

def bend_miter(angle, Di=None, Re=None, miter_method='Rennels'):
    """
    Calculate the loss coefficient (K) for a single-joint miter bend in a pipe.

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

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

    Args:
        angle (float): Angle of miter bend [degrees]
        Di (float, optional): Inside diameter of pipe (required for Miller and Blevins methods) [m] Default is None.
        Re (float, optional): Reynolds number of the pipe flow (required for Miller method) [-] Default is None.
        miter_method (str, optional): Calculation method Valid options: Rennels, Crane, Miller, Blevins. Default is 'Rennels'.

    Returns:
        float: Loss coefficient K for the miter bend [-]
    """
    try:
      try:
        angle = float(angle)
      except (ValueError, TypeError):
        return "Error: Angle must be a number."

      Di_value = None
      if Di is not None:
        try:
          Di_value = float(Di)
        except (ValueError, TypeError):
          return "Error: Di must be a number when provided."

      Re_value = None
      if Re is not None:
        try:
          Re_value = float(Re)
        except (ValueError, TypeError):
          return "Error: Re must be a number when provided."

      if angle <= 0:
        return "Error: Angle must be greater than 0 degrees."
      if Di_value is not None and Di_value <= 0:
        return "Error: Di must be positive when provided."
      if Re_value is not None and Re_value <= 0:
        return "Error: Re must be positive when provided."

      angle_limits = {
        'Rennels': 150,
        'Crane': 90,
        'Miller': 120,
        'Blevins': 120,
      }
      max_angle = angle_limits.get(miter_method)
      if max_angle is None:
        return "Error: Invalid miter_method."
      if angle > max_angle:
        return f"Error: Angle must be between 0 and {max_angle} degrees for {miter_method} method."

      kwargs = {'angle': angle, 'method': miter_method}
      if miter_method in ('Miller', 'Blevins'):
        if Di_value is None:
          return f"Error: {miter_method} method requires Di."
        kwargs['Di'] = Di_value
      if miter_method == 'Miller':
        if Re_value is None:
          return "Error: Miller method requires Re."
        kwargs['Re'] = Re_value

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

Online Calculator

angle *

Angle of miter bend [degrees]

Inside diameter of pipe (required for Miller and Blevins methods) [m]

Reynolds number of the pipe flow (required for Miller method) [-]

miter_method

Calculation method