DIFFUSER_SHARP

Computes the loss coefficient for a sudden expansion from a smaller to a larger pipe diameter.

The classical expression uses the diameter ratio term, commonly represented by K = (1-\beta^2)^2 with \beta = D_1/D_2, while alternate methods may include Reynolds effects.

The output is a dimensionless minor-loss coefficient for expansion pressure-drop calculations.

Excel Usage

=DIFFUSER_SHARP(Di_small, Di_large, Re, diff_sharp_method)

Di_small (float, required): Inside diameter of original (smaller) pipe [m]
Di_large (float, required): Inside diameter of following (larger) pipe [m]
Re (float, optional, default: 100000): Reynolds number in the smaller pipe (used for Hooper method) [-]
diff_sharp_method (str, optional, default: “Rennels”): Calculation method

Returns (float): Loss coefficient K for the sudden expansion [-]

Example 1: Basic sudden expansion (0.5m to 1m)

Inputs:

Di_small	Di_large
0.5	1

Excel formula:

=DIFFUSER_SHARP(0.5, 1)

Expected output:

0.5625

Example 2: Small expansion ratio

Inputs:

Di_small	Di_large
0.08	0.1

Excel formula:

=DIFFUSER_SHARP(0.08, 0.1)

Expected output:

0.1296

Example 3: Sudden expansion with Hooper method

Inputs:

Di_small	Di_large	Re	diff_sharp_method
0.5	1	100000	Hooper

Excel formula:

=DIFFUSER_SHARP(0.5, 1, 100000, "Hooper")

Expected output:

0.570595

Example 4: Large expansion ratio

Inputs:

Di_small	Di_large
0.1	0.5

Excel formula:

=DIFFUSER_SHARP(0.1, 0.5)

Expected output:

0.9216

Python Code

Show Code

from fluids.fittings import diffuser_sharp as fluids_diffuser_sharp

def diffuser_sharp(Di_small, Di_large, Re=100000, diff_sharp_method='Rennels'):
    """
    Calculate the loss coefficient (K) for a sudden pipe expansion (diffuser).

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

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

    Args:
        Di_small (float): Inside diameter of original (smaller) pipe [m]
        Di_large (float): Inside diameter of following (larger) pipe [m]
        Re (float, optional): Reynolds number in the smaller pipe (used for Hooper method) [-] Default is 100000.
        diff_sharp_method (str, optional): Calculation method Valid options: Rennels, Hooper. Default is 'Rennels'.

    Returns:
        float: Loss coefficient K for the sudden expansion [-]
    """
    try:
      try:
        Di1 = float(Di_small)
        Di2 = float(Di_large)
        Re = float(Re)
      except (ValueError, TypeError):
        return "Error: Di_small, Di_large, and Re must be numbers."

      if Di1 <= 0 or Di2 <= 0:
        return "Error: Diameters must be positive."
      if Di1 >= Di2:
        return "Error: Di_small must be less than Di_large."
      if Re <= 0:
        return "Error: Re must be positive."

      kwargs = {'Di1': Di1, 'Di2': Di2, 'method': diff_sharp_method}
      if diff_sharp_method == 'Hooper':
        kwargs['Re'] = Re

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

Online Calculator

Di_small *

Inside diameter of original (smaller) pipe [m]

Di_large *

Inside diameter of following (larger) pipe [m]

Reynolds number in the smaller pipe (used for Hooper method) [-]

diff_sharp_method

Calculation method