ORIFICE_EXPAND

This function calculates the orifice-plate expansibility factor \epsilon, which corrects differential-pressure flow equations for gas compressibility. The factor depends on beta ratio, pressure ratio, and isentropic exponent.

The implemented relation is:

\epsilon = 1 - \left(0.351 + 0.256\beta^4 + 0.93\beta^8\right)\left[1-\left(\frac{P_2}{P_1}\right)^{1/k}\right]

with \beta = D_o/D. For nearly incompressible behavior or small pressure drops, \epsilon approaches 1.

Excel Usage

=ORIFICE_EXPAND(pipe_diameter, orifice_diameter, upstream_pressure, downstream_pressure, isentropic_exponent)

• pipe_diameter (float, required): Upstream internal pipe diameter (m)
• orifice_diameter (float, required): Diameter of orifice at flow conditions (m)
• upstream_pressure (float, required): Static pressure upstream of orifice (Pa)
• downstream_pressure (float, required): Static pressure downstream of orifice (Pa)
• isentropic_exponent (float, required): Isentropic exponent of fluid (dimensionless)

Returns (float): Expansibility factor (1 for incompressible fluids, less than 1 for compressible fluids), dimensionless [-]

Example 1: Standard orifice with air flow

Inputs:

pipe_diameter	orifice_diameter	upstream_pressure	downstream_pressure	isentropic_exponent
0.0739	0.0222	100000	99000	1.4

Excel formula:

=ORIFICE_EXPAND(0.0739, 0.0222, 100000, 99000, 1.4)

Expected output:

0.997474

Example 2: High pressure drop case

Inputs:

pipe_diameter	orifice_diameter	upstream_pressure	downstream_pressure	isentropic_exponent
0.1	0.05	1000000	900000	1.3

Excel formula:

=ORIFICE_EXPAND(0.1, 0.05, 1000000, 900000, 1.3)

Expected output:

0.971147

Example 3: Low pressure drop case

Inputs:

pipe_diameter	orifice_diameter	upstream_pressure	downstream_pressure	isentropic_exponent
0.1	0.05	200000	199000	1.4

Excel formula:

=ORIFICE_EXPAND(0.1, 0.05, 200000, 199000, 1.4)

Expected output:

0.998675

Example 4: Nearly incompressible fluid

Inputs:

pipe_diameter	orifice_diameter	upstream_pressure	downstream_pressure	isentropic_exponent
0.1	0.05	200000	199500	1.4

Excel formula:

=ORIFICE_EXPAND(0.1, 0.05, 200000, 199500, 1.4)

Expected output:

0.999338

Python Code

Show Code

from fluids.flow_meter import orifice_expansibility as fluids_orifice_expansibility

def orifice_expand(pipe_diameter, orifice_diameter, upstream_pressure, downstream_pressure, isentropic_exponent):
    """
    Calculate the expansibility factor for an orifice plate based on geometry and pressure conditions.

    See: https://fluids.readthedocs.io/fluids.flow_meter.html#fluids.flow_meter.orifice_expansibility

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

    Args:
        pipe_diameter (float): Upstream internal pipe diameter (m)
        orifice_diameter (float): Diameter of orifice at flow conditions (m)
        upstream_pressure (float): Static pressure upstream of orifice (Pa)
        downstream_pressure (float): Static pressure downstream of orifice (Pa)
        isentropic_exponent (float): Isentropic exponent of fluid (dimensionless)

    Returns:
        float: Expansibility factor (1 for incompressible fluids, less than 1 for compressible fluids), dimensionless [-]
    """
    try:
      pipe_diameter = float(pipe_diameter)
      orifice_diameter = float(orifice_diameter)
      upstream_pressure = float(upstream_pressure)
      downstream_pressure = float(downstream_pressure)
      isentropic_exponent = float(isentropic_exponent)

      if pipe_diameter <= 0:
        return "Error: Pipe_diameter must be positive."
      if orifice_diameter <= 0:
        return "Error: Orifice_diameter must be positive."
      if orifice_diameter >= pipe_diameter:
        return "Error: Orifice_diameter must be less than pipe_diameter."
      if upstream_pressure <= 0:
        return "Error: Upstream_pressure must be positive."
      if downstream_pressure <= 0:
        return "Error: Downstream_pressure must be positive."
      if isentropic_exponent <= 0:
        return "Error: Isentropic_exponent must be positive."

      result = fluids_orifice_expansibility(
        D=pipe_diameter,
        Do=orifice_diameter,
        P1=upstream_pressure,
        P2=downstream_pressure,
        k=isentropic_exponent
      )
      return float(result)
    except (TypeError, ValueError):
      return "Error: All parameters must be valid numbers."
    except Exception as e:
      return f"Error: {str(e)}"

Online Calculator

pipe_diameter *

Upstream internal pipe diameter (m)

orifice_diameter *

Diameter of orifice at flow conditions (m)

upstream_pressure *

Static pressure upstream of orifice (Pa)

downstream_pressure *

Static pressure downstream of orifice (Pa)

isentropic_exponent *

Isentropic exponent of fluid (dimensionless)