Flow Meter

Overview

Flow measurement is fundamental to process control, custody transfer, and safety monitoring across industries from oil and gas to water treatment. While numerous technologies exist—including electromagnetic, ultrasonic, Coriolis, and turbine meters—differential pressure (DP) flow meters remain the most widely deployed in industrial applications due to their simplicity, robustness, standardization, and absence of moving parts.

Differential pressure flow meters operate on Bernoulli’s principle: a deliberate constriction in the flow path increases fluid velocity and creates a measurable pressure drop. Common DP meter types include orifice plates, venturi tubes, and flow nozzles, with orifice plates being the most prevalent due to their low cost and ease of installation. The fundamental relationship between flow rate Q and pressure drop \Delta P is:

Q = C_d A_t \sqrt{\frac{2 \Delta P}{\rho (1 - \beta^4)}}

where C_d is the discharge coefficient, A_t is the throat area, \rho is fluid density, and \beta is the beta ratio (throat diameter divided by pipe diameter). For compressible flows, an additional expansibility factor \varepsilon accounts for density changes across the meter.

These calculations are implemented using standard Python libraries including NumPy for numerical operations and fluids, a specialized library for fluid dynamics that provides ISO 5167-compliant correlations for discharge coefficients and pressure drop calculations.

Beta ratio (\beta = d/D) is a critical design parameter that affects meter sensitivity and permanent pressure loss. Typical values range from 0.2 to 0.75, with lower values providing higher differential pressure (better sensitivity) but greater non-recoverable pressure loss. The DIFF_PRESS_BETA tool helps engineers select the optimal beta ratio for their application, balancing measurement accuracy against energy costs.

Discharge coefficient (C_d) corrects the theoretical flow equation for real-world viscous, turbulent, and geometric effects. For orifice plates, the Reader-Harris-Gallagher correlation from ISO 5167 is the industry standard, accounting for Reynolds number, beta ratio, pipe diameter, and tap locations. The ORIFICE_DISCHARGE_C tool implements this correlation with uncertainty bands. For more general DP meters, DIFF_PRESS_C_EPS calculates both the discharge coefficient and expansibility factor.

Expansibility factor (\varepsilon) is essential for gas and steam applications where density changes significantly across the meter. It varies with pressure ratio, beta ratio, and isentropic exponent. The ORIFICE_EXPAND tool provides ISO-compliant calculations for compressible flows through orifice plates.

Pressure drop has two components: the differential pressure used for flow measurement (recoverable) and the permanent pressure loss (non-recoverable) due to turbulence and mixing downstream of the constriction. Non-recoverable pressure drop represents lost energy and operating cost. Tools like DIFF_PRESS_DP and ORIFICE_PRESS_DROP quantify this permanent loss for different meter geometries.

Flow rate calculation is the primary objective, converting measured differential pressure into mass or volumetric flow. The FLOW_METER_DISCH tool performs this calculation using measured upstream and downstream pressures along with meter geometry and fluid properties, providing the mass flow rate with appropriate corrections for real gas behavior and compressibility.

When designing a new DP meter installation, start with DIFF_PRESS_BETA to select an appropriate beta ratio, then use DIFF_PRESS_C_EPS or ORIFICE_DISCHARGE_C to determine the discharge coefficient. For operational calculations, use FLOW_METER_DISCH to convert field measurements into flow rates. Always evaluate permanent pressure loss using DIFF_PRESS_DP or ORIFICE_PRESS_DROP to understand the operating cost implications of your meter selection.

DIFF_PRESS_BETA

Calculate the beta ratio (diameter ratio) for a differential pressure flow meter.

Excel Usage

=DIFF_PRESS_BETA(D, D_two, beta_meter_type)
  • D (float, required): Upstream internal pipe diameter (m)
  • D_two (float, required): Meter characteristic diameter - orifice hole, venturi throat, cone end, or wedge height (m)
  • beta_meter_type (str, optional, default: “ISO 5167 orifice”): Type of differential pressure flow meter

Returns (float): Differential pressure meter diameter ratio (beta) (-)

Example 1: Standard orifice beta ratio

Inputs:

D D_two beta_meter_type
0.1 0.05 ISO 5167 orifice

Excel formula:

=DIFF_PRESS_BETA(0.1, 0.05, "ISO 5167 orifice")

Expected output:

0.5

Example 2: Venturi tube beta ratio

Inputs:

D D_two beta_meter_type
0.2 0.12 machined convergent venturi tube

Excel formula:

=DIFF_PRESS_BETA(0.2, 0.12, "machined convergent venturi tube")

Expected output:

0.6

Example 3: Cone meter beta ratio (uses special formula)

Inputs:

D D_two beta_meter_type
0.2575 0.184 cone meter

Excel formula:

=DIFF_PRESS_BETA(0.2575, 0.184, "cone meter")

Expected output:

0.699571

Example 4: Wedge meter beta ratio (uses special formula)

Inputs:

D D_two beta_meter_type
0.2027 0.0608 wedge meter

Excel formula:

=DIFF_PRESS_BETA(0.2027, 0.0608, "wedge meter")

Expected output:

0.502253

Python Code

Show Code 
from fluids.flow_meter import differential_pressure_meter_beta

def diff_press_beta(D, D_two, beta_meter_type='ISO 5167 orifice'):
    """
    Calculate the beta ratio (diameter ratio) for a differential pressure flow meter.

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

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

    Args:
        D (float): Upstream internal pipe diameter (m)
        D_two (float): Meter characteristic diameter - orifice hole, venturi throat, cone end, or wedge height (m)
        beta_meter_type (str, optional): Type of differential pressure flow meter Valid options: ISO 5167 Orifice, Orifice, Conical Orifice, Eccentric Orifice, Segmental Orifice, Quarter Circle Orifice, Venturi Nozzle, ISA 1932 Nozzle, Long Radius Nozzle, Machined Convergent Venturi Tube, Rough Welded Convergent Venturi Tube, As Cast Convergent Venturi Tube, Cone Meter, Wedge Meter. Default is 'ISO 5167 orifice'.

    Returns:
        float: Differential pressure meter diameter ratio (beta) (-)
    """
    try:
      if D <= 0:
        return "Error: D (upstream diameter) must be positive."
      if D_two <= 0:
        return "Error: D_two (meter diameter) must be positive."
      result = differential_pressure_meter_beta(
        D=D,
        D2=D_two,
        meter_type=beta_meter_type
      )
      return float(result)
    except Exception as e:
      return f"Error: {str(e)}"

Online Calculator

Upstream internal pipe diameter (m)
Meter characteristic diameter - orifice hole, venturi throat, cone end, or wedge height (m)
Type of differential pressure flow meter

DIFF_PRESS_C_EPS

Calculate discharge coefficient and expansibility factor for differential pressure flow meters.

Excel Usage

=DIFF_PRESS_C_EPS(D, D_two, m, P_one, P_two, rho, mu, k, c_eps_meter_type)
  • D (float, required): Upstream internal pipe diameter (m)
  • D_two (float, required): Orifice or meter characteristic diameter (m)
  • m (float, required): Mass flow rate through the meter (kg/s)
  • P_one (float, required): Static pressure upstream of meter at pressure tap (Pa)
  • P_two (float, required): Static pressure downstream of meter at pressure tap (Pa)
  • rho (float, required): Density of fluid at P1 (kg/m³)
  • mu (float, required): Viscosity of fluid at P1 (Pa·s)
  • k (float, required): Isentropic exponent of fluid (-)
  • c_eps_meter_type (str, optional, default: “ISO 5167 orifice”): Type of differential pressure flow meter

Returns (list[list]): 2D list containing discharge coefficient and expansibility factor [[C, epsilon]]

Example 1: ISO 5167 orifice with air flow

Inputs:

D D_two m P_one P_two rho mu k c_eps_meter_type
0.07366 0.05 7.702338 200000 183000 999.1 0.0011 1.33 ISO 5167 orifice

Excel formula:

=DIFF_PRESS_C_EPS(0.07366, 0.05, 7.702338, 200000, 183000, 999.1, 0.0011, 1.33, "ISO 5167 orifice")

Expected output:

Result
0.60977 0.971103
Example 2: Machined venturi tube

Inputs:

D D_two m P_one P_two rho mu k c_eps_meter_type
0.1 0.06 5 150000 140000 1000 0.001 1.4 machined convergent venturi tube

Excel formula:

=DIFF_PRESS_C_EPS(0.1, 0.06, 5, 150000, 140000, 1000, 0.001, 1.4, "machined convergent venturi tube")

Expected output:

Result
0.995 0.956963
Example 3: V-cone meter

Inputs:

D D_two m P_one P_two rho mu k c_eps_meter_type
0.2 0.15 10 300000 280000 850 0.002 1.3 cone meter

Excel formula:

=DIFF_PRESS_C_EPS(0.2, 0.15, 10, 300000, 280000, 850, 0.002, 1.3, "cone meter")

Expected output:

Result
0.82 0.959886
Example 4: Wedge flow meter

Inputs:

D D_two m P_one P_two rho mu k c_eps_meter_type
0.15 0.05 3 100000 95000 800 0.0015 1.35 wedge meter

Excel formula:

=DIFF_PRESS_C_EPS(0.15, 0.05, 3, 100000, 95000, 800, 0.0015, 1.35, "wedge meter")

Expected output:

Result
0.721384 0.968564

Python Code

Show Code 
from fluids.flow_meter import differential_pressure_meter_C_epsilon

def diff_press_c_eps(D, D_two, m, P_one, P_two, rho, mu, k, c_eps_meter_type='ISO 5167 orifice'):
    """
    Calculate discharge coefficient and expansibility factor for differential pressure flow meters.

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

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

    Args:
        D (float): Upstream internal pipe diameter (m)
        D_two (float): Orifice or meter characteristic diameter (m)
        m (float): Mass flow rate through the meter (kg/s)
        P_one (float): Static pressure upstream of meter at pressure tap (Pa)
        P_two (float): Static pressure downstream of meter at pressure tap (Pa)
        rho (float): Density of fluid at P1 (kg/m³)
        mu (float): Viscosity of fluid at P1 (Pa·s)
        k (float): Isentropic exponent of fluid (-)
        c_eps_meter_type (str, optional): Type of differential pressure flow meter Valid options: ISO 5167 Orifice, Orifice, Conical Orifice, Eccentric Orifice, Segmental Orifice, Quarter Circle Orifice, ISO 15377 Conical Orifice, ISO 15377 Eccentric Orifice, ISO 15377 Quarter-circle Orifice, Miller Orifice, Miller Conical Orifice, Miller Eccentric Orifice, Miller Segmental Orifice, Miller Quarter Circle Orifice, Hollingshead Orifice, Venturi Nozzle, ISA 1932 Nozzle, Long Radius Nozzle, Machined Convergent Venturi Tube, Rough Welded Convergent Venturi Tube, As Cast Convergent Venturi Tube, Hollingshead Venturi Smooth, Hollingshead Venturi Sharp, Cone Meter, Hollingshead V Cone, Wedge Meter, Hollingshead Wedge, Unspecified Meter. Default is 'ISO 5167 orifice'.

    Returns:
        list[list]: 2D list containing discharge coefficient and expansibility factor [[C, epsilon]]
    """
    try:
        result = differential_pressure_meter_C_epsilon(
            D=D,
            D2=D_two,
            m=m,
            P1=P_one,
            P2=P_two,
            rho=rho,
            mu=mu,
            k=k,
            meter_type=c_eps_meter_type,
            taps=None,
            tap_position=None,
            C_specified=None,
            epsilon_specified=None
        )

        # Result is a tuple (C, epsilon) - return as 2D list
        C, epsilon = result
        return [[float(C), float(epsilon)]]
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

Upstream internal pipe diameter (m)
Orifice or meter characteristic diameter (m)
Mass flow rate through the meter (kg/s)
Static pressure upstream of meter at pressure tap (Pa)
Static pressure downstream of meter at pressure tap (Pa)
Density of fluid at P1 (kg/m³)
Viscosity of fluid at P1 (Pa·s)
Isentropic exponent of fluid (-)
Type of differential pressure flow meter

DIFF_PRESS_DP

Calculate non-recoverable pressure drop across a differential pressure flow meter.

Excel Usage

=DIFF_PRESS_DP(D, D_two, P_one, P_two, C, dp_meter_type)
  • D (float, required): Upstream internal pipe diameter (m)
  • D_two (float, required): Meter characteristic diameter - orifice hole, venturi throat, cone end, or wedge height (m)
  • P_one (float, required): Static pressure upstream at pressure tap (Pa)
  • P_two (float, required): Static pressure downstream at pressure tap (Pa)
  • C (float, optional, default: 0.6): Coefficient of discharge (required for orifice plates and venturi nozzles) (-)
  • dp_meter_type (str, optional, default: “ISO 5167 orifice”): Type of differential pressure flow meter

Returns (float): Non-recoverable pressure drop of the flow meter (Pa)

Example 1: As-cast venturi tube pressure drop

Inputs:

D D_two P_one P_two dp_meter_type
0.07366 0.05 200000 183000 as cast convergent venturi tube

Excel formula:

=DIFF_PRESS_DP(0.07366, 0.05, 200000, 183000, "as cast convergent venturi tube")

Expected output:

1788.57

Example 2: Cone meter pressure drop

Inputs:

D D_two P_one P_two dp_meter_type
0.25 0.18 1000000 950000 cone meter

Excel formula:

=DIFF_PRESS_DP(0.25, 0.18, 1000000, 950000, "cone meter")

Expected output:

26290

Example 3: Wedge meter pressure drop

Inputs:

D D_two P_one P_two dp_meter_type
0.2 0.14 1000000 950000 wedge meter

Excel formula:

=DIFF_PRESS_DP(0.2, 0.14, 1000000, 950000, "wedge meter")

Expected output:

20344.8

Example 4: Orifice with discharge coefficient

Inputs:

D D_two P_one P_two C dp_meter_type
0.1 0.05 150000 145000 0.61 ISO 5167 orifice

Excel formula:

=DIFF_PRESS_DP(0.1, 0.05, 150000, 145000, 0.61, "ISO 5167 orifice")

Expected output:

3653.64

Python Code

Show Code 
from fluids.flow_meter import differential_pressure_meter_dP

def diff_press_dp(D, D_two, P_one, P_two, C=0.6, dp_meter_type='ISO 5167 orifice'):
    """
    Calculate non-recoverable pressure drop across a differential pressure flow meter.

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

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

    Args:
        D (float): Upstream internal pipe diameter (m)
        D_two (float): Meter characteristic diameter - orifice hole, venturi throat, cone end, or wedge height (m)
        P_one (float): Static pressure upstream at pressure tap (Pa)
        P_two (float): Static pressure downstream at pressure tap (Pa)
        C (float, optional): Coefficient of discharge (required for orifice plates and venturi nozzles) (-) Default is 0.6.
        dp_meter_type (str, optional): Type of differential pressure flow meter Valid options: ISO 5167 Orifice, Orifice, Conical Orifice, Eccentric Orifice, Segmental Orifice, Quarter Circle Orifice, Venturi Nozzle, ISA 1932 Nozzle, Long Radius Nozzle, Machined Convergent Venturi Tube, Rough Welded Convergent Venturi Tube, As Cast Convergent Venturi Tube, Cone Meter, Wedge Meter. Default is 'ISO 5167 orifice'.

    Returns:
        float: Non-recoverable pressure drop of the flow meter (Pa)
    """
    try:
      if D <= 0:
        return "Error: D (upstream diameter) must be positive."
      if D_two <= 0:
        return "Error: D_two (meter diameter) must be positive."
      result = differential_pressure_meter_dP(
        D=D,
        D2=D_two,
        P1=P_one,
        P2=P_two,
        C=C,
        meter_type=dp_meter_type
      )
      return float(result)
    except Exception as e:
      return f"Error: {str(e)}"

Online Calculator

Upstream internal pipe diameter (m)
Meter characteristic diameter - orifice hole, venturi throat, cone end, or wedge height (m)
Static pressure upstream at pressure tap (Pa)
Static pressure downstream at pressure tap (Pa)
Coefficient of discharge (required for orifice plates and venturi nozzles) (-)
Type of differential pressure flow meter

FLOW_METER_DISCH

Calculate mass flow rate through a differential pressure flow meter based on measured pressures and meter geometry.

Excel Usage

=FLOW_METER_DISCH(D, Do, P_one, P_two, rho, C, expansibility, disch_meter_type)
  • D (float, required): Upstream internal pipe diameter (m)
  • Do (float, required): Meter characteristic diameter - orifice hole, venturi throat, cone end, or wedge height (m)
  • P_one (float, required): Static pressure upstream at pressure tap (Pa)
  • P_two (float, required): Static pressure downstream at pressure tap (Pa)
  • rho (float, required): Density of fluid at P1 (kg/m³)
  • C (float, required): Coefficient of discharge of the meter (-)
  • expansibility (float, optional, default: 1): Expansibility factor (1 for incompressible, <1 for compressible) (-)
  • disch_meter_type (str, optional, default: “ISO 5167 orifice”): Type of differential pressure flow meter

Returns (float): Mass flow rate of fluid through the meter (kg/s)

Example 1: ISO 5167 orifice with air

Inputs:

D Do P_one P_two rho C expansibility disch_meter_type
0.0739 0.0222 100000 99000 1.1646 0.5988 0.9975 ISO 5167 orifice

Excel formula:

=FLOW_METER_DISCH(0.0739, 0.0222, 100000, 99000, 1.1646, 0.5988, 0.9975, "ISO 5167 orifice")

Expected output:

0.0112039

Example 2: Machined venturi with water

Inputs:

D Do P_one P_two rho C expansibility disch_meter_type
0.1 0.06 150000 145000 998 0.995 1 machined convergent venturi tube

Excel formula:

=FLOW_METER_DISCH(0.1, 0.06, 150000, 145000, 998, 0.995, 1, "machined convergent venturi tube")

Expected output:

9.52624

Example 3: Cone meter with oil

Inputs:

D Do P_one P_two rho C disch_meter_type
0.2 0.15 300000 290000 850 0.82 cone meter

Excel formula:

=FLOW_METER_DISCH(0.2, 0.15, 300000, 290000, 850, 0.82, "cone meter")

Expected output:

51.6774

Example 4: Wedge meter

Inputs:

D Do P_one P_two rho C disch_meter_type
0.15 0.05 100000 98000 800 0.73 wedge meter

Excel formula:

=FLOW_METER_DISCH(0.15, 0.05, 100000, 98000, 800, 0.73, "wedge meter")

Expected output:

7.03989

Python Code

Show Code 
from fluids.flow_meter import flow_meter_discharge

def flow_meter_disch(D, Do, P_one, P_two, rho, C, expansibility=1, disch_meter_type='ISO 5167 orifice'):
    """
    Calculate mass flow rate through a differential pressure flow meter based on measured pressures and meter geometry.

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

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

    Args:
        D (float): Upstream internal pipe diameter (m)
        Do (float): Meter characteristic diameter - orifice hole, venturi throat, cone end, or wedge height (m)
        P_one (float): Static pressure upstream at pressure tap (Pa)
        P_two (float): Static pressure downstream at pressure tap (Pa)
        rho (float): Density of fluid at P1 (kg/m³)
        C (float): Coefficient of discharge of the meter (-)
        expansibility (float, optional): Expansibility factor (1 for incompressible, <1 for compressible) (-) Default is 1.
        disch_meter_type (str, optional): Type of differential pressure flow meter Valid options: ISO 5167 Orifice, Orifice, Conical Orifice, Eccentric Orifice, Segmental Orifice, Quarter Circle Orifice, Venturi Nozzle, ISA 1932 Nozzle, Long Radius Nozzle, Machined Convergent Venturi Tube, Rough Welded Convergent Venturi Tube, As Cast Convergent Venturi Tube, Cone Meter, Wedge Meter. Default is 'ISO 5167 orifice'.

    Returns:
        float: Mass flow rate of fluid through the meter (kg/s)
    """
    try:
      if D <= 0:
        return "Error: D (upstream diameter) must be positive."
      if Do <= 0:
        return "Error: Do (meter diameter) must be positive."
      result = flow_meter_discharge(
        D=D,
        Do=Do,
        P1=P_one,
        P2=P_two,
        rho=rho,
        C=C,
        expansibility=expansibility,
        meter_type=disch_meter_type
      )
      return float(result)
    except Exception as e:
      return f"Error: {str(e)}"

Online Calculator

Upstream internal pipe diameter (m)
Meter characteristic diameter - orifice hole, venturi throat, cone end, or wedge height (m)
Static pressure upstream at pressure tap (Pa)
Static pressure downstream at pressure tap (Pa)
Density of fluid at P1 (kg/m³)
Coefficient of discharge of the meter (-)
Expansibility factor (1 for incompressible, <1 for compressible) (-)
Type of differential pressure flow meter

ORIFICE_DISCHARGE_C

Calculate the discharge coefficient for an orifice plate using the Reader-Harris-Gallagher correlation (ISO 5167 standard).

Excel Usage

=ORIFICE_DISCHARGE_C(pipe_diameter, orifice_diameter, density, viscosity, mass_flow_rate, orifice_taps)
  • pipe_diameter (float, required): Upstream internal pipe diameter (m)
  • orifice_diameter (float, required): Diameter of orifice at flow conditions (m)
  • density (float, required): Density of fluid (kg/m³)
  • viscosity (float, required): Viscosity of fluid (Pa·s)
  • mass_flow_rate (float, required): Mass flow rate of fluid through the orifice (kg/s)
  • orifice_taps (str, optional, default: “corner”): Orientation of the pressure taps

Returns (float): Coefficient of discharge of the orifice plate, dimensionless [-]

Example 1: Standard orifice with flange taps

Inputs:

pipe_diameter orifice_diameter density viscosity mass_flow_rate orifice_taps
0.07391 0.0222 1.165 0.0000185 0.12 flange

Excel formula:

=ORIFICE_DISCHARGE_C(0.07391, 0.0222, 1.165, 0.0000185, 0.12, "flange")

Expected output:

0.599033

Example 2: Orifice with corner taps

Inputs:

pipe_diameter orifice_diameter density viscosity mass_flow_rate orifice_taps
0.07391 0.0222 1.165 0.0000185 0.12 corner

Excel formula:

=ORIFICE_DISCHARGE_C(0.07391, 0.0222, 1.165, 0.0000185, 0.12, "corner")

Expected output:

0.600037

Example 3: Orifice with D taps

Inputs:

pipe_diameter orifice_diameter density viscosity mass_flow_rate orifice_taps
0.1 0.05 998.2 0.001 5 D

Excel formula:

=ORIFICE_DISCHARGE_C(0.1, 0.05, 998.2, 0.001, 5, "D")

Expected output:

0.607351

Example 4: Orifice with D/2 taps

Inputs:

pipe_diameter orifice_diameter density viscosity mass_flow_rate orifice_taps
0.1 0.05 998.2 0.001 5 D/2

Excel formula:

=ORIFICE_DISCHARGE_C(0.1, 0.05, 998.2, 0.001, 5, "D/2")

Expected output:

0.607351

Python Code

Show Code 
from fluids.flow_meter import C_Reader_Harris_Gallagher as fluids_c_reader_harris_gallagher

def orifice_discharge_c(pipe_diameter, orifice_diameter, density, viscosity, mass_flow_rate, orifice_taps='corner'):
    """
    Calculate the discharge coefficient for an orifice plate using the Reader-Harris-Gallagher correlation (ISO 5167 standard).

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

    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)
        density (float): Density of fluid (kg/m³)
        viscosity (float): Viscosity of fluid (Pa·s)
        mass_flow_rate (float): Mass flow rate of fluid through the orifice (kg/s)
        orifice_taps (str, optional): Orientation of the pressure taps Valid options: Corner, Flange, D, D/2. Default is 'corner'.

    Returns:
        float: Coefficient of discharge of the orifice plate, dimensionless [-]
    """
    try:
      pipe_diameter = float(pipe_diameter)
      orifice_diameter = float(orifice_diameter)
      density = float(density)
      viscosity = float(viscosity)
      mass_flow_rate = float(mass_flow_rate)

      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 density <= 0:
        return "Error: Density must be positive."
      if viscosity <= 0:
        return "Error: Viscosity must be positive."
      if mass_flow_rate <= 0:
        return "Error: Mass_flow_rate must be positive."

      result = fluids_c_reader_harris_gallagher(
        D=pipe_diameter,
        Do=orifice_diameter,
        rho=density,
        mu=viscosity,
        m=mass_flow_rate,
        taps=orifice_taps
      )
      return float(result)
    except (TypeError, ValueError):
      return "Error: All numeric parameters must be valid numbers."
    except Exception as e:
      return f"Error: {str(e)}"

Online Calculator

Upstream internal pipe diameter (m)
Diameter of orifice at flow conditions (m)
Density of fluid (kg/m³)
Viscosity of fluid (Pa·s)
Mass flow rate of fluid through the orifice (kg/s)
Orientation of the pressure taps

ORIFICE_EXPAND

Calculate the expansibility factor for an orifice plate based on geometry and pressure conditions.

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

Upstream internal pipe diameter (m)
Diameter of orifice at flow conditions (m)
Static pressure upstream of orifice (Pa)
Static pressure downstream of orifice (Pa)
Isentropic exponent of fluid (dimensionless)

ORIFICE_PRESS_DROP

Calculate non-recoverable pressure drop across an orifice plate based on geometry and discharge coefficient.

Excel Usage

=ORIFICE_PRESS_DROP(D, Do, P_one, P_two, C)
  • D (float, required): Upstream internal pipe diameter (m)
  • Do (float, required): Diameter of orifice at flow conditions (m)
  • P_one (float, required): Static pressure upstream of orifice at pressure tap cross-section (Pa)
  • P_two (float, required): Static pressure downstream of orifice at pressure tap cross-section (Pa)
  • C (float, required): Coefficient of discharge of the orifice (-)

Returns (float): Non-recoverable pressure drop of the orifice plate (Pa)

Example 1: Standard orifice pressure drop

Inputs:

D Do P_one P_two C
0.07366 0.05 200000 183000 0.61512

Excel formula:

=ORIFICE_PRESS_DROP(0.07366, 0.05, 200000, 183000, 0.61512)

Expected output:

9069.47

Example 2: Large orifice high beta ratio

Inputs:

D Do P_one P_two C
0.1 0.075 150000 145000 0.65

Excel formula:

=ORIFICE_PRESS_DROP(0.1, 0.075, 150000, 145000, 0.65)

Expected output:

2120.29

Example 3: Small orifice low beta ratio

Inputs:

D Do P_one P_two C
0.1 0.03 200000 180000 0.6

Excel formula:

=ORIFICE_PRESS_DROP(0.1, 0.03, 200000, 180000, 0.6)

Expected output:

17945.6

Example 4: High discharge coefficient

Inputs:

D Do P_one P_two C
0.05 0.03 100000 95000 0.7

Excel formula:

=ORIFICE_PRESS_DROP(0.05, 0.03, 100000, 95000, 0.7)

Expected output:

2931.69

Python Code

Show Code 
from fluids.flow_meter import dP_orifice

def orifice_press_drop(D, Do, P_one, P_two, C):
    """
    Calculate non-recoverable pressure drop across an orifice plate based on geometry and discharge coefficient.

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

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

    Args:
        D (float): Upstream internal pipe diameter (m)
        Do (float): Diameter of orifice at flow conditions (m)
        P_one (float): Static pressure upstream of orifice at pressure tap cross-section (Pa)
        P_two (float): Static pressure downstream of orifice at pressure tap cross-section (Pa)
        C (float): Coefficient of discharge of the orifice (-)

    Returns:
        float: Non-recoverable pressure drop of the orifice plate (Pa)
    """
    try:
      if D <= 0:
        return "Error: D (upstream diameter) must be positive."
      if Do <= 0:
        return "Error: Do (orifice diameter) must be positive."
      if C <= 0:
        return "Error: C (discharge coefficient) must be positive."
      result = dP_orifice(
        D=D,
        Do=Do,
        P1=P_one,
        P2=P_two,
        C=C
      )
      return float(result)
    except Exception as e:
      return f"Error: {str(e)}"

Online Calculator

Upstream internal pipe diameter (m)
Diameter of orifice at flow conditions (m)
Static pressure upstream of orifice at pressure tap cross-section (Pa)
Static pressure downstream of orifice at pressure tap cross-section (Pa)
Coefficient of discharge of the orifice (-)