DIFF_PRESS_C_EPS

This function returns the discharge coefficient C and expansibility factor \epsilon for a differential-pressure flow meter at specified operating conditions. These two factors are used together to convert measured pressure drop into mass flow rate.

The meter discharge relation has the form:

m = A_o C \epsilon \frac{\sqrt{2\rho (P_1 - P_2)}}{\sqrt{1-\beta^4}}

where A_o is the characteristic meter area, \rho is upstream density, and \beta is the meter beta ratio. The implementation uses meter-type-specific correlations from the wrapped library and returns the pair as [[C, epsilon]].

Excel Usage

=DIFF_PRESS_C_EPS(D, D_two, m, P_one, P_two, rho, mu, k, c_eps_meter_type, c_eps_taps, c_eps_tap_position)

• 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
• c_eps_taps (str, optional, default: null): Pressure tap orientation for orifice-meter correlations (-)
• c_eps_tap_position (str, optional, default: null): Pressure tap rotation for eccentric orifice configurations (-)

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

Example 1: ISO 5167 orifice with D taps

Inputs:

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

Excel formula:

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

Expected output:

Result
0.615125	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', c_eps_taps=None, c_eps_tap_position=None):
    """
    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'.
        c_eps_taps (str, optional): Pressure tap orientation for orifice-meter correlations (-) Valid options: Corner, Flange, D, D/2. Default is None.
        c_eps_tap_position (str, optional): Pressure tap rotation for eccentric orifice configurations (-) Valid options: 180 Degree, 90 Degree. Default is None.

    Returns:
        list[list]: 2D list containing discharge coefficient and expansibility factor [[C, epsilon]]
    """
    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."
        if m <= 0:
            return "Error: m (mass flow rate) must be positive."
        if P_one <= 0 or P_two <= 0:
            return "Error: P_one and P_two must be positive."
        if rho <= 0:
            return "Error: rho (density) must be positive."
        if mu <= 0:
            return "Error: mu (viscosity) must be positive."
        if k <= 0:
            return "Error: k (isentropic exponent) must be positive."
        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=c_eps_taps,
            tap_position=c_eps_tap_position,
            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

D *

Upstream internal pipe diameter (m)

D_two *

Orifice or meter characteristic diameter (m)

m *

Mass flow rate through the meter (kg/s)

P_one *

Static pressure upstream of meter at pressure tap (Pa)

P_two *

Static pressure downstream of meter at pressure tap (Pa)

rho *

Density of fluid at P1 (kg/m³)

mu *

Viscosity of fluid at P1 (Pa·s)

k *

Isentropic exponent of fluid (-)

c_eps_meter_type Optional 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

Type of differential pressure flow meter

c_eps_taps Optional Corner Flange D D/2

Pressure tap orientation for orifice-meter correlations (-)

c_eps_tap_position Optional 180 Degree 90 Degree

Pressure tap rotation for eccentric orifice configurations (-)