def Bhirud_normal(T, Tc, Pc, omega):
    r'''Calculates saturation liquid density using the Bhirud [1]_ CSP method.
    Uses Critical temperature and pressure and acentric factor.

    The density of a liquid is given by:

    .. math::
        &\ln \frac{P_c}{\rho RT} = \ln U^{(0)} + \omega\ln U^{(1)}

        &\ln U^{(0)} = 1.396 44 - 24.076T_r+ 102.615T_r^2
        -255.719T_r^3+355.805T_r^4-256.671T_r^5 + 75.1088T_r^6

        &\ln U^{(1)} = 13.4412 - 135.7437 T_r + 533.380T_r^2-
        1091.453T_r^3+1231.43T_r^4 - 728.227T_r^5 + 176.737T_r^6

    Parameters
    ----------
    T : float
        Temperature of fluid [K]
    Tc : float
        Critical temperature of fluid [K]
    Pc : float
        Critical pressure of fluid [Pa]
    omega : float
        Acentric factor for fluid, [-]

    Returns
    -------
    Vm : float
        Saturated liquid molar volume, [mol/m^3]

    Notes
    -----
    Claimed inadequate by others.

    An interpolation table for ln U values are used from Tr = 0.98 - 1.000.
    Has terrible behavior at low reduced temperatures.

    Examples
    --------
    Pentane

    >>> Bhirud_normal(280.0, 469.7, 33.7E5, 0.252)
    0.00011249654029488583

    References
    ----------
    .. [1] Bhirud, Vasant L. "Saturated Liquid Densities of Normal Fluids."
       AIChE Journal 24, no. 6 (November 1, 1978): 1127-31.
       doi:10.1002/aic.690240630
    '''
    Tr = T/Tc
    if Tr <= 0.98:
        lnU0 = 1.39644 - 24.076*Tr + 102.615*Tr**2 - 255.719*Tr**3 \
            + 355.805*Tr**4 - 256.671*Tr**5 + 75.1088*Tr**6
        lnU1 = 13.4412 - 135.7437*Tr + 533.380*Tr**2-1091.453*Tr**3 \
            + 1231.43*Tr**4 - 728.227*Tr**5 + 176.737*Tr**6
    elif Tr > 1:
        raise Exception('Critical phase, correlation does not apply')
    else:
        lnU0 = Bhirud_normal_lnU0_interp(Tr)
        lnU1 = Bhirud_normal_lnU1_interp(Tr)

    Unonpolar = exp(lnU0 + omega*lnU1)
    Vm = Unonpolar*R*T/Pc
    return Vm
def Bhirud_normal(T, Tc, Pc, omega):
    r'''Calculates saturation liquid density using the Bhirud [1]_ CSP method.
    Uses Critical temperature and pressure and acentric factor.

    The density of a liquid is given by:

    .. math::
        &\ln \frac{P_c}{\rho RT} = \ln U^{(0)} + \omega\ln U^{(1)}

        &\ln U^{(0)} = 1.396 44 - 24.076T_r+ 102.615T_r^2
        -255.719T_r^3+355.805T_r^4-256.671T_r^5 + 75.1088T_r^6

        &\ln U^{(1)} = 13.4412 - 135.7437 T_r + 533.380T_r^2-
        1091.453T_r^3+1231.43T_r^4 - 728.227T_r^5 + 176.737T_r^6

    Parameters
    ----------
    T : float
        Temperature of fluid [K]
    Tc : float
        Critical temperature of fluid [K]
    Pc : float
        Critical pressure of fluid [Pa]
    omega : float
        Acentric factor for fluid, [-]

    Returns
    -------
    Vm : float
        Saturated liquid molar volume, [mol/m^3]

    Notes
    -----
    Claimed inadequate by others.

    An interpolation table for ln U values are used from Tr = 0.98 - 1.000.
    Has terrible behavior at low reduced temperatures.

    Examples
    --------
    Pentane

    >>> Bhirud_normal(280.0, 469.7, 33.7E5, 0.252)
    0.00011249654029488583

    References
    ----------
    .. [1] Bhirud, Vasant L. "Saturated Liquid Densities of Normal Fluids."
       AIChE Journal 24, no. 6 (November 1, 1978): 1127-31.
       doi:10.1002/aic.690240630
    '''
    Tr = T/Tc
    if Tr <= 0.98:
        lnU0 = 1.39644 - 24.076*Tr + 102.615*Tr**2 - 255.719*Tr**3 \
            + 355.805*Tr**4 - 256.671*Tr**5 + 75.1088*Tr**6
        lnU1 = 13.4412 - 135.7437*Tr + 533.380*Tr**2-1091.453*Tr**3 \
            + 1231.43*Tr**4 - 728.227*Tr**5 + 176.737*Tr**6
    elif Tr > 1:
        raise Exception('Critical phase, correlation does not apply')
    else:
        lnU0 = Bhirud_normal_lnU0_interp(Tr)
        lnU1 = Bhirud_normal_lnU1_interp(Tr)

    Unonpolar = exp(lnU0 + omega*lnU1)
    Vm = Unonpolar*R*T/Pc
    return Vm
def Bhirud_normal ( T , Tc , Pc , omega ) : Tr = T / Tc if Tr <= 0.98 : lnU0 = 1.39644 - 24.076 * Tr + 102.615 * Tr ** 2 - 255.719 * Tr ** 3 + 355.805 * Tr ** 4 - 256.671 * Tr ** 5 + 75.1088 * Tr ** 6 lnU1 = 13.4412 - 135.7437 * Tr + 533.380 * Tr ** 2 - 1091.453 * Tr ** 3 + 1231.43 * Tr ** 4 - 728.227 * Tr ** 5 + 176.737 * Tr ** 6 elif Tr > 1 : raise Exception ( 'Critical phase, correlation does not apply' ) else : lnU0 = Bhirud_normal_lnU0_interp ( Tr ) lnU1 = Bhirud_normal_lnU1_interp ( Tr ) Unonpolar = exp ( lnU0 + omega * lnU1 ) Vm = Unonpolar * R * T / Pc return Vm
r'''Calculates saturation liquid density using the Bhirud [1]_ CSP method.
    Uses Critical temperature and pressure and acentric factor.

    The density of a liquid is given by:

    .. math::
        &\ln \frac{P_c}{\rho RT} = \ln U^{(0)} + \omega\ln U^{(1)}

        &\ln U^{(0)} = 1.396 44 - 24.076T_r+ 102.615T_r^2
        -255.719T_r^3+355.805T_r^4-256.671T_r^5 + 75.1088T_r^6

        &\ln U^{(1)} = 13.4412 - 135.7437 T_r + 533.380T_r^2-
        1091.453T_r^3+1231.43T_r^4 - 728.227T_r^5 + 176.737T_r^6

    Parameters
    ----------
    T : float
        Temperature of fluid [K]
    Tc : float
        Critical temperature of fluid [K]
    Pc : float
        Critical pressure of fluid [Pa]
    omega : float
        Acentric factor for fluid, [-]

    Returns
    -------
    Vm : float
        Saturated liquid molar volume, [mol/m^3]

    Notes
    -----
    Claimed inadequate by others.

    An interpolation table for ln U values are used from Tr = 0.98 - 1.000.
    Has terrible behavior at low reduced temperatures.

    Examples
    --------
    Pentane

    >>> Bhirud_normal(280.0, 469.7, 33.7E5, 0.252)
    0.00011249654029488583

    References
    ----------
    .. [1] Bhirud, Vasant L. "Saturated Liquid Densities of Normal Fluids."
       AIChE Journal 24, no. 6 (November 1, 1978): 1127-31.
       doi:10.1002/aic.690240630
r Calculates saturation liquid density using the Bhirud [ 1 ] _ CSP method . Uses Critical temperature and pressure and acentric factor .