def helical_turbulent_fd_Schmidt(Re, Di, Dc, roughness=0):
    r'''Calculates Darcy friction factor for a fluid flowing inside a curved 
    pipe such as a helical coil under turbulent conditions, using the method of 
    Schmidt [1]_, also shown in [2]_.
    
    For :math:`Re_{crit} < Re < 2.2\times 10^{4}`:
    
    .. math::
        f_{curv} = f_{\text{str,turb}} \left[1 + \frac{2.88\times10^{4}}{Re}
        \left(\frac{D_i}{D_c}\right)^{0.62}\right]
        
    For :math:`2.2\times 10^{4} < Re < 1.5\times10^{5}`:
        
    .. math::
        f_{curv} = f_{\text{str,turb}} \left[1 + 0.0823\left(1 + \frac{D_i}
        {D_c}\right)\left(\frac{D_i}{D_c}\right)^{0.53} Re^{0.25}\right]

    Parameters
    ----------
    Re : float
        Reynolds number with `D=Di`, [-]
    Di : float
        Inner diameter of the coil, [m]
    Dc : float
        Diameter of the helix/coil measured from the center of the tube on one
        side to the center of the tube on the other side, [m]
    roughness : float, optional
        Roughness of pipe wall [m]        

    Returns
    -------
    fd : float
        Darcy friction factor for a curved pipe [-]

    Notes
    -----    
    Valid from the transition to turbulent flow up to 
    :math:`Re=1.5\times 10^{5}`. At very low curvatures, converges on the
    straight pipe result.

    Examples
    --------
    >>> helical_turbulent_fd_Schmidt(1E4, 0.01, .02)
    0.08875550767040916

    References
    ----------
    .. [1] Schmidt, Eckehard F. "Wärmeübergang Und Druckverlust in 
       Rohrschlangen." Chemie Ingenieur Technik 39, no. 13 (July 10, 1967): 
       781-89. doi:10.1002/cite.330391302.
    .. [2] El-Genk, Mohamed S., and Timothy M. Schriener. "A Review and 
       Correlations for Convection Heat Transfer and Pressure Losses in 
       Toroidal and Helically Coiled Tubes." Heat Transfer Engineering 0, no. 0
       (June 7, 2016): 1-28. doi:10.1080/01457632.2016.1194693.
    '''
    fd = friction_factor(Re=Re, eD=roughness/Di)
    if Re < 2.2E4:
        return fd*(1. + 2.88E4/Re*(Di/Dc)**0.62)
    else:
        return fd*(1. + 0.0823*(1. + Di/Dc)*(Di/Dc)**0.53*Re**0.25)
r'''Calculates Darcy friction factor for a fluid flowing inside a curved 
    pipe such as a helical coil under turbulent conditions, using the method of 
    Schmidt [1]_, also shown in [2]_.
    
    For :math:`Re_{crit} < Re < 2.2\times 10^{4}`:
    
    .. math::
        f_{curv} = f_{\text{str,turb}} \left[1 + \frac{2.88\times10^{4}}{Re}
        \left(\frac{D_i}{D_c}\right)^{0.62}\right]
        
    For :math:`2.2\times 10^{4} < Re < 1.5\times10^{5}`:
        
    .. math::
        f_{curv} = f_{\text{str,turb}} \left[1 + 0.0823\left(1 + \frac{D_i}
        {D_c}\right)\left(\frac{D_i}{D_c}\right)^{0.53} Re^{0.25}\right]

    Parameters
    ----------
    Re : float
        Reynolds number with `D=Di`, [-]
    Di : float
        Inner diameter of the coil, [m]
    Dc : float
        Diameter of the helix/coil measured from the center of the tube on one
        side to the center of the tube on the other side, [m]
    roughness : float, optional
        Roughness of pipe wall [m]        

    Returns
    -------
    fd : float
        Darcy friction factor for a curved pipe [-]

    Notes
    -----    
    Valid from the transition to turbulent flow up to 
    :math:`Re=1.5\times 10^{5}`. At very low curvatures, converges on the
    straight pipe result.

    Examples
    --------
    >>> helical_turbulent_fd_Schmidt(1E4, 0.01, .02)
    0.08875550767040916

    References
    ----------
    .. [1] Schmidt, Eckehard F. "Wärmeübergang Und Druckverlust in 
       Rohrschlangen." Chemie Ingenieur Technik 39, no. 13 (July 10, 1967): 
       781-89. doi:10.1002/cite.330391302.
    .. [2] El-Genk, Mohamed S., and Timothy M. Schriener. "A Review and 
       Correlations for Convection Heat Transfer and Pressure Losses in 
       Toroidal and Helically Coiled Tubes." Heat Transfer Engineering 0, no. 0
       (June 7, 2016): 1-28. doi:10.1080/01457632.2016.1194693.