def eq_12_dimensionless_hrr_line(
        Q_dot_l_kW_m: float,
        rho_0: float,
        c_p_0_kJ_kg_K: float,
        T_0: float,
        g: float,
        L_A: float,
) -> float:
    """Equation 12 in Section 8.3.2.2 PD 7974-1:2019 calculates dimensionless heat release rate for line fire source.
    Note dimension ratio should be less than 0.4 (i.e. L_A / L_B) to use line fire source correlation.

    :param Q_dot_l_kW_m: in kW/m, fire heat release rate per unit length along the line.
    :param rho_0: in kg/m^3, density of ambient air.
    :param c_p_0_kJ_kg_K: in kJ/kg/K, specific heat capacity of ambient air.
    :param T_0: in K, ambient air temperature.
    :param g: in m/s^2, acceleration due to gravity.
    :param L_A: in m, length of line shaped fire source.
    :return Q_dot_star_rect: dimensionless, dimensionless heat release rate
    """

    # equation starts
    aa = Q_dot_l_kW_m
    bb = rho_0 * c_p_0_kJ_kg_K * T_0 * (g ** 0.5) * (L_A ** 1.5)
    Q_dot_star_line = aa / bb

    return Q_dot_star_line