def eq_15_plume_velocity(T_0: float, g: float, c_p_0_kJ_kg_K: float, rho_0:
    float, Q_dot_c_kW: float, z: float, z_0: float):
    """Equation 15 in Section 8.3.3 PD 7974-1:2019 calculates mean gas velocity along fire centre-line.

    :param T_0: in K, ambient air temperature.
    :param g: in m/s^2, acceleration due to gravity.
    :param c_p_0_kJ_kg_K: in kJ/kg/K, specific heat capacity of ambient air.
    :param rho_0: in kg/m^3, density of ambient air.
    :param Q_dot_c_kW: in kW, convective heat release rate.
    :param z: in m, height above fuel surface.
    :param z_0: in m, virtual fire origin.
    :return u_bar_cl: in m/s, mean gas velocity of plume.
    """
    aa = (g / (c_p_0_kJ_kg_K * rho_0 * T_0)) ** (1 / 3)
    bb = Q_dot_c_kW ** (1 / 3)
    cc = (z - z_0) ** (-1 / 3)
    u_bar_cl = 3.4 * aa * bb * cc
    return u_bar_cl
