def hoop_pressure_thick(t, D_o, P_o, sig):
    """
    Number [Pa], Number [Pa], Number [m], Number [Pa] -> Number [m]

    Returns the internal pressure that induces a stress, sig, in a thick
    walled pipe of thickness t.

    Equation (5)
    """
    return sig * (D_o ** 2 - (D_o - 2 * t) ** 2) / (D_o ** 2 + (D_o - 2 * t
        ) ** 2) + P_o
