import math


def width(theta, a_thr, b_3):
    """Calculate width volute vane at different angles.

    :param theta (float): angle at which eval. volute section [rad]
    :param a_thr (float): area at throat section [m^2]
    :param b_3 (float): volute width at section 3 [m]
    :return b, theta (tuple): volute widths [m] and relative angles [rad]
    """
    b = (2 * a_thr * theta / math.pi**2)**.5

    if b > b_3:
        return (b, theta)
    else:
        return None