def flow_number_poly(cappa):
    """Calculate flow number for a given pump's typical number.

    The polynomial has been calculated applaying the curve fitting at nodes
    cappa       .2 .3 .4 .5 .6 .7 .8 .9 1.0 1.1 1.2
    phi         .080 .093 .100 .110 .120 .130 .140 .150 .160 .165 .170
    weights     ones(cappa)
    n           5

    :param cappa (float): typical number
    :return phi (float): flow number
    """
    coef = [0.029, 0.416, -1.090, 1.665, -1.149, 0.288]
    phi = sum([val * cappa**idx for idx, val in enumerate(coef)])

    return phi