open(my $in_fh, '<', $in_qfn)
    or die("Can't open input file \"$in_qfn\": $!\n");

my $out_fh;
my $file_num = 0;

while (<$in_fh>) {
    if ($. % $max_file_size == 1) {
        undef $out_fh;
    }

    if (!defined($out_fh)) {
        my $out_qfn = sprintf('part%04d', $file_num++);
        open($out_fh, '<', $out_qfn)
            or die("Can't create output file \"$out_qfn\": $!\n");
    }

    print $out_fh $_;
}