foreach puts the diamond op (<>) in a list context, which means that it reads until EOF, then splits it up into a list. You want it in scalar context:

    while (<$FH>) {
        sleep $time;
        print;
    }
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By the way, I changed your $_ to $FH, because it was screwing with the $_ that's the default variable in a loop. I don't know how that didn't mess you up in your code... but it did when I tried it.