A command line utility to visualize how fast a file is growing?

tail -f file | pv > /dev/null

But beware that it involves acually reading the file, so it might consume a bit more resources than something that watches just file size.

progress (Coreutils progress viewer) or recent versions of pv can watch a file descriptor of a particular process. So you can do:

lsof your-file

to see what process ($pid) is writing to it and on which file descriptor ($fd), and do:

pv -d "$pid:$fd"

or:

progress -mp "$pid"

I have a little perl script that I put in my bash environment as a function:

fileSizeChange <file> [seconds]

Sleep seconds defaults to 1.

fileSizeChange() {
  perl -e '
  $file = shift; die "no file [$file]" unless -f $file; 
  $sleep = shift; $sleep = 1 unless $sleep =~ /^[0-9]+$/;
  $format = "%0.2f %0.2f\n";
  while(1){
    $size = ((stat($file))[7]);
    $change = $size - $lastsize;
    printf $format, $size/1024/1024, $change/1024/1024/$sleep;
    sleep $sleep;
    $lastsize = $size;
  }' "$1" "$2"
}