Content-Length header value is not equal to real content length

Question

Trying to close connection with browser and keep php process alive, but browser waiting for the process end. I think that the problem is in real content length. There is my code in ZF1:

ob_end_clean();
header("Connection: close");
ignore_user_abort(true);
ob_start();
echo Zend_Controller_Front::getInstance()->getResponse()->getBody();
$size = ob_get_length();
header("Content-Length: $size");
Zend_Session::writeClose();
ob_end_flush();
ob_flush();
flush();

sleep(5); // for example

So browser keeps connection for 5 sec. Variable $size value is equal with content characters count. When trying to print empty content and set $size variable to 0, then browser work as expected and don't wait for 5 seconds. Could you please share your ideas what the problem can be?