Flock() doesn't seem to be working for me?

I have three files in a directory as follows;

  1. A text file with some text: file.txt
  2. A simple script to lock the file: lock_file.php
<?php
	$file = "./file.txt";
	$fp = fopen($file, "a");
	flock($fp, LOCK_EX);
	echo $file . " locked!<br />";
	?>
  1. A script to output the text from the file: read_file.php
<?php	
	$file = "./file.txt";
	$text = file_get_contents($file);
	echo $text;
	?>

First I run lock_file.php and then I open read_file.php. I expected read_file.php not to work, because lock_file.php should have locked file.txt. However, when I run read_file.php it outputs the text from file.txt, as if file.txt has not been locked. Why is that?

Thanks!