How to setup sub uri based Rails apps with Nginx and Unicorn?

I am trying to use the instructions at http://jrochelly.com/post/2013/08/nginx-unicorn-multiple-rails-apps/ to setup the sub uri (www.mydomain.com/site1 www.mydomain.com/site2) based Rails applications using Nginx and Unicorn.

I started with Droplet that had Unicorn and Nginx pre-installed from DO and it works fine. Now I want to setup multiple sites/Rails apps based on Sub uri.

As per the instructions I have updated nginx.conf by adding follwoing to current nginx.conf

upstream unicorn_socket_for_site2 {
  server unix:/home/navjeetc/site2/current/tmp/sockets/unicorn.sock fail_timeout=0;
}

Then I created a file site2 under sites-enabled as below:

server {
  location /site2/ {
    try_files $uri @unicorn_proxy;
  }

  location @unicorn_proxy {
    proxy_pass http://unix:/home/navjeetc/site2/current/tmp/sockets/unicorn.sock;
    proxy_set_header X-Forwarded-For $proxy_add_x_forwarded_for;
    proxy_set_header Host $http_host;
    proxy_redirect off;
    proxy_set_header X-Forwarded-Proto $scheme;
  }

}

And then made changes to my site2 Rails app as suggested. I did not change unicorn conf file.

But the request to http:/subdomain.mydomain.com/site2 is still going to the old Rails app and I get a 404.

The nginx config file for the old Rails app is:

server {
    listen 80;
    root /home/rails/current/public;
    server_name _;
    index index.htm index.html;

    location / {
        try_files $uri/index.html $uri.html $uri @app;
    }

    location ~* ^.+\.(jpg|jpeg|gif|png|ico|zip|tgz|gz|rar|bz2|doc|xls|exe|pdf|ppt|txt|tar|mid|midi|wav|bmp|rtf|mp3|flv|mpeg|avi)$ {
    try_files $uri @app;
    }

  location @app {
    proxy_set_header X-Forwarded-For $proxy_add_x_forwarded_for;
    proxy_set_header Host $http_host;
    proxy_redirect off;
    proxy_pass http://app_server;
  }

}

How can I fix this?