CentOS6.7にpassengre+sinatra
を、なるべく、一括でできるようにまとめてみました

必要なアプリをインストール

yum -y install git gcc gcc-c++ libcurl-devel httpd httpd-devel openssl-devel readline-devel zlib-devel

git clone https://github.com/sstephenson/rbenv.git ~/.rbenv

echo 'export PATH="$HOME/.rbenv/bin:$PATH"'>> ~/.bashrc
echo 'eval "$(rbenv init -)"' >> ~/.bashrc
source ~/.bashrc
mkdir ~/.rbenv/plugins
cd ~/.rbenv/plugins
git clone git://github.com/sstephenson/ruby-build.git

rbenv install 2.2.5

rbenv shell 2.2.5
gem install bundler

cd
mkdir sina
cd sina
mkdir vendor
mkdir vendor/bundle
mkdir public
mkdir tmp
touch tmp/always_restart.txt
bundle init
echo 'gem "sinatra"' >> Gemfile
echo 'gem "passenger"' >> Gemfile
bundle install --path vendor/bundle

bundle exec passenger-install-apache2-module

・結果表示
Here's what you can expect from the installation process:
 
 1. The Apache 2 module will be installed for you.
 2. You'll learn how to configure Apache.
 3. You'll learn how to deploy a Ruby on Rails application.
　　：
　　：
Press Enter to continue, or Ctrl-C to abort.

１を、選択
・結果表示
Use <space> to select.
If the menu doesn't display correctly, press '!'
 
 ‣ ⬢  Ruby
   ⬢  Python
   ⬡  Node.js
   ⬡  Meteor

entrで、進んで行く

bundle exec passenger-install-apache2-module --snippet >> /etc/httpd/conf/httpd.conf
echo "DocumentRoot /root/sina/public" >> /etc/httpd/conf/httpd.conf

echo "#coding: utf-8"    >app.rb
echo "require 'sinatra'" >>app.rb
echo "get '/' do"        >>app.rb
echo "'Hello World'"     >>app.rb
echo "end"               >>app.rb
echo "require File.expand_path(File.dirname(__FILE__)) + '/app'"  >config.ru
echo "run Sinatra::Application"                                   >>config.ru

/etc/rc.d/init.d/httpd restart

getenforce
Enforcing

setenforce 0 

getenforce
Permissive

curl 'http://localhost/'
chmod o+x "/root"

curl 'http://localhost/'
Hello World

■確認
いまく、いかない時には
以下の内容を確認してください。

path

cd
cd sina
pwd

・結果表示
/root/sina

ファイルの内容１

cd
cd sina
ls
・結果表示
Gemfile  Gemfile.lock  app.rb  config.ru  public  tmp  vendor

ファイルの内容２

ls tmp
・結果表示
always_restart.txt

appの内容

cat app.rb
・結果表示
#coding: utf-8
require 'sinatra'
get '/' do
'Hello World'
end

config.ruの内容

cat config.ru
・結果表示
require File.expand_path(File.dirname(__FILE__)) + '/app'
run Sinatra::Application

httpd.confの内容

cat /etc/httpd/conf/httpd.conf
・結果表示（終わりの行）
　　：
#</VirtualHost>
DocumentRoot /root/sina/public
LoadModule passenger_module /root/sina/vendor/bundle/ruby/2.2.0/gems/passenger-5.0.28/buildout/apache2/mod_passenger.so
<IfModule mod_passenger.c>
  PassengerRoot /root/sina/vendor/bundle/ruby/2.2.0/gems/passenger-5.0.28
  PassengerDefaultRuby /root/.rbenv/versions/2.2.5/bin/ruby
</IfModule>

SELinuxの内容

getenforce
・結果表示
Permissive

/rootの権限

ls /root -l
・結果表示
drwxr-xr-x. 6 root root  4096  6月 22 09:17 2016 sina