The typical approach is slightly different than you describe.
Typically you would place the webserver on vswitch0 AND vswitch1, with the database server on vswitch1. It would look like:
client
|
Internet
|
vswitch0
|
web server
|
vswitch1
|
database
This permits your web server and database to chat, and the client and the web server to chat, but prevents the client from chatting with the database.