To move your Project Server 2010 PWA site(s) to a different or new web application, follow these steps:
1) If the PWA site is not currently in its own content database, create a new content database in the appropriate web application and move the PWA site there.
2) Document the Published, Draft, Archived, and Reporting content database names for the existing PWA site (in the Project Web App Service Application, select View in the drop-down menu for the PWA site). You will use these same content database names later.
3) Delete (unprovision) the existing PWA site. Be sure to uncheck the box next to "Delete site collection from SharePoint". Wait until the PWA site disappears from the page view.
4) Remove the content database (from Step 1) from the original web application and add it to new web application.
5) Clear the configuration cache in SharePoint 2010. For step-by-step instructions, please see James Waymire's blog post here.
6) If other non-PWA content databases exist in the new web application, set their status to Offline (Application Management, Mange content databases, and click on the content database name).
7) Provision the PWA site in new web application using the same database names documented in step 2.
8) Set existing non-PWA content databases in new web application back to Ready status.
9) Verify PWA site functionality in the new web application.
All done.
