svnadmin dump /path/to/svnrepository | svndumpfilter include projectName --drop-empty-revs --renumber-revs > dump-project_name
The tricks is done by svndumpfilter that export only the projectName revision.
–drop-empty-revs doesn’t export revision of other projects and –renumber-revs, renumber the revisions due to hole created by –drop-empty-revs.
If you have other problems during dump, read also this blog entry.