Do you mean the actual physical disk? Or free/used space within the volume?
Which protocol are you using to present the storage to the departments? CIFS, NFS, SAN?
If you are talking CIFS or NFS, you will need to make sure each department share is within its own qtree (quota tree) and you have quotas enabled.
/cifs_vol1/accounting_qtree
/cifs_vol1/engineering_qtree
'accounting' share points to /cifs_vol1/accounting_qtree
'engineering' share points to /cifs_vol1/engineering_qtree
I may be way off depending on what you are actually trying to do. You mention "a number of volumes" in your original post. If you really are presenting each department with its own volume, none of this would really apply.