In this short video we take a quick look at System Center Virtual Machine Manager Interface then we walk through the process of adding (and then removing) a SCSI disk to a running domain controller which is a guest running on a Hyper-V Machine while the DC if running.  
In a nutshell, the process for doing this is logging into SCVMM, going to the properties of the machine and looking at the hardware.  As long as the machine has a SCSI controller, you can add a disk to that SCSI controller under Add Disk.  We then login to the DC and open Disk Manager to confirm the disk is there, bring the disk online, create a partition (format disk) and show that we can read and write data to the new machine.   We then show how to remove media from a running machine.  (Bring disk offline [in disk manager], and then remove it using SCVMM) 

 

If you want to do this without SCVMM see my Hyper-V blog post at How To Hot Add Storage To A Hyper-V Guest–Super Simple And No Service Interruption