You don't specify what tools / scripts are you willing to use.
If you are willing to run a simple query against the pacsdb database you could try something like this:
This is easier if you don't have more than one configured file system... so do a query against the files table using instance_fk to only get files from instances that belong to a particular study (you'll need to go instance -> series -> study) using the Study Instance UID to uniquely identify the study.
This will basically give you a list of all files that belong to a study, feed that output to something that calculates the size of each file and then the total sum.
Example:
select filepath from files,instance,series,study where instance.pk = files.instance_fk and series.pk = instance.series_fk and study.pk = series.study_fk and study.study_iuid = "1.2.826.0.1.3680043.9.67.1499365157610.33333";
Remember, this only works if you have a single file system , if you have more than one, you'll need to take the
filesystem table into account because the full file path is going to be filesystem.dirpath + files.filepath, same if you are using NEARLINE storage since the same study could be duplicated in both storages.
You could always simply take a look at the path where the files are stored from within the GUI (See attachment)
All instances of a study are going to be stored (generally) on the same folder, they could be spread among many folders if additional series were sent to the PACS at different times, but if you identify a single folder simply check the size of it.