Hey Jonny ,
I think you want a query by which you can fetch all the users (institute) enrolled in particular course. You can do it by many ways.
1) use get_enrolled_users(parameter) function. It will give you the list of enrolled users in particular course.
2) use enrol_get_course_users(parameter)
3)Direct hit this query. It will give you all the information of enrooled users in particular course.
SELECT ue.id AS ueid, ue.userid as user, ue.status AS uestatus, e.courseid as course,ue.enrolid AS ueenrolid, ue.timestart AS uetimestart,
ue.timeend AS uetimeend, ue.modifierid AS uemodifierid, ue.timecreated AS uetimecreated,
ue.timemodified AS uetimemodified,
u.username FROM mdl_user_enrolments ue
JOIN mdl_enrol e ON e.id = ue.enrolid
JOIN mdl_user u ON ue.userid = u.id where e.courseid = $courseid
Thanks,
Mayank Tyagi