Placing a commercial HEPA air purifier in a classroom without analysis could be deceptive and could lead to a false sense of security. Schools are a very difficult problem to solve due to movement of active young people, a beehive of interaction especially in hallways.
For classrooms where students are seated, effectiveness depends on your choice of a HEPA purifier and its deployment, whether students are masked or unmasked, and whether students remain distanced at all times or not.
In a classroom, where all students are masked and distanced, a strong HEPA purifier would be effective and reduce transmission from an infected intruder to the others, so long as students do not crowd together. In addition, students should be advised to only wear surgical masks. For other scenarios such as where students are unmasked, greater consideration must be given to deployment engineering.
In general however, most HEPA purifiers have a wide projection pattern that is insufficient to be effective and could make matters worse instead of better, because without the wearing of masks there are 10 times more aerosols, and also, large microdroplets come into play when a student speaks creating a different set of dynamics. Therefore in this scenario, particle deflection is the key [view here in Part 2].
Simply placing a HEPA purifier in a classroom corner will not prevent transmission between students on the other side of the room of the installation, or even in the center of the room, even though the air can be considered purified. In this case, HEPA purifiers would be met with “Purifying the air in classrooms with HEPA purifiers doesn’t work”, not different from hospitals that are getting infected despite HEPA filtering in their HVAC systems (see references in Question Q5). Here, every student must feel a noticeable breeze at all times for mitigation to be effective, which is the first line of defense. In that respect, another consideration is that the physical properties HEPA purifiers that claim HEPA performance are in opposition: it is impossible to get HEPA performance and get enough airflow rate to deflect large microdroplets at a reasonable distance away from a commercial purifier.
Therefore, multiple HEPA purifiers placed strategically in a classroom where each student feels a strong breeze at all times would be effective but prohibitively expensive to purchase and maintain. For unmasked students, airflow direction would have to be downward, meaning an effective solution would require multiple overhead purifiers with focused air vents directed downwards. School hallways would benefit greatly with overhead strong HEPA purifiers, where spacing is optimized so that a strong downward breeze is felt all along the hallway. Consult Consumer Reports for a better understanding of commercial HEPA purifier performance.
However, if you want an expeditious solution for hallways, a series of downward-pointing ceiling-mounted crosswind units without air concentrators (baffles only [view here in Part 2]), would be very effective, and much lower cost to purchase and maintain. In this hallway case as an example of re-engineering, the wide airflow pattern would be preferred in order to minimize the number of units along the hallway because the distance between students' heads and air exit ports is not greater than 2 meters. See also related Question Q5.