I'm not an engine expert. However I am a flight instructor an do operate a flight school.
The first thing you need to accept in this business is that students do make mistakes. It's your job to do everything you can to prevent those mistakes. You also have to be realistic and accept that "**** happens". The way you handle the situation with a student that makes a mistake is the difference between the end of the relationship or securing a very loyal customer. The problem though is that it's not always that simple. You also don't want someone to kill themselves. You need to really think these things through before you start accusing a customer of anything.
I could completely see how a scenario like this could happen. It's completely realistic for a student at some point in his/her training to get left alone with an airplane. If I've already taught someone how to pump gas, I might watch them once after that, but the third time I'm going to walk away intentionally. You have to let people "solo" even on operations like that on the ground. Just check their work afterwords.
I would say that the majority of students would never do something like this. They would recognize that it's not their airplane, they don't know what is under that cowling, and directing a massive stream of water into something they don't own without permission would be a really irresponsible thing to do. So I do think it's important for you in this scenario to accept the fact that you did something irresponsible. That might sound harsh but I do not intend it that way. I've done irresponsible things in my life too and will do one again. The important thing is whether you own it.
Now remember earlier where I said that it's important for a flight school to remember that "**** happens"? Just because someone made a irresponsible mistake and the damage could be expensive doesn't automatically mean you should burn the relationship with the customer. First off it is possible there isn't any damage. If there is no damage then you're going to cause way more damage by getting emotional and firing the customer. Even if there is damage you might still be better off to let the customer off easy and teach them something to make them safer for life.
If you do decide to get ****ed off and collect money from the customer. First off you will lose their business forever, possibly some of their friends, and anyone they ever would have referred. That alone could easily cost you more than the damage. That isn't your only problem though. You need to invest your time into trying to collect. That could be a lot of time. You could have put that time towards more proactive work building your business. Instead you're wasting it on a reaction that gains you nothing and costs you future business.
Now enters the tricky part about running a flight school. At the end of the day you need to remember that you are creating pilots. You have a morale obligation to think about how to make this into a lesson for the student. Thoughtless mistakes like this in aviation get people killed. Do you want to hear about a fatality some day involving the student? Do you want to not be able to sleep that night because you remember the time where you should have taught them something instead of just thinking about the business? No thanks..not me..I'd do everything I could to turn this into a great training moment.
So I'm a logical person. I'd stick to that for handling this. The moment I saw a student directing a hose of water into the cowling I would obviously ask them to stop. Once stopped I would first try to cool the situation in whatever manner was appropriate for their personality. Often times it'd be some sort of joke and distraction.
Once I felt like we were over the emotional part of fact that the situation occurred I would explain that there are lots of components under the cowling that were basically submerged in water. Those components were really hot and now they're not. The cooling occurred rapidly in a way that the engineers of the components may not have anticipated. It's definitely not the same as flying in rain. That involves by far more air than water all while rapidly moving OUT of the cowling.
Since I'm not the guy that designed all of the **** under the cowling I recognize that I'm not an expert. Even if I were there really isn't a soul out there that could say whether that was damaged or reduced life on the engine. Because of that I definitely would not just fire it up, do a runup, and take flight. Remember, we're creating new pilots, and we want them to be safe so that we can sleep at night. I lean heavily towards what is the safest reasonable action. My students will mock me. I need to recognize that and own it.
I would proceed to de-cowl the airplane with the student present. From there our conversation would very depending on their mechanical knowledge. It'd be a great time to really explain how an engine works and point out all of the components. The more a pilot knows about their engine the safer they are.
I would also point out the places where the water could have caused us problems. There are many.
I would give the student a flashlight and send them a hunt looking for cracks. I'd be watching them search.
Hopefully we'd be at home base. If so then we would be doing compression checks. I'd explain how sometimes there are cylinder cracks that you won't find with your eyes but you will find with a compression check.
I would make it very clear to the student that it would never be "OK" to just tear into someone's airplane after an incident like this without their permission. We're doing it because this a great opportunity for them to learn some things and ultimately this is now the work I have to do as a result of the action of their mistake. Therefore they will be helping me
The entire lesson would have shifted from whatever we were doing that day to teaching them everything I can about why you don't want to do what they did all while teaching them more about engines and trying to do it in a way that doesn't make them feel like ****. I personally believe it's unlikely that any damage took place so I'd try to be very positive throughout this.
I believe we wouldn't find any damage. I'd accept the reality that I'll never know whether or not that reduced the life span of a component. For all I know it could cost me dearly next week. Lesson learned. Include discussions about hoses with new students into training. You can't make someone pay for damage you can't prove took place.
What if this student a month later does something similar that implies their thought process hasn't changed? I'd fire the customer. This is the bad part about this business. Sometimes you have to fire people knowing it will damage your business both short and long term. Nobody wins.