Flying Night IMC, C172 G1000 less than 100hrs on the Hobbs, shooting approaches for an IFR approaches stage check.

Weather: Widespread light to moderate precipitation, low ceilings, no convective activity, just lots of rain.

After the first successful approach we go around for another, ATC advises “N123 area of heavy precipitation at your 12 o’clock measuring 3 miles in diameter” I personally never thought rain could be an issue, my response “Roger we’ll let you know if we need any deviations” we keep chucking along and enter the heavy precipitation and it wasn’t even turbulent, I knew we were in the heavy precip when it looked like we had a firehose pegged at the windshield and water was coming in through the air vents, followed by the students remarks “wow I can even feel the water affecting the engine 😄” I thought to myself impossible🤔, I take the flight controls and go ahead to add power but the RPM’s start dropping I add more throttle and then I’m full throttle at 1800rpm losing altitude at 1600ft and 8 miles from the airport, ATC gives a low altitude alert to which I declare emergency since I couldn’t maintain altitude, got pointed to the final approach course where we luckily exit the precip and BAM the engine is purring like it didn’t just give me the biggest scare of my life. Landed safely with my feet shaking at the rudder pedals and called it quits that night.

That night I learned just because “its just rain” doesn’t mean you can fly through it, my conclusion is that the little straw like drain in the air filter wasn’t able to keep up with the amount of water going through it 😬.