Hi Student pilot here.
Lets say Mr pilot is flying at FL75 and QNH is set at 995 hpa, however there is a mountain in the way at 7000', will he below or above the mountain?
If you could visually explain that would be even better.
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Since you used the term "Flight Level" (FL75), we must assume that the altimeter is set to 1013.25, and that the altimeter reads 7500'.
The math is basically this: each milibar (or hPa) is worth about 27 feet. We know that his altimeter is set to 1013 hPa, but the actual QNH is 995 hPa, a difference of 18.
18 * 27 = 486. So, the aircraft is either 486 feet ABOVE 7500, or 486 feet BELOW 7500.
So.... how do you know whether to add or subtract? We can remember the phrase "High to low, look out below"... but what does that really mean?
Let's say that an aircraft is in an area where the QNH is really 1013, and is at an altitude of 7500'. The pilot flies along the route for a while without adjusting his altimeter. The QNH has been steadily dropping (unbeknownst to the pilot) and is now 995 hPa. Since the pilot failed to obtain the local QNH as he passed by various stations (or, by asking Air Traffic Control every hour or so), he has also failed to adjust his altimeter to the new QNH reading.
Here is what has happened: As the aircraft continues to fly from the higher pressure area into a lower pressure area ("High to low"), the altimeter will start to go up. The pilot will unknowingly descend in an attempt to keep the aircraft at the desired altitude of 7500'. The aircraft will continue to get lower and lower ("look out below"), but all the while the pilot thinks he is maintaining straight and level.
So, we know that the aircraft is 486 feet BELOW his indicated altitude. Therefore, the aircraft is actually at an altitude of 7014'. He will BARELY miss that mountain peak that is at 7000'. If the QNH was one milibar lower, he would be at 6987'and hit the mountain.
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$\begingroup$ Let's hope there are no trees at the top of the mountain, lest Mr Pilot might clear the mountain proper but still end up with the aircraft in a rather undesirable state. $\endgroup$– userMar 7, 2019 at 11:59
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$\begingroup$ Yeah, lots of things wrong with this scenario, including the use of the term “Flight Level” to mean altitude. There would not be a FL75 in mountainous terrain. But, the exercise was to calculate the math, so I hope I helped the OP understand it better. $\endgroup$– JimmyMar 7, 2019 at 14:46
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$\begingroup$ Much appreciated Jimmy! this helped me allot. Just finished my initial batch of 9 tests (AGK,POF,FPP,NAV,COM,HUM,OPS,LAW,MET) passed them all, and just completed my 7th flight. $\endgroup$ Mar 10, 2019 at 22:04
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$\begingroup$ It should be noted that in practice the transition level will be high enough (FL100+ in this case) to prevent this scenario from happening, so the question may be intended to illustrate why that's needed. $\endgroup$– StephenSNov 24, 2019 at 16:59