Here are the basic workings of a diesel engine: air is put into a cylinder.
The piston comes up and compresses the air.
Near the top of the piston's travel the injector adds fuel to the air.
The air/fuel mixture is compressed (gases are heated when they are compressed, and they are cooled when they are expanded- air is a gas) to the point that the mixture explodes.
This forces the piston back down, creating power.
The amount of fuel, the amount of air, the timing of the injection of fuel, the timing of the air entering the cylinder, the timing of the combusted fuel/air leaving the cylinder, and the temperature of both the fuel and air all effect the power created by that cylinder's power cycle.
The main forms of increasing power in a diesel are to add fuel and air to the power cycle of all cylinders.
By putting a device that compresses the air and forces more of it into the cylinder you can increase the power of the engine.
If you compress the air, you also heat it.
This is called Boyle's law, after the Irishman Robert Boyle.
By cooling the incoming air, you effectively decrease it's volume- than thus are able to add more of it to the cylinders power cycle.
That does not give you more power (actually is does give more power, but in terms of less than one or two percent) so when you add more air the engine also needs more fuel to burn with the air.
All engines are considered forced induction (FI) or naturally aspirated (NA) engines.
There are two forms of FI- superchargers (aka compressors) and turbo chargers.
By adding fuel and air to the power cycle, you add power.
Nearly all diesels increased power over stock levels are concentrated on these two items.
After the power cycle, you need to evacuate the exhaust- and a restriction on the exhaust causes power loss.
This is why larger exhausts are needed with increased power over stock levels.
Factoring in all of these and more is the life long game of tinkering with your diesel to produce the more power.
Water injection both does and does not cool the air, but it does allow you to air more fuel/air at the same temp.
The relationship is not simple.
William

MTUPower,

Thanks for this other very good point.

I'll edit my original post and add your comment in the bullet points.

Bye,

__________________
BigBen

'98 E300 Turbodiesel 244 000km
RIP '92 300D 2,5 Turbo 632 859,4km due to engine failure