Coolant leak at small hose under turbo on 6.0 diesel

If you have a coolant leak at the rear of the engine, there are not too many choices that it could be. Either the turbo itself, the coolant hose to the turbo, or possibly a hose going to the heater core.

black smoke is over fuel and in a diesel with a turbo that indicates that
1 the turbo variable vanes are not adjusting to low rpm
2- the turbo turbine wheel is not spinning up
3-the intercooler or hoses are leaking boost air
4-- bad injectors -- squirting and not atomizing

Out the exhaust, unless a small amount of coolant
is going into the transmission

Have to use an exhaust gas analyzer at the exhaust
tail pipe or coolant fill cap or over flow container

You got a failed head gasket or worse, a crack that opens
up whenever it wants to

possible radiator leaking
split hose or faulty thermostat.

locate the waste-gate and see if you can cover it temporarily while driving. see if this changes it any. It could have a pin sized hole in the diaphragm. just a guess.

Sounds like a pin hole in one of your smaller hoses, perhaps over the motor where the water that's lost is hitting on the engine & drying before it gets to the ground. Can add some dye or food coloring to the water to make it a little easier to find. After pulling into the driveway, with the motor still running, inspect all the smaller hoses, heater hoses, etc. with gloves & a rag move the hoses from side to side, if the hole is under a clamp this should allow you to see the leak, especially with coloring in the water. If the hole is under a clamp it will only be lost under operating pressure.

No, under the turbo there is a cooling hose with a heat wrap around it that kind of looks like tin foil, that hose probably has a pinhole in it and needs to be changed, which is a difficult job (bad design).

its the fuel line that goes right next or under turbo, the factory bracket vibrates and makes a hole in the line need to be repalced approx 150.00

well the question is where did the coolant go. if it didnt leak out it must have went out the pipe. As you stated, white smoke, white smoke is coolant. You definately need to get this to the shop. You cannot drive it this way or further damage will occur.

I think the labor to check out the leak is too much.
If a qualified tech. pressurizes the system, he should tell more or less where it's coming from.
Could be freeze out plug.