PDR1 on this one I'm afraid you're wrong. The primary reason the Harrier and the Pegasus use water injection is to cool the turbine section of the engine so that in cooler weather you have a lower JPT for the same thrust or in warmer weather you do not lose thrust due to the engine TGT limiting.
I speak from experience with over 1000 hrs on the ac and an A2 QFI rating. I've got countless <90 second "Press Up" sorties in the log book in the back of the T Bird and the reason for this is because they could not achieve jet borne flight without the cooling effect of the water. Given that the 500 lbs of water was used in 90 seconds that gave you about 40 seconds in the hover which made instructing "interesting"!
The other thing to consider is that the thrust that comes out of the Hot and Cold Nozzles is totally different! The front cold nozzles are at about 200 degrees C and the air that is coming out has not gone through the combustion process, it has only been accelerated by the front fan. The rear hot nozzles are at about 700-750 degrees C and the air/water has. If the Water Injection were to increase the mass flow and thrust then this would only have an affect on the rear ones which would cause a nose down pitch effect when the water flowed and I can assure you this did not happen!
Finally if you ran out of water you did not lose thrust, the JPT simply rose by 25 degrees. Provided this was still below the short lift wet temp limit of 755 degrees nothing happened, you just put more Life Counts on the engine. If it did go above 755 the DECS would trim the fuel flow to maintain 755 degrees and you would lose thrust. You would not crash though as you could "Trip the Limiters" which muted the JPT signal into the DECS and the engine limited purely on RPM.
As a pilot of the Carbon Fibre Death Provider you had to have a VERY intimate knowledge of the engine logic or you were in trouble. We used to have a "Weeds Brief" on a regular basis to refresh us to keep us out of those weeds!!!!!!!!!!!!!!
Oh what happy days! Oh what an AMAZING aircraft built by pipe smoking and tea drinking legends!
