Bonus Points if you make ptolemaic kingdom survive and make a map about this alternate history
Un modern days you can connect the oaises with the nile to the depression by the way plants work by absorbing water and letting most of the humidity back out leading to more water and thus more plants thus which means more water repeat the cicle etc could mean more rainfall that balances diverting the nile in fact this cycle is one explanation for the prehistorical green saharah the natural increase of a little rain allowed for more plants and thus the cycle bgean .What benefit would they possibly get out of this? I believe if you divert the Nile then all you get is a mediocre agricultural region that while potentially useful today as Egypt has a huge population and great demand for food, it also reduces the flow of the main Nile. If you use the Mediterranean than you get a salt lake useless for anything but fishing.
The technology that makes the Qattara Lake useful, like power generation, mining industrial chemicals from the lake, or knowledge of how it positively alters climate, did not exist in Antiquity
Although maybe Ptolemaic Egypt survives another 2 millennia and then builds the project in the modern era.
Qattara is not a particularly deep depression so the effect would be pretty limited and regional. IIRC the additional moisture from Qattara would mostly benefit Sinai and the Levant, which isn't a total loss for Egypt since they ruled a lot of that area.Un modern days you can connect the oaises with the nile to the depression by the way plants work by absorbing water and letting most of the humidity back out leading to more water and thus more plants thus which means more water repeat the cicle etc could mean more rainfall that balances diverting the nile in fact this cycle is one explanation for the prehistorical green saharah the natural increase of a little rain allowed for more plants and thus the cycle bgean .
I think it's one of those opportunity cost things, since there's a hell of a lot of other things Ptolemaic Egypt could do with that huge amount of manpower and money required. Qattara is about 250 kilometers away from Faiyum, and that's a huge waterway to dig--and maintain (and the waterways around Faiyum were already silting up in the Ptolemaic era).So doing it might very well be worth it of course by 100bc no one would know the science behind this
oh of course the quatara depresion wont cause a green sahara just explaning that is how it began water came to the coast due to moonsones plants made more moisture and depressions turned in to lakes , so this one would turn the coast and the surrounding region green over 2000 years of reduced albedo could mean that egypt in its entirety along with the levant sinai and some parts of lybia would be as well as the entire coast but not the interior as that would that would take many more thousand years or filling more depressions.Qattara is not a particularly deep depression so the effect would be pretty limited and regional. IIRC the additional moisture from Qattara would mostly benefit Sinai and the Levant, which isn't a total loss for Egypt since they ruled a lot of that area.
I think it's one of those opportunity cost things, since there's a hell of a lot of other things Ptolemaic Egypt could do with that huge amount of manpower and money required. Qattara is about 250 kilometers away from Faiyum, and that's a huge waterway to dig--and maintain (and the waterways around Faiyum were already silting up in the Ptolemaic era).