In my desert canal world all water is supplied from the poles to the temperate zones via a canal network. I want to work out the amount of water that that is needed, so that I can work out the dimensions of the canals and the flow rate in the canals.
The total population living on the canal network is about 50 million. The level of civilization is pre 400CE. They whole area is a desert similar to the Sahara but crisscrossed by a canal network 3000km across. The lands near the canals are agricultural with mixed vegetation including woodland, grassland and a variety of crops including wheat. Every year the land is flooded to prevent the build-up of salts in the soil. The world is roughly earth like but has much less water and most of what there is, is locked up in the icecaps hence the canals.
Roughly how much water do I need to move from the poles into the network each year in order to maintain this civilization? What other factors do I need to consider that I have overlooked?
If this is too tall an order, any pointers to a general method of solving this problem would be appreciated.