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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.

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    $\begingroup$ Evaporative loss is an important consideration also. Read up on the Colorado river. nytimes.com/2016/05/22/opinion/… $\endgroup$ – pojo-guy Nov 24 '17 at 4:37
  • $\begingroup$ What technology level is your civilization. the ancient romans used about 200 gallons per person while a modern civilization uses around 800-1000 gallon or more per person per day once you include irrigation and other industrial uses. $\endgroup$ – John Nov 24 '17 at 15:28
  • $\begingroup$ @John it’s an ancient civilization similar to that of Rome or ancient Egypt, but all of their water must be supplied as there is virtually no rain and it’s a desert. Domestic use is probably the least of their worries think miles of agricultural fields, woods and grassland all needing regular water and an annual flood. $\endgroup$ – Slarty Nov 24 '17 at 16:30
  • $\begingroup$ see my answer below, you are right irrigation is your biggest issue. $\endgroup$ – John Nov 24 '17 at 16:35
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    $\begingroup$ @CortAmmon Yes but blame the forerunners of the Bene Gesserit. All we can do is make use of what was left to us...;o) $\endgroup$ – Slarty Nov 26 '17 at 19:42
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This kind of practical questions are best resolved by looking at the real world around us. In the real world around us, Egypt is (and always was) a country which relies entirely on one river which brings water from elsewhere; the average annual precipitation in Egypt (with the exception of a narrow strip near the Mediterranean coast) is just about zero.

The average annual discharge of the Nile above Aswan is about 90 km³ per year, or about 2800 m³ per second, as reported in "Nile river discarge" by Herbert Riehl, Mohamed El-Bakry and José Meitín, Monthly Weather Review vol. 107 (1979), pp. 1546 sqq. According to the Wikipedia article on the Aswan High Dam, of the 55 km³ of water per year discharged downstream of the dam, 46 km³ per year are diverted to irrigation canals.

The population of Egypt at the beginning og the 1st century CE is estimated at about 4 million people; the population of Egypt today is about 93 million people.

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AQUASTAT is your friend

AQUASTAT is the UN's water usage database. According to this source Egypt has 3,761,000 hectares under permanent cultivation, and uses 67,000 million m$^3$ of water per year for agricultural purposes; or 1.8 million m$^3$ per km$^2$.

For some comparable numbers from dry-ish nations, check out Pakistan at 21,280,000 hectares and 172,371 million m$^3$ usage (0.8 million m$^3$ per km$^2$); India at 169,623,000 hectares and 688,000 million m$^3$ usage (0.4 million m$^3$ per km$^2$). Depending on how dry you want your equatorial community to be, you can choose the ratio.

Assuming that you need 1 hectare to feed a person (using ancient technology), and you are irrigating at a high rate (1 million m$^3$ per km$^2$); for a population of 50 million you will need 500,000 million m$^3$ of water per year; or 500 km$^3$ per year.

How to get 500 km$^3$ of water across a desert

Fortunately, for us, you said the desert is like the Sahara, and we already have a 'canal' crossing the Sahara already, called the Nile river. As it turns out, evaporation is pretty low. Average flow from the Blue Nile, White Nile, and Atbara combined sum to 85.4 km$^3$ per year discharged from the African Great Lakes and Ethiopia. Meanwhile 84.1 km$^3$ are seen at the Aswan dam in Egypt. All in all, not much water is lost to evaporation, as long as the river is swift flowing and not a stagnant swamp.

For your irrigation purposes, even a long haul would not result in too much water loss so long as the canals are designed with depth and minimum exposed surface area for evaporation.

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  • $\begingroup$ thanks for that reference Aquastat is just what I need. Further to the lead given by AlexP yesterday I managed to come up with a figure of 553 cubic km per year which seems to be remarkably close to what you have assuming your units of measure are millions of cubic metres. Seems I need more water than I first thought at one sixth of the Amazon I’m going to need bigger canals. $\endgroup$ – Slarty Nov 26 '17 at 13:27
  • $\begingroup$ I fixed the numbers which I had obviously gotten wrong; It is a lot of water, but five or six Nile sized canals spread around the planet would do it. Also, you can make assumptions of less intense irrigation to reduce water demands a lot. Ancient Egyptions wasted water because they had plenty of it. $\endgroup$ – kingledion Nov 26 '17 at 15:38
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a minimum of 10,000,000,000 gallons a day, but probably closer to 10,000,000,000,000 gallons per day.

Roman cities averaged 200 gallon per person per day, one of the downside of an open canal system is the water keeps flowing even if it is not being used. That is nearly twice that of modern cities which use a closed system, even though we use more water for bathing and such, although modern cities use a lot more for industrial purposes.

Now of course that is not including all the water you will need for irrigation, which will likely increase the usage by several orders of magnitude. And that is using modern efficient irrigation you might want to add another 10% to that if they are using flood irrigation, although you can improve that somewhat by using a lined canal and pulse flooding.
source 1

source 2

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3000km canal network would be quite an achievement for a BCE civilization. One of the earliest channel systems on Earth was the irrigation system in Mesopotamia, spreading across the plain between Tigris and Euphrates. This source, for example, calls efforts to create 50km channel between those rivers "elaborate feat of engineering of 3rd century CE". I'd say it would be much worse if they had to dig it in a desert and the upkeep costs could have brought them to knees, since desert storms in a dense atmosphere can move around amazing amounts of sand.

Also note that Earth radius depends on whether it is polar or equatorial. The height surplus is around 20km near the equator, and water is not known to eagerly flow upwards. It is common situation among rocky planets, Moon being one of the most uniform bodies in this respect, but it still has 2km surplus difference and quite rough surface above that.

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    $\begingroup$ Earth (and all planets/moons with sizeable rotation speed) are "geoid shaped", something similar to an ellipsoid with equator more distant from center than poles. This, however, does not mean you need to dig all that "height surplus" as the geoid surface is equipotential and can be thought as "flat" for all practical uses; in particular water will flow along this surface as if it was completely flat and gravity force (composition of gravity pull and centrifugal acceleration) will always be perpendicular to the surface (possibly not pointing to planet center). $\endgroup$ – ZioByte Nov 24 '17 at 15:20
  • $\begingroup$ Yes for sure - the people who inhabit the canal system in this time period did not build it, they inherited it. The builder’s civilization had our level of technology, but was destroyed long before. Re the equatorial bulge true but it doesn't stop massive rivers like the Mississippi from running south. And if the seas dried out all bets are off... $\endgroup$ – Slarty Nov 24 '17 at 15:22
  • $\begingroup$ @ZioByte good point $\endgroup$ – Slarty Nov 24 '17 at 15:22
  • $\begingroup$ @Slarty, you still have to mind upkeep costs. You know how many times they tried to dig out Sphinx? And it's rather small, if compared to 3000km. $\endgroup$ – A.C. Nov 24 '17 at 15:29
  • $\begingroup$ @ZioByte yes something that has been troubling me and was almost the subject of another question. I was wondering if such a system could become "naturalised" with the current keeping it swept. Another option - perhaps have chevron like ridges pointing up stream in the canal bed at regular intervals to collect sediment and direct it into the sides directly into the intake of the water wheel driven pumps used for irrigation. May be another question there. $\endgroup$ – Slarty Nov 24 '17 at 16:23

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