Why are waterways fuel-efficient?
I am assuming you mean fuel efficient for boats and transports to use in moving people or goods from one point to another. For one thing, you can move a very large amount of goods on the waterway in one vessel with little danger of it sinking, as opposed to aircraft, which have load limits and are more dangerous to operate, or land vehicles, which also have load limits and you need in more numbers, as well as the highways to run them on.
There is also a natural current that can be used in waterways. rivers already flow in one direction, and running a ship with that current uses relatively little fuel, oceans have similar currents, and experienced captains know this, and run with the current whenever possible.
Waterways are more fuel efficient than transportation by other forms including by rail, road, or air. This is to do with the lower friction that an object moving in water has to move against. According to estimates using a liter of fuel a load weighing 105 tons can be transported over a kilometer by a waterway, whereas by the next most efficient way of transportation which is by rail one can move a only 85 tons for a kilometer and by road only 24 tons can be moved for a kilometer.
This is the reason why transportation by waterways on a larger scale is being explored in many nations around the world.
Four factor contribute to making water transport more efficient than than either land or air transport. First, because of buoyancy of water, the effective weight experienced by a transport vessel like a ship in water is less than that by a land vessel or air plane for comparable mass.
Second, because of the lower friction between water and surface of water vessels, as compared to friction experienced by the wheel and axle system of land vehicles, the force required to move the same weight is lower for water vessels than for land transports.
Next, land transportation frequently usually takes place over roads with many upward and downward slopes and with many turns. In comparison, water transport is usually on surfaces without any slopes. Water transport, particularly that in seas, has many fewer turns in the transport route. Finally, it is possible to make the water transport vessels very large to achieve economies of scale.
It is worthwhile noting that air transport also has the advantages mentioned in the second and third points above. However, such advantages of air planes are more than offset by the need to make the airplanes very light as compared to its size. This means that for every kilograms of total goods and passenger weight transport a much larger weight of the transport vessel must also be transported. This ratio of vessel weight to total weight is highest for land transport.