How do you tell from a map which way a river flows?

Two more that work without needing to read contours:

Zoom out until you find the sea. Crude and effective. Follow the water until it reaches an ocean, a large lake, or a river you recognise. Everything drains somewhere, and once you have the outlet, direction is fixed for the whole system.

Look for reservoirs and dams. A dam has a lake on the upstream side and a river on the downstream side, visible on any satellite imagery. Same for weirs and barrages. These are unmistakable direction markers and large rivers are full of them.

There are also web tools published by some national mapping and geological agencies that let you click a point on a river and highlight everything downstream of it. Where one exists for your area it is by far the fastest method, and it also shows you the whole catchment.

The reliable answer is to stop using a road map and use a topographic map, where the information is present by design.

On a topo map, contour lines crossing a watercourse form a V that points upstream. That is not a convention somebody chose — it falls out of the geometry, because the valley floor is lower than the ground either side, so the contour has to bend uphill as it crosses. Once you have seen it, you can read flow direction off any stream on the map at a glance, including tiny ones with no name.

Second method on the same map: read the elevation figures at two points along the river. Water goes downhill. This is slower and it is completely unambiguous.

Third: follow the junctions. Tributaries join the main river at an acute angle pointing downstream, like the branches of a tree pointing towards the trunk. At any confluence, the shape of the join tells you which way everything is going.

One planning note that follows from your reason for asking: the volume question is not only about the confluence.

A crossing gets harder after rain, after snowmelt, and later in the day in glacier-fed catchments — sometimes dramatically. So knowing you are above a confluence is necessary and not sufficient. Time of day and recent weather often matter more than position in the system, and a crossing that is trivial at eight in the morning can be impassable by four in the afternoon.

In the field, without a map, several things tell you immediately:

• Watch something float. A leaf, a twig. Even in slow water, thirty seconds of watching settles it.
• Look at obstructions. Debris piles up on the upstream side of rocks and fallen trees, and the water surface has a smooth bulge upstream and turbulence downstream.
• Vegetation lies downstream. Grass and reeds in and beside the channel are combed flat in the direction of flow, and this persists after the water level drops.
• Sand and gravel bars form on the inside of bends with the tail pointing downstream.

The floating object works everywhere and takes no expertise. The rest are useful when the water is too slow to see, or when you are reading a dry channel after the fact.