Geography · Lesson g03

The Water Cycle & Rivers

The water in your glass may once have been a cloud over Japan and a river in Bavaria. Water is always on a journey — and it carves the world as it travels.
A landscape showing the water cycle: sun over the sea, clouds, rain over mountains, and a river winding to the sea

Earth has had the same water for billions of years — it just keeps going round and round. It rises invisibly into the sky, gathers into clouds, falls as rain, races down rivers to the sea, and rises again. This endless loop is the water cycle, and it explains rain, rivers, and why so many towns sit on riverbanks. Best of all, it's built from two ideas you've already met — changes of state from chemistry, and downhill slope from maths.

💧 Big idea 1 — the water cycle

Water moves through four main stages, over and over:

  1. Evaporation — the Sun heats seas, lakes and rivers; water turns to invisible vapour and rises.
  2. Condensation — high up it cools, turning back into tiny droplets that form clouds.
  3. Precipitation — droplets join, grow heavy, and fall as rain, hail or snow.
  4. Collection & run-off — water gathers in rivers and lakes and flows back downhill to the sea, ready to start again.
Science connection — this IS your chemistry lesson (s09): evaporation is a liquid → gas change of state; condensation is gas → liquid; snow forming is gas/liquid → solid. The water cycle is the particle model of matter, playing out across the whole planet. Same idea, planet-sized.
condensation evaporation precipitation river runs downhill → sea sea
The Sun lifts water up (evaporation); height cools it into clouds (condensation); it falls (precipitation) and runs back downhill to the sea. Forever.
🏞️ Big idea 2 — rivers shape the land

Rain that lands on high ground flows downhill — always from high to low — gathering into a river. A river starts at its source (usually mountains), travels down, and ends at its mouth (usually the sea). Along the way the moving water erodes (wears away) rock and soil, carves valleys, and drops that material lower down — slowly reshaping the whole landscape.

This is also why so many towns sit on rivers (remember g01): fresh water, flat fertile banks, and a route to travel and trade.

Height Distance downstream → source — steep mouth — gentle big drop small drop
A river's long profile: a steep gradient near the source, flattening toward the sea.
Maths connection — a river's gradient is slope (Lesson 17): how steeply a river drops is its gradient — the vertical fall divided by the horizontal distance, exactly $\dfrac{\text{rise}}{\text{run}}$. Because a river always goes downhill, its slope is negative in direction (falling). Steep near the source, gentle near the mouth.
Worked Examples
Worked Example 1 — name the stage and the change of state

Dew forms on the grass on a cold morning. Which stage of the water cycle is this, and what change of state is happening?

Air holds invisible water vapour; overnight the ground cools it until the gas turns back into liquid droplets on the grass. That's condensation — a gas → liquid change of state (the same one that fogs a cold window in your chemistry lesson).

Worked Example 2 — a river's gradient (slope)

A mountain stream falls 300 m in height over a horizontal distance of 5 km. What is its gradient (slope)?

Put both in the same units: 5 km = 5 000 m.

$$\text{gradient} = \frac{\text{fall}}{\text{distance}} = \frac{300}{5\,000} = 0.06$$

A slope of 0.06 (a 6% drop). Near the sea the same river might fall only 5 m over 5 km — a gradient of $\frac{5}{5000} = 0.001$, far gentler. Rivers start steep and flatten out.

Warm-Up
  1. Problem 1
    Put the four water-cycle stages in the right order, starting from the sea: precipitation, evaporation, collection & run-off, condensation.
    order them →
  2. Problem 2
    Name the change of state (from chemistry) happening at each stage: (a) evaporation, (b) condensation, (c) snow forming in a cloud.
    liquid→gas? gas→liquid? →
  3. Problem 3
    What are the two ends of a river called — where it begins and where it finishes — and where is each usually found?
    source and mouth →
Core Problems
  1. Problem 4
    A river falls 200 m over a horizontal distance of 4 km. Find its gradient (slope). (Remember to convert km to m first.)
    gradient $= \dfrac{\text{fall}}{\text{distance}}$
    4 km → m → divide →
  2. Problem 5
    Explain, using the water cycle, how a puddle in a Barcelona courtyard can end up as a raincloud over the Alps. Name each stage the water passes through in order.
    follow the water: evaporate → … →
  3. Problem 6
    Near its source a river's gradient is 0.08; near its mouth it is 0.002. (a) Where is the river steeper? (b) The moving water erodes (wears away) the land more where it flows faster and steeper — so where would you expect the deepest, most dramatic valleys: near the source or the mouth? Explain.
    compare gradients → link steepness to erosion →
  4. Problem 7 Challenge
    Two rivers each drop 600 m in total. River A does it over 10 km; River B over 30 km. (a) Find each river's gradient. (b) Which is steeper, and by how many times? (c) A stable owner wants gentle, safe riverside trails for horses — which river's valley should she choose, and why?
    two gradients → ratio between them → choose →
  5. Problem 8 Open
    Trace the journey of a single raindrop from the moment it falls on a mountain to the moment it evaporates from the sea days later. Write it as a short story (5–8 steps), naming each water-cycle stage and each change of state along the way. There's no single right answer — make it vivid and correct.
    your raindrop's story →
Think like a geographer 🧭 — A river looks like it's just flowing, but it's really a slow-motion sculptor. Given enough time, that thin ribbon of water can carve a canyon a mile deep. Geography's biggest lesson: small forces, repeated for long enough, reshape the whole planet.
Show answers
Problem 1
Evaporation → condensation → precipitation → collection & run-off (then it repeats).
Problem 2
(a) evaporation = liquid → gas · (b) condensation = gas → liquid · (c) snow forming = gas/liquid → solid (freezing/deposition).
Problem 3
The source (the start, usually in hills or mountains) and the mouth (the end, usually where it meets the sea or a lake).
Problem 4
4 km = 4 000 m. Gradient = 200 ÷ 4 000 = 0.05 (a 5% drop).
Problem 5
The puddle water evaporates into vapour → rises and condenses into a cloud → wind carries the cloud to the Alps → it cools and falls as precipitation (rain/snow). Same water, moved by the cycle.
Problem 6
(a) Steeper near the source (0.08 > 0.002). (b) Near the source — steeper, faster water erodes more, carving the deepest, most dramatic valleys and gorges there; near the mouth the gentle river drops material instead.
Problem 7
(a) River A: 600 ÷ 10 000 = 0.06. River B: 600 ÷ 30 000 = 0.02. (b) River A is steeper — 0.06 ÷ 0.02 = 3 times steeper. (c) River B's valley — gentler gradient means flatter, safer trails for horses.
Problem 8
Open. Look for the correct cycle in order — falls as precipitation, runs downhill in a river (collection/run-off) to the sea, then evaporates (liquid → gas) — with changes of state named correctly at evaporation and condensation.
Next up → g04: People on the Move — Population & Cities You've met the physical world — climate, water, land. Next we turn to the human side: why cities keep growing, why people move across the world (like your own family!), and how geographers map where billions of people live.
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