Learn

Learning preferences

Make learning more comfortable. Changes apply immediately.

Enlarges page content, including diagrams and their labels. You can also use your browser’s zoom.

Choose the colours that are easiest for you to distinguish. Applies to lesson diagrams and lab plots. Labels, shapes, hatching and line patterns also distinguish meanings. Source photographs and raw image brightness stay unchanged; mask-only views are available for image overlays.

ExampleComparisonSample link

Saved in this browser on this device. Preferences are separate from progress backups.

Learn through experiments

A full reservoir can hide a shortage

How long can stored water conceal demand greater than replenishment?

Entering midway? Revisit Enough energy, at the wrong time for the preceding worked example, or start here and use the explanation below.

1 · Try

Start with a concrete question

Original synthetic reservoir: initial stock 60 units, capacity 100, twelve months; recharge is halved in months five through eight.

Try the initial inputs, then write a prediction before changing one setting. All calculations run locally on your CPU.

Go directly to the experiment · Review basic mathematics

2 · Predict

What do you expect?

Predict whether withdrawal 12 and normal recharge 10 can be sustained for the year without a shortage.

3 · Experiment

Change one thing. Inspect what happens.

  1. Inspect the defaults, especially the four dry months; distinguish a declining stock from unmet demand.
  2. Increase demand to 15 and identify the first month with a shortage.
  3. Find a conservation setting that prevents shortages in this twelve-month run.
  4. Set recharge to 20 and low demand. Explain why overflow means not all recharge can be saved for later.
Experiment inputs
Inputs
Your settingsMechanism
Calculation belowEvidence
Compare outcomes
Final stock16 units
Unmet demand0 units
Overflow0 units

Compare the current results

Every bar starts at zero and uses the same numeric scale in this chart. The upper bound automatically adjusts to the largest current value (at least 1), so compare the numbers when changing inputs. Units and quantities come from each label; different kinds of quantity are not interchangeable. Displayed values are rounded to at most six significant digits.
058
  • Month 1 stock58
    Month 1 stock: 58Horizontal bar from zero to 58, on the shared zero to 58 numeric axis.
  • Month 2 stock56
    Month 2 stock: 56Horizontal bar from zero to 56, on the shared zero to 58 numeric axis.
  • Month 3 stock54
    Month 3 stock: 54Horizontal bar from zero to 54, on the shared zero to 58 numeric axis.
  • Month 4 stock52
    Month 4 stock: 52Horizontal bar from zero to 52, on the shared zero to 58 numeric axis.
  • Month 5 stock45
    Month 5 stock: 45Horizontal bar from zero to 45, on the shared zero to 58 numeric axis.
  • Month 6 stock38
    Month 6 stock: 38Horizontal bar from zero to 38, on the shared zero to 58 numeric axis.
  • Month 7 stock31
    Month 7 stock: 31Horizontal bar from zero to 31, on the shared zero to 58 numeric axis.
  • Month 8 stock24
    Month 8 stock: 24Horizontal bar from zero to 24, on the shared zero to 58 numeric axis.
  • Month 9 stock22
    Month 9 stock: 22Horizontal bar from zero to 22, on the shared zero to 58 numeric axis.
  • Month 10 stock20
    Month 10 stock: 20Horizontal bar from zero to 20, on the shared zero to 58 numeric axis.
  • Month 11 stock18
    Month 11 stock: 18Horizontal bar from zero to 18, on the shared zero to 58 numeric axis.
  • Month 12 stock16
    Month 12 stock: 16Horizontal bar from zero to 16, on the shared zero to 58 numeric axis.

Follow the calculation

  1. Month 1: 60.00 + recharge 10.00 - spill 0.00 - supplied 12.00 = 58.00 units; unmet 0.00.
  2. Month 2: 58.00 + recharge 10.00 - spill 0.00 - supplied 12.00 = 56.00 units; unmet 0.00.
  3. Month 3: 56.00 + recharge 10.00 - spill 0.00 - supplied 12.00 = 54.00 units; unmet 0.00.
  4. Month 4: 54.00 + recharge 10.00 - spill 0.00 - supplied 12.00 = 52.00 units; unmet 0.00.
  5. Month 5: 52.00 + recharge 5.00 - spill 0.00 - supplied 12.00 = 45.00 units; unmet 0.00.
  6. Month 6: 45.00 + recharge 5.00 - spill 0.00 - supplied 12.00 = 38.00 units; unmet 0.00.
  7. Month 7: 38.00 + recharge 5.00 - spill 0.00 - supplied 12.00 = 31.00 units; unmet 0.00.
  8. Month 8: 31.00 + recharge 5.00 - spill 0.00 - supplied 12.00 = 24.00 units; unmet 0.00.
  9. Month 9: 24.00 + recharge 10.00 - spill 0.00 - supplied 12.00 = 22.00 units; unmet 0.00.
  10. Month 10: 22.00 + recharge 10.00 - spill 0.00 - supplied 12.00 = 20.00 units; unmet 0.00.
  11. Month 11: 20.00 + recharge 10.00 - spill 0.00 - supplied 12.00 = 18.00 units; unmet 0.00.
  12. Month 12: 18.00 + recharge 10.00 - spill 0.00 - supplied 12.00 = 16.00 units; unmet 0.00.

A reservoir can mask an imbalance temporarily. Seasonal recharge and storage limits make an annual average insufficient for checking shortages.

Captures keep your inputs, prediction and observation. Results are recalculated from those inputs. Resetting inputs keeps your captures and challenge history.

4 · Understand

Explain the mechanism

What the experiment explains

Original synthetic reservoir: initial stock 60 units, capacity 100, twelve months; recharge is halved in months five through eight.

A stock is an accumulated quantity; a flow is a change per time interval. A positive stock can temporarily support demand above recharge.

At defaults, eight normal months add 80 and four dry months add 20. Annual demand is 144, so stock falls from 60 to 16 even though every month receives some recharge.

Shortage is counted only when available water cannot meet reduced demand. Avoiding shortages this year does not establish sustainability over repeated years or under different droughts.

Read the relationship

Available = min(capacity, previous stock + recharge). Supplied = min(available, demand × (1 − conservation fraction)). Next stock = available − supplied; unmet = reduced demand − supplied.

Use the trace as evidence

The trace recomputes from your current controls. Change one control at a time, record what changed, and compare the result with your prediction. The bars use the same quantities as the numerical trace; a larger bar is not automatically a better outcome.

Boundaries of the model

  • Invented units and seasonal pattern; no evaporation, water quality, ecological minimum flows, or recharge uncertainty.
  • Recharge arrives before withdrawal in each month. Conservation is assumed to reduce demand without rebound effects.

Continue with Enough energy, at the wrong time to investigate a different mechanism.

5 · Apply

Try a fresh case

A new reservoir starts with 20 units. Over three months recharge is 4 each month and demand is 10 each month. Capacity is 100. What is the final stock?

This is a public practice check. Retries support learning; matching a number does not certify independent proficiency.

Take the investigation further

Choose any extension. These are project prompts for you to carry out; they are not automatically assessed.

School investigation

Make a stock-and-flow diagram and explain why litres and litres/month are different quantities.

College investigation

Simulate multiple years with varied drought schedules and report shortage duration separately from volume.

Workplace investigation

Prepare a conservation brief with a reserve target, uncertain recharge scenarios, and evidence needed before implementation.

6 · Continue

Keep the evidence, choose your next step

Completion records your own decision that you have worked through this investigation. Practice checks and independent project evidence are separate.