Student classroom guide

Mixing tank: can a smooth curve be trusted?

What does agreement with an analytic solution check, and what does it leave untested?

50 minutes · Introductory modeling · pairs

Before you begin

Derivatives, units, Python functions and arrays. This is a 50-minute introduction to the existing approximately 150-minute workshop, not its completion.

The well-mixed tank is an invented teaching system. No measured equipment, mixing validation or plant-safety result is supplied.

One-class sequence

5 min
Predict the long-run level
Sketch a 20 L tank: 2 L/min enters at 10 g/L; equal outflow, reaction 0.05/min, initial concentration 0. Will concentration reach 10 g/L?
10 min
State assumptions and balance mass
Write accumulation as inflow minus outflow minus reaction. Explain why volume is constant and outlet concentration equals tank concentration; check units.
10 min
Check two steps, then implement
Use the initial-value problem below to calculate two Euler steps. Complete student_model and the Euler update in student_euler using your balance.
$y'=-y,\qquad y(0)=1,\qquad h=0.1$
$y_{n+1}=y_n+h\,f(t_n,y_n)$
15 min
Run, change one condition, refine
Run the default, then set reaction to 0.2 per minute. Return to default physical parameters and halve the time step to 0.25 minutes. Record your actual run’s errors and checks, including failures. If time permits, try zero reaction.
5 min
Separate two kinds of evidence
What would an analytic-solution match tell you? Propose one tracer observation that would challenge the perfect-mixing assumption.
5 min
Leave a short evidence record
Write one result, one check and one limitation. Answer the exit question and export the original workshop’s Draft JSON or report; do not mark the full workshop complete.

Settings to apply manually

This form updates this classroom page and its share link only. It never loads settings into the activity or changes a saved draft.

Flow Q (L/min): 2
Volume V (L): 20
Reaction k (1/min): 0.05
Inlet concentration (g/L): 10
Initial concentration (g/L): 0
Time step (min): 0.5
Experiment seed: 2026

All comparison settings

Default balance

Flow Q (L/min): 2
Volume V (L): 20
Reaction k (1/min): 0.05
Inlet concentration (g/L): 10
Initial concentration (g/L): 0
Time step (min): 0.5
Experiment seed: 2026

No reaction

Flow Q (L/min): 2
Volume V (L): 20
Reaction k (1/min): 0
Inlet concentration (g/L): 10
Initial concentration (g/L): 0
Time step (min): 0.5
Experiment seed: 2026

Stronger reaction

Flow Q (L/min): 2
Volume V (L): 20
Reaction k (1/min): 0.2
Inlet concentration (g/L): 10
Initial concentration (g/L): 0
Time step (min): 0.5
Experiment seed: 2026

Default physics, half step

Flow Q (L/min): 2
Volume V (L): 20
Reaction k (1/min): 0.05
Inlet concentration (g/L): 10
Initial concentration (g/L): 0
Time step (min): 0.25
Experiment seed: 2026

Open the original activity

English / Traditional Chinese workshop.

Open the workshop and use its task, Python and results panels.
Apply the settings below manually and keep your prediction before running. Opening this link does not load the preset or reset a saved draft.
Start Python only when ready. Complete student_model and student_euler before running; unfinished starter functions are expected to fail checks.

Open Mixing-tank workshop

Device / Python fallback

Start Python downloads the scientific runtime on demand from jsDelivr. Test the classroom network beforehand. If loading fails, use the labelled precomputed reference and reference CSV/notebook; these are not a learner’s own run. Notebook execution requires Python with NumPy, SciPy and Matplotlib.

Precomputed reference CSV · Reference notebook

Keep this evidence

A mass balance with units and three assumptions; two hand-calculated Euler values.
An actual run or explicitly labelled reference, a refinement comparison and a limitation, exported from the original workshop where available.

Use the original workshop’s Draft JSON export/import and report. Drafts stay in this browser; the classroom page never reads or writes them. When storage is unavailable, the workshop labels session-only memory and provides export. Export before changing device.

Exit question

Your numerical curve matches the analytic curve. Does that establish perfect mixing in a real tank? What further evidence is needed?

Printable worksheet

Write on a printed copy or keep notes separately. This page has no answer storage. Use the original activity to save digital work.

My prediction and system boundary:

Balance / units / assumptions:

Two Euler hand values and update rule:

Settings / actual run or reference / error / failed checks:

One result, one check, one limitation and exit response:

Source and further reading

Sequence adapted from workshop-01 “A tank, a boundary, a balance”, v1.0.0, its existing exercise and reference assets. The 50-minute pacing is an introductory lesson plan; nondimensionalization, failure experiments and extended writing remain in the full workshop.

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