How is the water volume updated each minute?

Volume increases by inflow and decreases by the drain rate while never dropping below zero.

What prevents negative volume when the drain exceeds inflow?

The simulation clamps volume to at least zero after each update.

Where do the probe values come from?

The run process emits water_volume, inflow and outflow every minute so the charts show how they change.

Bathtub Fill and Drain

A bathtub simulation illustrating stock and flow of water volume.

Level:Beginner

stocks-flows capacity

Stocks:water_volume
Flows:inflow, outflow
Probes:water_volume, inflow, outflow

Run

Stocks and Flows

Learn about the foundational concepts of Stocks and Flows in systems thinking and how they interact to create system behavior.

Explore Stocks and Flows

simulation.py

Filling and emptying a bathtub

This pared‑down example highlights the essence of stocks and flows. Water pours in from the tap while some trickles down the drain. By keeping things simple we can watch how the water level changes from one minute to the next.


from tys import probe, progress

Simulate water level in a tub with inflow and drain.

def simulate(cfg: dict):

    import simpy
    env = simpy.Environment()

    volume = cfg["initial_volume"]  # water in tub (liters)
    inflow = cfg["inflow_rate"]     # liters per minute entering
    drain = cfg["drain_rate"]      # liters per minute leaving
    minutes = cfg["minutes"]

    done = env.event()

Update the water volume each minute.

    def run():
        nonlocal volume
        for m in range(minutes):
            volume += inflow - drain
            volume = max(0, volume)
            probe("water_volume", env.now, volume)
            probe("inflow", env.now, inflow)
            probe("outflow", env.now, drain)
            progress(int(100 * (m + 1) / minutes))
            yield env.timeout(1)
        done.succeed({"final_volume": volume})

    env.process(run())
    env.run(until=done)
    return done.value


def requirements():
    return {
        "builtin": ["micropip", "pyyaml"],
        "external": ["simpy==4.1.1"],
    }

Default.yaml

initial_volume: 0
inflow_rate: 8
drain_rate: 3
minutes: 20

Charts (Default)

water_volume

CSV

Samples	20 @ 0.00–19.00
Values	min 5.00, mean 52.50, median 52.50, max 100.00, σ 28.83

inflow

CSV

Samples	20 @ 0.00–19.00
Values	min 8.00, mean 8.00, median 8.00, max 8.00, σ 0.00

outflow

CSV

Samples	20 @ 0.00–19.00
Values	min 3.00, mean 3.00, median 3.00, max 3.00, σ 0.00

Final Results (Default)

Metric	Value
final_volume	100.00

FAQ

How is the water volume updated each minute?: Volume increases by inflow and decreases by the drain rate while never dropping below zero.
What prevents negative volume when the drain exceeds inflow?: The simulation clamps volume to at least zero after each update.
Where do the probe values come from?: The run process emits water_volume, inflow and outflow every minute so the charts show how they change.

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