System Dynamics | Foundation 3: Flows
Go With the Flow: Pipes, Currents, and Traffic Jams (A Love Story)
If stocks tell you where you are, flows tell you where you’re going.
A Quick Reminder
In the last module, we established that stocks are accumulations, water in the bathtub, money in the bank, expertise in your head. They characterize the state of the system and provide it with memory and inertia.
But stocks don’t change by themselves. Flows change them.
A quick note: Flows can’t be explained without stocks, they’re two sides of the same coin. If some concepts feel familiar from the last module, that’s by design. We’re shifting perspective from “what accumulates” to “what drives the accumulation.”
What Flows Actually Are
A flow is a rate, the speed at which something moves into or out of a stock.
Not the amount. The rate.
Production isn’t the inventory sitting in your warehouse (that’s the stock). Production is how many units you add per day.
Learning isn’t the knowledge you have (that’s the stock). Learning is how much you absorb per hour of study.
Traffic isn’t the cars on the highway (that’s the stock). Traffic is the rate at which cars enter and exit per minute.
This distinction matters enormously because flows are what you can actually control. You can’t instantly change your bank balance, but you can change how much flows in or out starting today. You can’t immediately become an expert, but you can change your learning rate right now.
Flows are the levers. Stocks are the results.
Three Love Stories About Movement
Let’s explore what makes flows tick through three everyday systems:
Story 1: The Pipes (Structure Shapes Flow)
Turn on your shower. Water flows out. Simple, right?
Not quite. The flow rate isn’t determined by how desperately you want water. It’s constrained by:
Pressure in the system (how much potential energy exists)
Pipe diameter (the physical capacity for flow)
Distance from the source (resistance along the path)
Competing demands (whether your neighbor is also showering)
A firm’s production capacity works identically. You can’t just decide “we need 10,000 units tomorrow” any more than you can make water flow faster by yelling at your showerhead. The structure of the system determines maximum possible flow.
This is why “work harder” often fails as strategy. If the pipes are narrow, pressure is low, or the path is blocked, cranking up effort doesn’t increase output. You need to change the structure.
The insight: Flows aren’t limitless. They’re shaped by the architecture of the system they move through.
Story 2: The Currents (Time Makes Everything Accumulate)
Watch a river. After a storm, it swells. During drought, it shrinks. The river is constantly changing because its inflows (rain, tributaries, snowmelt) rarely equal its outflows (evaporation, irrigation, flow to the sea).
This is the fundamental dynamic: when inflows and outflows don’t match, the stock must change. We saw that, right? Do you remember the bathtub?
Inflow > Outflow → Stock grows
Inflow < Outflow → Stock shrinks
Inflow = Outflow → Stock holds steady (dynamic equilibrium)
Your expertise follows this pattern. If learning (inflow) exceeds forgetting (outflow), knowledge grows. If you stop learning but keep working in a changing field, the outflow of obsolescence exceeds the inflow of new knowledge. Your expertise stock erodes.
The insight: Accumulation is just the integral of net flow over time. Every stock you see is a historical record of past flow imbalances.
Story 3: The Traffic Jam (When Math Becomes Destiny)
You’re stuck in traffic. Here’s what’s happening:
Inflow: 60 cars/minute entering at the on-ramp
Current stock: 500 cars on this highway stretch
Outflow: 40 cars/minute (accident ahead)
Net change: +20 cars per minute
The jam must grow. Not because of bad luck or Murphy’s Law. Because of mathematics.
This is the brutal honesty of flow dynamics:
Stock(ending time) = Stock(starting time) + (Inflow - Outflow) × (ending time-starting time)
No amount of honking changes this equation. The traffic will keep getting worse until either:
Inflow decreases (police block the on-ramp), or
Outflow increases (accident clears)
Only when inflow equals outflow does the stock stabilize.
This same dynamic governs organizational backlogs. If customer orders arrive at 100/day but you can only fulfill 80/day, your backlog grows by 20/day. Every. Single. Day. Being stressed about it doesn’t help. Working weekends might temporarily boost outflow, but unless you fundamentally change the flow rates, the backlog keeps growing.
The insight: When flows don’t balance, stocks change predictably. You can’t bargain with math.
The Mathematics of Flows
Optional Part: For those comfortable with equations, yet it’s rather easy. Don’t be scared (:
All three stories, pipes, currents, traffic, follow the same fundamental logic: The quantity in any stock equals the accumulation of inflows minus outflows over time. Let’s formalize what we’ve learned.
The Integral Form (Accumulation)
Stock(t) = Stock(t₀) + ∫ [Inflow(s) - Outflow(s)]ds (from t₀ to t)
t₀ → The time we are at now
t → The time we will be
Stock(t₀) → Where we are at the moment
Stock(t) → Where we’ll be at time t, in the some time future
∫ [Inflow(s) - Outflow(s)]ds (from t₀ to t) → Sum of all the inflows minus sum of all the outflows during the time between t and t₀
Translation: The stock at any time equals its starting value (at t₀) plus everything that flowed in minus everything that flowed out (in the duration of t-t₀).
The Differential Form (Rate of Change)
dStock/dt = Inflow(t) - Outflow(t)
Translation: The rate at which a stock changes equals the inflow rate minus the outflow rate.
These aren’t separate truths, they’re two ways of saying the same thing. The integral tells you the accumulated result. The differential tells you what’s happening right now.
Don’t let the notation intimidate you. These equations simply formalize what you already know from watching your bathtub fill: stocks accumulate their flows. The net flow into a stock is the rate at which the stock changes.
The bathtub diagram, the integral, and the differential equation are precisely equivalent. They contain exactly the same information. Pick whichever representation helps you think most clearly.
How to Spot Flows in the Wild
The Units Test
Flows are always measured as quantity per time:
Hiring rate: people per month
Production: widgets per day
Cash burn: dollars per week
Learning: concepts per hour
Erosion: tons of soil per year
If there’s no “ blahblah per [time unit],” it’s not a flow, probably it’s a stock.
The Snapshot Test
Stocks can be captured in a snapshot. Flows require a video, they only exist when time passes.
You can photograph cars on a highway (stock), but to see traffic flow, you need to watch them move. You can count money in an account (stock), but to see cash flow, you need to track transactions over time.
The Control Test
Here’s my favorite, the most practical test. Ask: Can you directly change it right now?
You can’t instantly change your bank balance (stock), but you can cash out today (outflow).
You can’t immediately become fit (stock), but you can exercise more this week (inflow).
You can’t instantly shift company culture (stock), but you can change hiring criteria today (inflow).
Flows are the variables under your control. Stocks respond to flows, but flows are where intervention happens.
Tricky Cases: Mental Stocks vs. Observable Flows
Take your time and think. Go back and look at the tests. Don’t let me intimidate you..
Is price a stock or a flow?
Price is a stock. It’s a state, the current exchange rate between goods and money. It stays constant until someone actively changes it. Even rapidly fluctuating prices in financial markets are stocks with very high rates of change.
The rate of price change would be a flow.
Is average speed a stock or a flow?
Imagine yourself driving, glancing at your dashboard. It shows 100 km/hr - but which number are you looking at? Current speed or average speed?
Your current speed changes moment to moment as you accelerate or brake.
Your average speed is a stock. You drove 90 km/hr for the first hour, then 110 km/hr for the second hour - now your average sits at 100 km/hr. It persists even when you stop at a red light at the end of 2 hours (current speed = 0). Floor it to 130 km/hr for ten minutes? Your average barely budges. As you can see, it has inertia.
The flows are those moments of acceleration and braking that slowly update your average.
This is why “average” anything is usually a stock. It’s accumulated information that changes slowly, even when reality has already shifted. A manager’s “expected order rate” works the same way, since its his business knowledge or expectation that has being built over the years in his career.
Why Flow Blindness Kills
We’re naturally better at seeing stocks than flows. Stocks are visible, we can count them, measure them, dashboard them. Flows are invisible, rates happening beneath the surface.
The stock is the score. The flows are the game being played.
So why call this a love story?
Because stocks and flows need each other. Flows without stocks have nowhere to accumulate, they’re events without memory. Stocks without flows never change, they’re frozen, static, dead.
And here’s the beautiful part: once you see flows, you see the possible futures.
Stocks tell you where you are. Flows tell you where you’re going:
Huge inventory but production halted? It’ll vanish.
Deep expertise but no time to learn? It’ll erode.
Packed highway at 8am with 5,000 cars/hour entering a section that handles 3,000? Gridlock by 9am.
Master flows, and you can anticipate problems before they show in the numbers, intervene where it matters (at the valves, not the tank), and design systems that self-regulate. Ignore flows, and you’re just hoping yesterday’s inertia carries you forward.
But Wait, There’s More
We’ve covered how flows work, but not what controls them.
Flows don’t happen randomly. They respond to conditions in the system: high inventory triggers production cuts, low water pressure triggers the pump, traffic jams cause drivers to reroute.
When flows respond to stocks, when the system starts reacting to its own state, that’s when things get truly interesting. That’s when we get growth, collapse, oscillation, and all the complex patterns that make systems fascinating and frustrating.
That’s when we start to talk about feedback loops. But before, we need to learn how to visualize all of these to understand and see, in other words causal loop and stock-flow diagrams.
And that’s our next chapter.
👋🏽 Before You Go
Next time you look at a number that matters to you, your bank account, your relationship, your company’s customer base, pause and ask yourself: What invisible flows are filling or draining this right now? And if those flows stay the same, where will I be in three months?
🧩 What’s Coming Next
This foundations series will build your systems thinking toolkit step by step:
2 | Stop! Let’s Talk Stocks: Not Wall Street, Just Bathtubs ✔️
3 | Go With the Flow: Pipes, Currents, and Traffic Jams (A Love Story) ✔️
📚 Main Resources
Meadows, D. H. (2015). Thinking in Systems. Chelsea Green Publishing.
Sterman, J.D. (2000) Business Dynamics: Systems Thinking and Modeling for a Complex World. Irwin McGraw-Hill, Boston.
My lecture notes from “System Dynamics” and “Simulation” classes :)
Some explanations and phrasings closely follow or directly quote these sources. The text was refined for coherence and citation accuracy with the assistance of large language models.
I was always wondering how states/empires would collapse. How could such a huge system stop working? Weren't there any signs of upcoming turmoil, revolt, economic shortcomings, ineffective policies? After reading this I guess people in charge were not able to realize the change in flows: warfare, decreased trust of citizens in decisions, shifting global trade etc. Waiting for the flow to cuase a signifanct change in stocks to start acting seems to doom systems to fail...