Why is it dangerous to walk through a flooded street?
― Even knee-deep water can sweep an adult off their feet, if it's flowing
"Knee-deep water should be walkable." People who go outside thinking that keep getting swept off their feet by the current. The cause is a tug-of-war between two forces. The force of water pushing on your legs rises sharply with the speed of the flow. At the same time, a submerged body gets lighter, and your shoes lose their grip on the ground.
On a night of heavy rain, brown water is flowing into the street outside your house. It's about knee-deep. The shelter is a 10-minute walk away.
You've probably walked through knee-deep water in a pool before. It felt a bit heavy, but nowhere near enough to knock you over.
But at the same depth, once the water is flowing, everything changes. What exactly is different?
The danger comes from a tug-of-war between two forces
When the flow's speed doubles, the force pushing on your legs quadruples. Even a small increase in speed makes the push suddenly much stronger.
Buoyancy acts on you in the water, making your body lighter. As the force pressing your body into the ground drops, your shoes can't hold their grip as well.
Whether a person gets swept away depends on which is bigger: the force of the current pushing on them, or the force their shoes can grip with. Let's look at each in turn.
Why does the force of the current suddenly get so strong?
Flowing water hits your legs and changes direction. The momentum the water hands off to your legs in doing so is the force pushing on them.
When the speed doubles, twice as much water hits you each second. And each bit of water that hits you also carries twice the momentum. Two doublings multiply together, so the pushing force quadruples. That's what "grows with the square of the speed" means.
On top of that, the deeper the water, the more leg area it hits. Double the depth, and the pushing force roughly doubles too. Try changing the flow speed with the slider in Figure 1.
1.6 m/s is about how fast an adult walks when hurrying slightly. For water flowing down a street, that's not an unusual speed at all.
Why does being submerged make it harder to hold your footing?
We can stand on the ground because our body weight presses our shoes against it. The harder that press, the harder it is for the shoes to slip, even when pushed sideways.
But in water, buoyancy acts on whatever part is submerged. If a 60 kg person is submerged up to above the knee, their body gets about 10 kg lighter — equal to the weight of the water their legs displaced. That means less force pressing the shoes down, so they slip more easily.
Worse, a flooded street's surface is often slick with mud — far more slippery than dry ground. The deeper the water, the more the push increases and the more the grip decreases. Both changes work against you at once.
And while walking, the moment one foot lifts off the ground, the other foot alone has to withstand the whole force of the current. That's why walking is more dangerous than standing still.
In murky water, you can't see your footing. During a flood, water pressure can pop manhole covers loose, and the line between the street and a ditch or irrigation canal disappears. A single misstep can drop you into deep water and sweep you away.
So what should you do?
- Evacuate before the water arrivesLeave while the roads are still dry. Going outside once flooding has started is dangerous in itself.
- If the water has already arrived, don't force your way outsideMoving up to the second floor or higher of your home or a sturdy nearby building counts as evacuating too.
- If you see someone being swept away, don't jump into the waterStay back, call emergency services, and throw something that floats while you wait for help.
Disaster-prevention agencies warn that even adults find walking dangerous once the water reaches about 50 cm, and that a current can sweep someone's feet out from under them at a depth of just 20 cm. Rubber boots fill with water and get heavy, so lace-up athletic shoes are recommended instead. Check the ground ahead with a stick, and never walk alone — go with others, tied together with a rope if possible. But this is only for when there's truly no other choice. The best option is always to finish evacuating before the water arrives.
Summary
People get swept away on flooded streets because of two things working together: ① the force of the current pushing on the legs grows with the square of the speed, and ② the deeper you're submerged, the lighter buoyancy makes you, weakening your footing. Judging by depth alone misses the force of the current.
Water sweeps people away by its "speed," more than its depth.
So finish evacuating before the water arrives.
In flooding, a different force — the sheer "weight" of water, not the current — is what jams a car door shut. For more on that, see Why a car door won't open on a flooded road. For why a river can rise suddenly even under clear skies, try Why rivers can suddenly rise even when it's sunny.
- In the bathtub, spread your palm and move it slowly sideways. Then move it the same distance quickly.
- Notice how much stronger the push-back on your palm is when you move it fast. Double the speed means four times the force.
- While sitting in the tub, lift your hips slightly. You should feel your body rise much more easily than it would on land. That's buoyancy.
If you have access to a lazy river pool, standing against the current there gives you a good sense of the pushing force. Never try this on an actual flooded street.
Want to go deeper? ― terms, formulas, and textbook linksWe mark which level each topic belongs to, from junior-high science up to university specialist courses
- JHSCovered in junior-high-school science
- HSCovered in high-school "Basic Physics / Physics"
- HS+High-school advanced content, or a textbook sidebar topic
- UnivNot covered in high school — university-level specialist content (fluid dynamics)
- ResearchNot yet settled even at university level — something researchers are actively studying
JHSTerms: this phenomenon has names
- Drag force: the force pushing an object placed in a current, in the direction of the flow. This is the force pushing on the legs.
- Buoyancy: the upward force an object submerged in water (etc.) receives, equal to the weight of the water it displaces.
- Friction force: the force resisting slipping between two surfaces. The harder the surfaces press together, the greater it is.
JHSHSChecking with formulas: comparing the force of the current with the grip force
Let's calculate both forces for a 60 kg adult standing in a current 50 cm deep. The numbers below are rough figures meant to illustrate the mechanism.
| In symbols | F = ½ × ρ × C × A × v² and R = μ × ( m × g − ρ × V × g ) |
| In words | Pushing force = ½ × water density × shape coefficient × area facing the water × speed squared. Max grip force = friction coefficient × (body weight − buoyancy) |
| Where these formulas come from | The pushing force comes from the momentum of water that hits the legs and is brought to a stop. The grip force combines the law of friction with Archimedes' principle. When the pushing force exceeds the grip force, the feet start to slip. |
| Symbol | Meaning and unit |
|---|---|
| F | Force of the current pushing on the legs (drag force). Unit: N (newtons) |
| ρ | Density of water. Unit: kg/m³ |
| C | Drag coefficient. A dimensionless number determined by the object's shape |
| A | Frontal area of the legs facing the water. Unit: m² |
| v | Flow speed. Unit: m/s |
| R | Maximum grip force of the shoes. Unit: N |
| μ | Friction coefficient between shoe sole and ground. Dimensionless |
| V | Volume of the submerged part of the legs. Unit: m³ |
| Density of water | 1000 kg/m³ |
| Drag coefficient for a leg-like cylinder | roughly 1.0 |
| Frontal area facing the water (two legs, 12 cm wide each, 50 cm deep) | roughly 0.12 m² |
| Flow speed | taken as 1.5 m/s |
| Body weight | 60 kg |
| Submerged leg volume (equal to 10 kg of water) | roughly 10 L |
| Friction coefficient between muddy wet road and shoe sole | assumed 0.3 |
| Speed squared | 1.5 × 1.5 = 2.25 |
| Half the water density (multiplying by coefficient 1.0 changes nothing) | 1000 ÷ 2 = 500 |
| Multiply by area | 500 × 0.12 = 60 |
| Pushing force F | 60 × 2.25 = 135 N |
| Weight from body mass | 60 × 9.8 = 588 N |
| Buoyancy (weight of 10 kg of water) | 10 × 9.8 = 98 N |
| Force pressing on the ground | 588 − 98 = 490 N |
| Max grip force R | 490 × 0.3 = 147 N |
| Speed squared at which pushing force equals grip force | 147 ÷ 60 ≒ 2.45 |
| That speed | the square root of 2.45 is about 1.57 (roughly 1.6 m/s) |
At 1.5 m/s, the pushing force is 135 N — just short of the 147 N grip limit. A tiny bit faster, and the feet start to slip.
| Converting the 135 N push into an equivalent weight | 135 ÷ 9.8 ≒ 13.8 kg |
| At double the speed, 3 m/s, the pushing force is | 135 × 4 = 540 N |
A current of 1.5 m/s is like being pushed sideways by a 14 kg load, continuously. At 3 m/s, that becomes equivalent to about 55 kg — like having an adult continuously shoving into you. And the instant one foot lifts, your grip drops even further.
HSHS+Balance of forces, and resistance that scales with speed squared
HSBasic Physics teaches that the maximum static friction force equals the coefficient of static friction times the normal force. In water, buoyancy reduces the normal force, so the same shoes produce less maximum friction. Buoyancy itself is found from Archimedes' principle: it equals the weight of the displaced liquid.
HS+Resistance from water or air comes in two kinds: resistance proportional to speed (viscous drag) and resistance proportional to speed squared (inertial drag). For something leg-sized moving through water at around 1 m/s, it's generally enough to consider only the speed-squared term. This is the same idea behind the terminal velocity of a raindrop or a falling object.
UnivDrag coefficient, Reynolds number, and Kármán vortices
The drag coefficient changes with the Reynolds number (speed × size ÷ kinematic viscosity), which describes the character of the flow. For water at 1 m/s around a leg-sized cylinder, the Reynolds number comes out to around 100,000. In that range, a cylinder's drag coefficient is typically about 1 to 1.2. Vortices also form alternately on either side behind the cylinder (Kármán vortices), so the legs get shaken periodically sideways as well as along the direction of the flow.
📖 For the derivation of the formula and further reading: Drag force (Japanese Wikipedia) ／ Archimedes' principle (Japanese Wikipedia)
ResearchWhat isn't fully understood yet
- Where exactly is "water you can't walk through"? Methods have been proposed for judging danger from depth multiplied by flow speed, but the limit varies hugely by body size, age, and footwear, so it can't be captured by a single line.
- The force of water carrying mud and debris. Real floodwater is mixed with mud and driftwood. How much that heavy, murky water increases the pushing force is far less understood than experiments with clean water.
- The effects of darkness and fear. How darkness, not being able to see your footing, and panic change the way people walk, and how much they raise the risk of falling, is a hard thing to reproduce in experiments.
In other words, this article too is "an explanation based on what's currently known." Precisely because the limit can't be pinned down exactly, it matters to act before the water arrives.
Links to textbooks (by level)
| Level | Subject / unit | Where in this article |
|---|---|---|
| JHS | Science, "How forces work" / "Water pressure and buoyancy" | Buoyancy making the body lighter |
| HS | Basic Physics, "Friction" / "Buoyancy" | Grip force = friction coefficient × (body weight − buoyancy) |
| HS+ | Physics, advanced "air resistance and terminal velocity" | Pushing force growing with the square of the speed |
| Univ | Fluid dynamics, "drag and Reynolds number" | Drag coefficient and Kármán vortices |
| Research | Disaster-prevention engineering / hydraulic engineering | How to determine the limits of walkability |
| ― | Connection to daily life | Deciding when to evacuate during heavy rain |
- Cabinet Office (Disaster Management) (内閣府 防災担当), "Guidelines on Evacuation Information"
- Ministry of Land, Infrastructure, Transport and Tourism (国土交通省), "River Disaster Prevention Information" and explanatory material on evacuation during flooding
- The Japan Society of Mechanical Engineers (日本機械学会), Fluid Dynamics (JSME Textbook Series), Maruzen Publishing
- Kyoto University Disaster Prevention Research Institute, Uji River Open Laboratory (京都大学防災研究所 宇治川オープンラボラトリー), report on walking experiments in flood conditions
※ This article is a general-audience science explainer. The figures given are rough estimates meant to illustrate the underlying mechanism. The actual depth and speed at which a person starts to be swept away vary greatly depending on body size, footwear, and road conditions. During heavy rain, please follow the instructions and evacuation information issued by fire departments, local authorities, and other official agencies.