How does the energy of tornadic winds compare to floodwaters?

I have been watching The Weather Channel for a month straight following the hurricanes. One of the meteorologists warned people not to drive into floodwaters, saying that water moving at about 6 miles per hour has the same amount of power as an EF5 tornado.

How did they figure that out?

• This is something you can study in fluid dynamics; heavier fluid with slower speeds do resemble the effect of lighter fluid with higher speeds (accurate when needed dimensionless numbers describing the setup are taken into account). Commented Sep 22, 2017 at 7:40
• See also earthscience.stackexchange.com/questions/12339/… and wx.graphics/tropical and engineeringtoolbox.com/hydropower-d_1359.html may also be helpful (it's similar to how dams generate power from moving water)
– user967
Commented Sep 22, 2017 at 14:46
• That's what people always underestimate in floods: one cubic meter of water weighs one ton! If it wasn't fluid it would destroy anything. Worse for mud. Commented Sep 27, 2017 at 7:53
• Here is a graphic from the NWS on what water can do, though it does not address any comparison to tornadoes. Commented Oct 8, 2017 at 19:36

• The force exerted by a moving fluid (gas or liquid) per unit area is proportional to its density $D$ and to the square of its velocity $V^2$.
• The power delivered by a moving fluid (gas or liquid) per unit area is proportional to its density $D$ and to the cube of its velocity $V^3$.

Water is about $800$ times as dense as air.
So water moving at $(\frac{1}{800})^{1/2}$ or about $\frac{1}{28}$ as fast as air exerts the same force per unit area,
and water moving at $(\frac{1}{800})^{1/3}$ or about $\frac{1}{9}$ as fast as air delivers the same power per unit area.

Or in other words air must move $800^{1/2}$ or about $28$ times as fast as water to exert the same force per unit area, and $800^{1/3}$ or about $9$ times as fast to deliver the same power per unit area.

Thus water moving at $6$ mph exerts the same force per unit area as air moving at about $170$ mph (a $170$ mph wind), and delivers the same power per unit area as air moving at about $55$ mph (a $55$ mph wind).

So it is not the power of 6 mph water that equals that of an EF4 (not EF5) tornado, but the force.
$6$ mph water has the same power as a 55 mph whole gale.

• Thank you! While I'm not good at math or scientific equations, I still understand your answer. Now I know how they determined how much force from a flashflood can rival a tornado. 😁 Commented Sep 27, 2017 at 21:17
• Your welcome! I'm glad that I could be of help. Commented Oct 1, 2017 at 22:05

In addition to the answer posted by Jack, there is also buoyancy that must be accounted for.

By shear force, six inches of water will sweep you off your feet. Effectively what could happen is the same as taking a dive into a shallow water slide- possible head injury and the possibility of drowning, alongside being swept away. Those same six inches may flood your car.

One foot of water, even stagnant water, will float your car. If the water is rapidly moving, I'd hypothesize it may even roll your car, maybe even carry it off.

An EF2 tornado has wind speeds of 111-135 mph and can lift cars off the ground, but might not be thrown. An EF3 tornado, with wind speeds between 136-165 mph, will throw cars.

Very few people are foolish enough to drive into tornadoes (the tornado interceptors are an exception- they have proper equipment). The same can't be said about floodwaters. I've seen people drive through unsafe waters during a rain storm and have their cars stall in the middle of the road.

• The effect of fluid flow speed alone can be obtained by considering an object A of density N times that of water (N > 1) in air and another object B of the same size and shape as object A but of density (N + 1) times that of water in water. The extra density of object B cancels the buoyancy effect, so that the effect of fluid flow speed alone can be realized. Commented Sep 26, 2017 at 23:24