High School How to stop insulation from floating when flooded

[CWatters]

Elsewhere someone is planning to install Under Floor Heating (UFH) in a house that is prone to flooding. UFH systems typically comprise a layer of insulation then a layer of concrete screed with UFH pipes in it.

Given this recent news story http://www.dailymail.co.uk/news/art...th-car-park-float-raises-floor-four-feet.html I'm trying to work out what thickness of screed you need to stop the insulation floating.

I think I've done the sums right but perhaps someone could check them for me?

The buoyancy force is equal to the weight of water displaced by the insulation and screed...

Water weighs 1000kg per m^3. If Ti and Ts are the thickness of the insulation and screed in mm and g = acceleration due to gravity, then the buoyancy force per square meter is..

= 1000 * g * (Ti + Ts)/1000
= g * (Ti + Ts) N/m^2

Insulation is very light so I'll ignore it's weight. Screed weighs about 2200 kg per m^3 so the downward force due to the weight of the screed is about

= 2200 * g * Ti /1000
= 2.2 * g * Ti N/m^2

The latter must be greater than the former to stop it floating so

2.2 * g * Ti > g * (Ti + Ts)
g cancels
2.2 * Ti > Ti + Ts
rearrange to give
Ts > 0.83 Ti
so the screed must be at least 0.83 times the thickness of the insulation.

If the insulation was 200mm thick the screed would need to be 0.83 * 200 = 166mm thick to stop it floating in a flood.

I've ignored the fact that there is UFH pipe in the screed making it lighter.

Any mistakes?

 

[jbriggs444]

Looks good.

It passes the sanity check: 1 meter of insulation plus 0.83 meters of screed would be to 0.83 * 2200 ~= 1830 kg per square meter. By no coincidence, 1.83 meters of water is also 1830 kg per square meter.

 

[russ_watters]

Given this recent news story http://www.dailymail.co.uk/news/art...th-car-park-float-raises-floor-four-feet.html

Wow, good day to be driving a fiat! (a sentence never before spoken)

 

[CWatters]

Thanks folks.