• ## Bainite

It's not pearlite or martensite. A blog written by Mathew Peet.

## How do trees raise water?

Capillarity can raise liquid against gravity, I was interested to know how much this can account for the movement of water in trees, is capillarity alone enough to lift water up a tree trunk?

For water in a tube there is an equation like this;
``` h = 2T cos (theta) / pgr where; T = 0.0728 J/m^2 at 20 degrees C, the contact angle theta = 20 degrees, density of water, p = 1000 kg/m^3, and the local acceleration due to gravity can usually be taken to be 9.8 m/s^2. ```

So the height is given by;
``` h = 1.4x10^{-5) / r ```

So tubes of the following diameters can lift water to the following heights.

 Diameter (mm) Height (m) 1 0.014 0.1 0.14 0.01 1.4 0.001 14 0.0001 140

If we assume perfect contact these heights become only slightly larger. (cos(theta)=1)
1 micrometre diameter tube can lift water 14.85 m, it’s necessary to have a tube 0.1 micrometres or 100 nanometers to lift water a height of 148 meters by capillary action alone, if the above equations are valid. Looking around on the internet gave a size of xylem in a tree to be around 20-30 micrometres (0.02 – 0.03 mm) in size, which if true enough to lift water around half a meter. It would be interesting to see if this value is correct.

If you are interested to find more there is a 2004 nature article on the limits of tree height here.