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  1. Problems
  2. /Water rises in a very thin tube by capillary action, h = 2T/(ρ g r)…
HardBiologyHigh School (9–10)GeneralTissues and Organs › Plant TissuesNumerical

Water rises in a very thin tube by capillary action, h = 2T/(ρ g r)…

StemPy LabContributed by StemPy Lab

Try it on paper first. A hint, the key idea and the worked solution are here when you need them.

Water rises in a very thin tube by capillary action, h=2Tρgrh = \dfrac{2T}{\rho g r}h=ρgr2T​. Find the height in a tube of radius 8 μm8\ \mu\text{m}8 μm. Use T=0.0728 N/mT = 0.0728\ \text{N/m}T=0.0728 N/m, ρ=1000 kg/m3\rho = 1000\ \text{kg/m}^3ρ=1000 kg/m3 and g=9.8 m/s2g = 9.8\ \text{m/s}^2g=9.8 m/s2. Could this alone lift water to the top of a 30 m tree?

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Need a reminder? The key ideaShowHide

Xylem carries water and minerals up, and is mostly dead cells. Phloem carries food up and down, in living sieve tubes with companion cells. Capillary rise: h=2Tρgrh = \dfrac{2T}{\rho g r}h=ρgr2T​.

The worked solution

Have you tried it?

Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.

Step 1. The radius. r=8×10−6 mr = 8 \times 10^{-6}\ \text{m}r=8×10−6 m.

Step 2. The top and the bottom. 2T=2×0.0728 N/m=0.1456 N/m2T = 2 \times 0.0728\ \text{N/m} = 0.1456\ \text{N/m}2T=2×0.0728 N/m=0.1456 N/m. For the bottom, ρgr=1000 kg/m3×9.8 m/s2\rho g r = 1000\ \text{kg/m}^3 \times 9.8\ \text{m/s}^2ρgr=1000 kg/m3×9.8 m/s2 × 8×10−6 m\times\ 8 \times 10^{-6}\ \text{m}× 8×10−6 m =0.0784 N/m2= 0.0784\ \text{N/m}^2=0.0784 N/m2.

Step 3. The height. h=0.1456 N/m0.0784 N/m2=1.86 mh = \dfrac{0.1456\ \text{N/m}}{0.0784\ \text{N/m}^2} = 1.86\ \text{m}h=0.0784 N/m20.1456 N/m​=1.86 m.

Step 4. The tree. No: 1.86 m1.86\ \text{m}1.86 m is far less than 30 m30\ \text{m}30 m. Transpiration from the leaves is the main pull.

Answer: 1.86 m1.86\ \text{m}1.86 m; not enough on its own.

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  1. Complex permanent tissues: xylem and phloemPlant Tissues

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