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I have a problem to understand a passage in the article "Modeling the dynamics of pressure propagation and diameter variation in tree sapwood" that you can find here: ftp://ftp.bgc.mpg.de/pub/outgoing/athuille/Publications/2005/Peraemaeki_TP_2005.pdf

I haven't understood how equation (3) is obtained from conservation of water mass. In particular, let us consider a tree stem as tapering pipe of elastic porous material with permeability $k=k(h)$, where $h$ is stem height, and sapwood area $A_{sw}=\pi (r^2-r_{hw}^2)$, where $r=r(h)$ is the stem radius and $r_{hw}=r_{hw}(h)$ is radius of the heartwood (notice that: heartwood is the inner part of stem, without water, while sapwood is the part through the which water flows). So, authors claim that conservation of water mass of a stem segment of length $\partial h$ gives the equation of the continuity:

$\dfrac{\partial A_{sw}}{\partial t}+\dfrac{\partial Q}{\partial h}+S=0$

where $S$ is the sink caused by transpiration and $Q$ is sap flow in $m^3/s$. Any ideas?

Thank you in advance!

Donald Webb
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    you need to present the exact context and the precise problem that you are facing in the question itself... – Bruce Lee Jan 30 '16 at 15:26
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    @BruceLee is pointing out that he (and I) are not going to go to some random web site to pull a technical article and read through it to answer your question. However, you could put the necessary equations in your question for all to read without effort. – Jon Custer Jan 30 '16 at 15:30
  • What's worse, the download appears to be restricted to members – docscience Jan 30 '16 at 15:34
  • You're right...sorry...I hope that now the question is clear...if not, please let me know! – Donald Webb Jan 30 '16 at 15:39
  • @docscience Are you sure the link doesn't work? It doesn't appear as restricted... anyway, if you are interested, I think you could find a free copy with google: try looking for "Modeling the dynamics of pressure propagation and diameter variation in tree sapwood". – Donald Webb Jan 30 '16 at 16:04

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