Darcy's correlation in ecohydrology
This is a supplementary article for Darcy's Law in Predicting Tree's Inevitable End.
So you read the article and was brave enough to venture into the confusing world that is Totally Common Nomenclature and Equivalent Terms.
But no worries! I've did the digging, head scratching, and head goofing-ups to make them make sense for you, so you don't have to.
You might also find it helpful to read the article that I've cited here, although the terms used are slightly different, the analysis is definitely worth a read. [1]
Let's start with electrical analogy, so from Ohm's Law:
and since conductance is the reciprocal of resistance:
Rearranging gives:
In hydraulic terms:
where q is flow rate, and ΔP is pressure difference;
When Darcy's Law is converted for ecohydrology there are some terms that we may recognise:
1. Both Ψs– Ψl and D represent pressure difference but in different context;
2. Ks is the equivalent term for κ, permeability
3 ƞ is the alternative symbol for μ, dynamic viscosity.
4. h is dx.
We can now rewrite the complicated equation from the article as
and if you could recall, we also know this equation of flow rate that uses permeability rather than hydraulic conductivity:
Rearranging for κ and substituting into (5):
Et voila, this is essentially what we have from (4)!
Note: Al, area of leaf, is there for us to get the specific conductance for leaf of a species, since multiple values obtained from several species of plants were compared, this was likely done to aid comparison.
[1]D. Reid, U. Silins, C. Mendoza and V. Lieffers, "A unified nomenclature for quantification and description of water conducting properties of sapwood xylem based on Darcy's law", Tree Physiology, vol. 25, no. 8, pp. 993-1000, 2005. Available: 10.1093/treephys/25.8.993.