APPENDIX A: SOLUTION OF EQUATION 12 FOR FLOW UNDER TENSION
We model the water pathway with the idealized vein doublet discussed above, where the
dimensions of the smaller vein-node pair are 1/bth the larger. Repeating eq 9:
1.94 10 -3 dv
G2 (1 + b4 )
where G = 3.2 10 m3. The volume v of water re-entering the sample is ΦV, where V
(= 250 cc) is the sample volume. With v measured as 0.2 cc we take porosity as about 0.001.
The water re-entry pressure PWn is given by eq 5d
PWn = 0.1180/dv.
For assumed values of ki and b, eq A1 yields the vein width dv. Eq A2 then provides the
re-entry pressure PWn.
We solve eq 11, A1 and A2 simultaneously by trial and error, inputting values for ki and b
until the observed time is matched for a height of z = 0.043. This simplified scenario should