How do trees lift water higher than 10 meters?
Disclaimer: This is not my field of research.



First, this is not a complete answer to our question. A nice explanation of the current hypothesis of water transport in trees (Dixon-Joly cohesion-tension theory, originally proposed 1894) can be found at The Amazing Physics of Water in Trees but also in Tyree (1997). The key points are that the stoma (leaf surface pores) are so small that the menisci can withstand huge water columns, that water has strong cohesive forces, and that water is transported using the negative pressure that is created by transpiration. The webpage linked above contains a beautiful visualization of how multitudes of stomata and menisci create strong negative pressures:



Second, much of the current discussion in the comments (an indication that the question might be a poor fit for Bio-SE?) revolves around the plausibility of the cohesion-tension theory, and specifically on whether water can sustain strong negative pressures. Caupin &amp; Herbert (2006) review metastability and cavitation in water (in a physics journal), and contains experimental results on negative pressures in water. The paper references a large number of experiments under various experimental setups (I cannot fairly judge these). In their conclusion they state that:


  Among the countless cavitation experiments, only the ones with special care about water purity can reach large negative pressures; with a variety of techniques, they all obtain Pcav around −25 MPa at room temperature (see Fig. 3 (b)), which falls far away from the theoretical value (from −120 to −140 MPa). There is a notable exception: experiments with mineral inclusions achieve −140 MPa. The large gap between these data requires special attention.


So basically, the theoretical estimates lie at -130MPa and empirical results at -25MPa (-250 atmospheres), and water can clearly achieve large negative pressures. This would also mean that the current estimates are much larger than what is needed for the cohesion-tension theory to work (atmospheric pressure= 0.1MPa, negative pressure in water column at 50m ~ -0.5MPa).

They also have a section specifically discussing trees:


  7.1. Water in nature
  The law of hydrostatics teaches us that the pressure drop in a water column of 10.2 m is 0.1 MPa. This points out that negative pressures can be reached in the ascending sap of tall trees. In fact additional effects (viscous flow, drought) make the pressure in the sap negative even at smaller heights. The cohesion-tension theory, first proposed by Dixon and Jolly [56], explains that the sap column is held at the top by the meniscus in the pore of the leaves: by Laplace’s law, the meniscus curvature allows a pressure jump between the outside air pressure and the negative pressure in the sap. The trees thus contain large amounts of metastable liquids. Cavitation may sometimes occur, disrupting the liquid column and stopping the flow (xylem emboly). The complex hydraulic architecture of trees limits the damage, and strategies exist to refill the embolied xylem channels. Much work has been devoted to this topic, and is reviewed in Refs. [110,111].


There is also evidence that the risk of xylem embolism increases with tree height, and this creates a trade-off between water transport efficiency and structural adaptations to deal with embolism (Domec et al. 2008). This is for instance facilitated by the pit aperture diameter of tracheids, with apertures decreasing with height along a tree, causing increased resistance to embolism but at the same time lower water conductance. This will clearly limit the height of trees, and the paper indicates that the tallest Douglas firs are at the edge of what they can achieve.

Another recently published paper that should be relevant is 'Methods for measuring plant vulnerability to cavitation: a critical review' by Cochard et al. (2013), but I haven't had time to look closely at this. See abstract below:


  Abstract:
  Xylem cavitation resistance has profound implications for plant physiology and ecology. This process is characterized by a ‘vulnerability curve’ (VC) showing the variation of the percentage of cavitation as a function of xylem pressure potential. The shape of this VC varies from ‘sigmoidal’ to ‘exponential’. This review provides a panorama of the techniques that have been used to generate such a curve. The techniques differ by (i) the way cavitation is induced (e.g. bench dehydration, centrifugation, or air injection), and (ii) the way cavitation is measured (e.g. percentage loss of conductivity (PLC) or acoustic emission), and a nomenclature is proposed based on these two methods. A survey of the literature of more than 1200 VCs was used to draw statistics on the usage of these methods and on their reliability and validity. Four methods accounted for more than 96% of all curves produced so far: bench dehydration–PLC, centrifugation–PLC, pressure sleeve-PLC, and Cavitron. How the shape of VCs varies across techniques and species xylem anatomy was also analysed. Strikingly, it was found that the vast majority of curves obtained with the reference bench dehydration-PLC method are ‘sigmoidal’. ‘Exponential’ curves were more typical of the three other methods and were remarkably frequent for species having large xylem conduits (ring-porous), leading to a substantial overestimation of the vulnerability of cavitation for this functional group. We suspect that ‘exponential’ curves may reflect an open-vessel artefact and call for more precautions with the usage of the pressure sleeve and centrifugation techniques.