Answer: The leaves and petals of plants contain many small pores, called stoma. Water evaporates through these pores. As it does so, the plant draws water through its stem, and ultimately from its roots via the surrouding soil (or from the water in the vase). This process of water transport is called transpiration. It occurs in vascular bundles in the stem, called phloem. Blue or red dye is very good for outlining the phloem in the plant as it draws the water + dye up the stem. You can see it quite clearly if you cut the stem and look at it in cross-section.
Hope this provides the answer to your question!
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