VACETS Regular Technical Column

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August 27, 1996

How High Can You Suck

You were walking across the Sahara desert. A seam of dunes lay across your path. There was no sign of water. The heat poured down like boiling oil. Your mouth felt swollen and your lips were cracking. You hadn't had a drink for days and were at the brink of collapse. Death seemed inevitable. Suddenly you looked up to see a well among the thornbush in the far distance. Used all the remaining strength, you crawled to the well and looked inside. You were so disappointed for the well were more than 10 m deep and there was nothing around that you could use to get the water from the deep well up. Walking around the well, you saw a sign on the side of it saying "WISHING WELL." "Well well, I need a coin to make this come true." And so you search all your pockets and luckily found the only coin, a penny. Dropping the penny into the well and wishing... Suddenly, a study long straw appeared. "I'm saved," you cried out loud. Putting the straw into the well, you tried to suck the water up into your mouth but got nothing. Sucking with all your might, you could see that the water column could come up to a distance of only about 2 m above the water surface. There was no way you could lift the water up more than 10 m to the top of the well, unless you were Superman. Now you wished that you had wished for a bucket and a long rope instead of the straw. Looking up the bright sky, you saw a bird. No, it is an airplane. No, it is Superman.

"Need some help," said Superman.

"Yeah, I couldn't suck the water up this well," came your reply.

"Stand aside, weakling. I'll do it for you."

So Superman started to suck on the straw and the water came up and up and ... almost to the top. He tried again and again but each time, the water came up few decimeters short. Superman, the man of steel who could move mountains but could not pull the water up slightly more than 10 m deep well. He was disturbed by this fact, but then remembered some idea he learned in a physics class in his freshmen year in college. Instead of sucking on the straw, he started to blow into the well and a column of water came up through the straw and sprayed all over. And you were saved.

So what did Superman learn in his freshmen physics class and why could he lift the water up a distance of tens of meters by blowing into the well but couldn't suck the water up more than 10 m?

To answer all that, we may start with the question "What does it mean to suck?" Normally, we think of sucking through a straw as pulling the liquid up, but actually the liquid is being pushed up the straw by the difference between the atmospheric pressure on the surface of the liquid outside the straw and the lower pressure in your mouth. The atmospheric pressure on earth is equivalent to that created under a depth of about 10 m of water. So, ideally you could suck water up a height of 10 m if you created a vacuum at the top of a straw. Clearly most people can suck water only a small fraction of this distance. As for Superman, being the man of steel, he could create a perfect vacuum, but that was just able to bring the water up a distance of 10 m and no more. And that also applies to any mechanical devices such as the water pumps. A perfect water pump can only suck the water up a distance of no more than 10 m just like Superman. "So how do you pump the water up from some hundreds of meter deep well? Do you have to connect many pumps together at a distance of 10 m a pump?" No, you don't have to. The height of the water column is proportional to the difference of the atmospheric pressure (1 ATM) and the pressure that you create. The lowest pressure you can create is the vacuum which could bring the water up a distance of only 10 m. However, if you go the other way, that is, create a pressure larger than the atmospheric pressure then the water can be pushed up by your larger pressure. So if your water pump can create a pressure of 10 ATM then the difference between the pressure of the pump and the atmosphere is 9 ATM which then can push the water up a height of 90 m. So now you see how Superman could only suck the water up a distance of only 10 m but when he blew into the well, he could push the water up the straw up to a distance of tens of meters. When he blew into the well, he increased the pressure on the surface of the liquid outside the straw to many ATM and that pushed the water inside the straw up to a distance far above the 10 m limit.

"So how do the trees grow to some height greater than 10 m? I know some kinds of trees grow to a height of 100 m or more. In order to photosynthesize the sunlight incident on its leaves, a tree needs to pump water up from the roots to the leaves. How can a tall tree accomplish this task? Does it have some kinds of mechanical or biological pumps that could push the water up from the roots to the leaves at the top?"

The water flows upward through very narrow channels in the tree. As you just learned that even if a tree could create a vacuum at the top of the channels, it could only lift the water a distance of only 10 m. But this height limitation applies only to water being pushed up by atmospheric pressure. No such 10-m height limitation applies to water being pulled up a very narrow channel (capillary). Capillarity is the action by which the surface of a liquid where it is in contact with a solid is raised or lowered depending upon the relative attraction of the molecules of the liquid for each other and for those of the solid. For water, capillary action can pull the water up because for a very narrow capillary the surface attraction of the water molecules to the capillary wall often exceeds the attraction of the water molecules to each other. The narrower the capillary, the greater the ratio of the surface attraction to the weight of the fluid, and hence the higher the liquid will spontaneously rise. If you want to observe an example of capillarity, hold the bottom of a piece of cloth in the water. You will observe the water slowly move upward through the fibers of the cloth. But capillary action does have its limits. For example, for an extremely narrow capillary (about 0.1 millimeter diameter), water will rise spontaneously only about 15 centimeters. For the water to rise higher, the capillary must be even narrower. Clearly, capillary action alone is insufficient to raise water to the 100-meter height of the tallest trees, since a prohibitively narrow capillary would be required.

The primary action that carries the water up the trees is due to the cohesion forces between water molecules. In fact, the attractive forces are so strong that if there were a way to pull one end of a freestanding water column, it could be pulled up to a height of 2.8 km before the column would break due to its weight. Essentially, as long as the water in a capillary forms a continuous cylinder without breaks, we may think of the water as comprising a rope. The source of energy that pulls water up the capillaries of a tree is provided by sunlight. When sunlight shines on the uppermost leaves, water at the top of the capillaries evaporates. Given the extremely strong cohesion between water molecules, the molecules that leave the top of the water column during the act of evaporation pull the entire column of water upward slightly to take their place. The higher a tree gets, the greater is the work needed to raise water from the roots to the top leaves. Apparently, much above 100 m, trees just cannot get the water up fast enough to satisfy the needs of photosynthesis which explains why there are not many trees that are more than 100 m height.

Vo~ Ta' Du+'c, Ph.D.

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