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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Copyright © 1996 by VACETS and Vo Ta Duc
