Pressure in Fluids

Porter W Johnson               Illinois Institute of Technology
                               Department of Physics
                               Chicago IL 60616-3793
                               (312) 567-3375

Objectives:

We shall study the properties of fluids under a variety of circumstances to 
understand the role or pressure in their behavior, and to relate to everyday 
circumstances. 

Materials Needed:

Several two liter "pop bottles" and assorted plastic bottles, several "push 
pins" for making holes, a medicine dropper for the cartesian diver, a large 
clear funnel with a stand for holding it in place, several plastic straws and a 
supply of strong plastic tape or Duck Tape, and at least one "middle range" 
water pistol, a "battery operated" model being preferable. 

Strategy:

The first phase is a demonstration of the flow of water out of holes punched 
with push pins and some enlarged with nails in plastic bottles of various shapes 
and sizes.  Let the students report their observations, and write them on the 
board.  Be sure to record every correct observation, whether it is directly 
relevant for the points you intend to make.  Here is a non-inclusive list of 
observations that might be made. 

     1.  If the hole is punched straight into the bottle, the water
         initially moves horizontally, and gradually drops as it gets
         further away from the vessel.   
     2.  As the water drains from one of the bottles and the level
         drops, the water comes out with lesser speed, and falls on
         an arc that does not extend as far. 
     3.  The stream of water initially gets smaller as it leaves
         the hole,  and it will break into droplets if it falls far
         enough.  Try this with a hole punched in the bottom of the
         bottle.
     4.  If the cap is put back on the bottle the flow slows and
         eventually stops.  If you blow hard into the bottle the rate
         of flow is increased.
     5.  With two holes of the same size, the one that is deeper in
         relation to the "water level" in the bottle will have a
         greater exit speed.
     6.  The size of the hole has relatively little effect on the
         speed of water that exits, although, a bigger stream of
         water flows out of the larger hole.

Next go outside with the water pistol and shoot it from shoulder level.  Have 
the students divide into groups of three or four, with each group estimating its 
maximum distance of travel in meters by stepping or pacing the distance.  Be 
sure to take along an extra supply of water for reloading the pistol.  Go back 
inside, and record the various answers.  You should measure the distance in 
advance, so that the various answers obtained can be compared with the standard.  
For the Drencher AdvantageTM power pistol, a range of about 9 meters was 
obtained.  

Fill a two liter pop bottle with water.  Take a medicine dropper and fill it 
partially, so that the dropper just sinks in the water inside the bottle.  It 
will take some experimentation to find the right amount of water in the dropper.  
Then put the lid tightly onto the bottle.  Squeeze the sides of the bottle.  
Notice that, as the water pressure inside the bottle is increased thereby, the 
air in the dropper is compressed, and the dropper falls.  You might enjoy 
repeating the experiment with an oval-shaped bottle.  The device is called a 
Cartesian Diver. 

Fill a bottle completely with water, and insert a plastic straw.  Use tape to 
hold the straw a few millimeters above the top of the bottle and to seal the 
bottle.  Blow gently over the straw, either directly or by means of another 
straw.  If possible, use an air pump to force air over the top of the straw. You 
will notice that water comes out of the bottle.  The water is forced up and out 
of the straw because of the Bernoulli Principle.  This mechanism is used aerosol 
cans, in that a liquid is ejected from the reservoir by passing a gas over a 
tube at high speed. 

Many many people believe that the water in a flushing toilet or a draining 
bathtub will circulate in one sense in the Northern Hemisphere, and in another 
sense in the Southern Hemisphere, because of the Coriolis Force, which is 
responsible for clockwise circulation around high pressure regions and counter-
clockwise circulation around low pressure regions in the atmosphere.  Actually, 
it is difficult to build a toilet or tub that does not have some directional 
bias and it is simpler to study the effect in a large clear funnel.  Fill the 
funnel with water and add dye to enhance visibility while holding your finger on 
the bottom of the funnel.  You will have to pour the water into the funnel 
symmetrically and wait for several minutes to avoid any residual circulation of 
the water.  Do you see the effect of the Coriolis Force? 

Performance Assessment: 

                               Laboratory Exercise:

Punch a hole on the side of a 2 liter pop bottle near the bottom, and fill it 
with water.  Place the bottle on the edge of a table.  When the level of water 
is at a depth d above the hole, determine the horizontal distance s that the 
fluid stream lies when it has fallen to a fixed distance of, say, 20 cm below 
the hole.  Make measurements of h for various values of d, and make a graph of d
versus h.  Does the graph correspond to a straight line? 

                                Written question:

How does a water pistol work?

                               Satisfactory Answer:

A pump [mechanical or electrical] builds up pressure inside the vessel partially 
filled with water, and water is forced out of the hole in the barrel.  The 
operation is exactly the same as that of blowing into the partially filled 
bottle with a hole in it below the water level. 


Conclusions:

The consequences of Pascal's Principle [the pressure in a liquid increases with 
depth and its extension the Bernoulli Principle [lower pressure corresponds to 
higher speed along the path of flow of a fluid] have been explored, and their 
implications in everyday experiences are examined. 

Multi-cultural Components:

A story by Hans Christian Anderson describes the little Dutch boy who put his 
finger into the dike to block whole North Sea.  The boy is often depicted 
wearing wooden shoes. 

     Q:  Why are wooden shoes popular in Holland and other lowland countries?
     A:  They are very effective in walking through mud, and it is quite easy to 
           remove the mud afterward without damaging the shoes. 

You may know that there is a difference in ocean levels of the locks at the two 
ends of the Panama Canal.  Part of this difference occurs because the Pacific 
Ocean is more salty and therefore more dense, so that its level should be lower.  
Incidentally, the locks on the Atlantic side of the canal are further West than 
those on its Pacific side! 

References:

      Jearl Walker
      The Flying Circus of Physics With Answers
      Wiley 1975
      ISBN 0 - 471 - 02984 - X