Draining The Swimming Pool

Byrne, William                   Martin Luther King H.S.
                                 1-312-536-8680
                           

Objectives:

    To do some experiments that suggest a way to solve the general work problem: 
                 
If A can do a job in X hours and B can do the same job in Y hours, how long will it 
take A and B working together to complete the job? 

More specifically, if one pipe can drain a swimming pool in 4 hours and another pipe 
can drain the pool in 7 hours, how long will it take to drain the pool using the two 
pipes together? 


Apparatus Needed:

  Plastic container holding 2 or 3 liters, several plastic tubes of different inside 
diameter ( eg. 1/2", 1/4", 3/16" ) each about 4 feet long, stopwatch or clock with 
second hand, several pails for holding water.                    

Transparencies  

   Use overhead to show fractional parts of container drained in a given number of 
seconds. 

Recommended Strategy:

  The equation given in textbooks to solve the swimming pool problem is usually 
stated as X/4 + X/7 = 1.  It is not immediately obvious why this formula works or how 
it was derived.  The following is a strategy for leading up to the formula. 

   Determine the number of seconds or minutes it takes to drain the same amount of 
water from the plastic container using each of the plastic tubes separately.  You can 
ask for student volunteers, one to hold a tube and another to siphon the water.  
Students at their desks can use the clock to determine the times.  Have the students 
write down the times next to the i.d. of the tubes.  Many questions can be raised 
along the way.  For example what is the relationship between the i.d. of the tube and 
the draining time for that tube?  If the radius of the tube is doubled what happens 
to the inside area of the tube, the amount of water it will carry and thus the 
draining time?  Make estimates and then test them using the appropriate tube.  An 
important question is what fraction of the container is drained by one or more tubes 
in 1 sec.  Suppose the draining times for two tubes are 25 and 40 sec.  Then in 1 
sec., (1/25 + 1/40 ) of the container will be drained.  Ask the students to find a 
proportion using this idea.  Hopefully after a few minutes working in groups they 
will come up with this proportion: (1/25 + 1/40) / 1 sec = 1 / X sec , where X is the 
time to drain using two tubes at the same time.  Now choose two tubes, do the 
experiment and see if the time you get agrees with the solution you get using the 
equation.  The equation given at the beginning follows from the proportion.