Instructor Information
JCE Classroom Activity: #63
Determining Rate of Flow through a Funnel
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Martin Bartholow Shawnee Mission North High School, Overland Park, KS 66204;
[email protected] In this Activity, students make funnels using plastic beverage bottles and rubber stoppers with differing numbers of holes or sizes of holes. They then determine the rate of the flow of water through the funnels and identify factors that affect the rate of flow.
Integrating the Activity into Your Curriculum
About the Activity Students graph volume of water versus emptying time to examine the rate of flow from the slope of the line. After obtaining rates for one stopper (size 4 stoppers fit well in the mouths of the plastic beverage bottles) with varying amounts of water, student form a hypothesis of how changes in the funnel will influence the emptying time. Suggestions for investigation include: changing the number of holes in the stopper, changing the size of the hole in the stopper, and varying the initial heights of water using different diameter containers. In testing, when the author’s set of 1-, 2-, 3-hole stoppers were used, a graph of number of holes versus emptying time is non-linear. A graph of 1/(# of holes) versus time gives a straight line. This graph indicates that the rate of flow is proportional to the number of holes per stopper. If the diameter of the stopper hole is increased, the rate also increases; students may understand the inverse relationship between emptying time and the area of the stopper hole. A change in height for the same volume of water in different funnels is an interesting investigation. Students may hypothesize that a funnel with a greater initial water column height will “push” the solution out faster. Instructors may wish to offer a buret with the stopcock removed and a rubber stopper inserted into the bottom of the buret. Data from a similar investigation and others are available in the online supplement.W An additional investigation could recreate the situation in question 7 and compare the rate of flow of various portions of a volume of water. A balance could measure the mass of the water as it empties; alternately, a buret with volume markings could be used.
perforated
Answers to Questions 1. Smaller volumes are harder to measure because of the inherent problems of manually timing short events. It is difficult to accurately determine exactly when water flow begins and ends. 2. Yes, the rate changes slightly depending on the volume of water used. Larger volumes of water have a higher rate. An overall rate can be calculated from the slope of the line as well. 3. The slope is an overall rate of flow with units of volume over time, usually mL/s. 4. Answers will vary depending on the variable tested. See the About the Activity section for more discussion. 5. Stopper color: no effect; material the stopper is made from: no effect; shape of the funnel: possible effect if height of water is changed; length and diameter of a straw placed in the stopper: various effects depending on length and diameter; the distance of the funnel from the collection beaker: no effect if method of time measurement is kept constant; different liquids (oil vs. water): liquids with a higher viscosity will have a slower flow rate; diameter of hole in the stopper: larger diameter has faster flow rate. 6. The changing slope shows the rate (speed) of the runner is changing. While the overall rate might be 10 m/s, the runner will be at a higher rate at the end. 7. The slope of the line, and therefore the rate, changes. Other experiments also suggest the column height affects the rate of flow. More Things To Try: The rate-determining step (the flow through the stopper) generally involves the funnel with the smallest hole, no matter its position in the sequence of funnels. Overall times are similar.
This Classroom Activity may be reproduced for use in the subscriber’s classroom.
fold here and tear out
This Activity uses easy-to-observe phenomena that model a chemical reaction with an identifiable rate-controlling step. Other experiments that model kinetics are available (1–3). This Activity can introduce the use of graphs in kinetics before students study an actual chemical reaction (4, 5).
References, Additional Related Activities, and Demonstrations 1. 2. 3. 4.
Sanger, Michael J. Flipping Pennies and Burning Candles: Adventures in Kinetics. J. Chem. Educ. 2003, 80, 304A–B. Davenport, Derek A. Capillary Flow: A Versatile Analog for Chemical Kinetics. J. Chem. Educ. 1975, 52, 379–381. Beauchamp, G. Dissolution Kinetics of Solids: Application with Spherical Candy. J. Chem. Educ. 2001, 78, 523–524. Arce, Josefina; Betancourt, Rosa; Rivera, Yamil; Pijem, Joan. The Reaction of a Food Colorant with Sodium Hypochlorite: A Student-Designed Kinetics Experiment. J. Chem. Educ. 1998, 75, 1142–1144. 5. Cortes-Figueroa, José E.; Moore, Deborah A. Using CBL Technology and a Graphing Calculator to Teach the Kinetics of Consecutive First-Order Reactions. J. Chem. Educ. 1999, 76, 635–638. Roser, Charles E.; McCluskey, Catherine L. Lightstick Kinetics. J. Chem. Educ. 1999, 76, 1514–1515. JCE Classroom Activities are edited by Erica K. Jacobsen
www.JCE.DivCHED.org •
Vol. 81 No. 5 May 2004 •
Journal of Chemical Education
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JCE Classroom Activity: #63
Student Activity
Determining Rate of Flow through a Funnel Determining how fast something occurs is a common problem for both non-scientist and chemist. Usually an observer measures the time to complete a particular process. A rate is expressed as a ratio, such as the distance of a race to the elapsed time. For example, the gold medal winner of the women’s 100 meter dash in the 2000 Olympics ran 100 meters in 10.75 seconds. The rate of the race was 100 m/10.75 s, or about 9 m/s. A chemist may measure the time from the mixing of two solutions to the appearance of a distinctive color, such as the dark blue of an iodine–starch complex. In this Activity you will determine the rate of the flow of water through funnels and identify factors that affect the rate.
Try This You will need: scissors, ruler, several plastic 0.5-, 1- or 2-liter beverage bottles, several rubber stoppers that fit the bottles’ mouths (usually size 4) with differing numbers of holes (1-, 2-, 3-hole stoppers) or sizes of holes, measuring cups or graduated cylinder, water, stopwatch, and ring stand and rings or other support to hold the inverted bottles. __1. Carefully cut the bottom off a 2-liter plastic beverage bottle 15 cm below the bottle mouth. Save the bottom to use as a container to catch drained water. Insert a one-holed rubber stopper into the mouth of the bottle. Invert the bottle and place it in a ring stand or other support. This inverted bottle/stopper assembly forms a funnel. Place the cut beverage bottle bottom below the funnel to catch drained water. __2. Measure 1/2 cup (120 mL) of water. Block the stopper hole with a finger. Pour the water into the funnel. Quickly remove your finger. With a stopwatch, measure and record the time it takes the water to flow through the funnel. __3. Repeat step 2 using the same volume of water. The recorded times for this volume of water should be within 5% of each other before you try other volumes. Calculate an average time for the trials. __4. Repeat steps 2 and 3 using two or three significantly different volumes of water (such as 1/4 cup and 1 cup). __5. Graph the volume of water versus the emptying time. Graph the time on the x-axis. __6. Form a hypothesis of how a change in the funnel will influence the time it takes water to flow through the funnel. Some possibilities are: number of holes in the stopper, size of the holes in the stopper, different starting heights of water in different containers. Collect the necessary equipment and test your hypothesis. To examine the effect on the rate of the variable you test, graph the volume of water versus emptying time.
More Things To Try __1. Set up a series of three funnels using a different (1-, 2-, or 3-hole) stopper for each on a ring stand with three rings so that each funnel empties into the one immediately below it. Place a container below the bottom funnel to catch water. Block the stopper hole of the top funnel with a finger. Pour 1 cup (240 mL) of water into the top funnel. Quickly remove your finger. Measure and record the time for the water to empty from the bottom funnel. __2. Place the funnels in a different order and maintain the same distance between each funnel. Repeat step 1. How does the order of funnels affect the time?
Questions 1. Why is it harder to obtain results reproducible within 5% for 10 mL than 100 mL? 2. The expression for the rate the water flows through the funnel is: rate = volume/time. Calculate the rates from your step 5 graph. Does the rate change in steps 2 through 5 when different volumes of water are used? 3. In a graph of volume versus time, why is the slope of the line important? 4. What do you conclude from the graph of volume versus time for the variable that you chose in step 6? 5. How would you expect each of the following to affect the emptying time? Explain. Color of the stopper; material the stopper is made from; shape of the funnel; length and diameter of a straw placed in the stopper; the distance of the funnel from the collection beaker; different liquids (oil vs. water); and diameter of hole in the stopper? 6. A sprinter is timed every 10 m during a race. The slope increases on a graph of distance versus time. What is the significance of the changing slope? 7. A one-holed stopper is placed at the bottom of a meter-tall tube that holds 100.0 mL. Times were recorded as every 10 mL of the water drained (see the graph above). What is the significance of the graph’s slope?
Information from the World Wide Web (accessed February 2004) Ask a Scientist: Water and Funnels. http://www.newton.dep.anl.gov/askasci/gen99/gen99939.htm ChemTeam: Kinetics. http://dbhs.wvusd.k12.ca.us/Kinetics/Kinetics.html This Classroom Activity may be reproduced for use in the subscriber’s classroom.
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Journal of Chemical Education •
Vol. 81 No. 5 May 2004 •
www.JCE.DivCHED.org
