Teacher Notes



Water Spouts—Kinetic vs. Potential EnergyDemonstration Kit
Publication No. 12160
IntroductionScientific discovery often begins with observations that spark curiosity. If a full water tank has three outlets—one at the top of the tank, one in the middle and one near the bottom of the tank—will the water flow from the three different outlets in the same manner? This “spouting bottle” demonstration is a visual way to have physics concepts spout in the classroom! Concepts
BackgroundA spouting bottle will be made that demonstrates Torricelli’s law. Three holes are made in the bottle at different heights. Each outlet will exhibit a different flow pattern dependent on the height. The results will be interpreted in terms of gravity and potential versus kinetic energy. MaterialsFood coloring (optional)
Water Butane safety lighter Marker, finepoint Paper clip Plastic soda bottle with cap, 1 L* Ruler, 30 cm* Sink or water catch basin Tape, masking *Materials included in kit. Safety PrecautionsUse caution when working with hot objects. Food dye will stain clothing. Wear safety glasses. Wash hands thoroughly with soap and water before leaving the laboratory. Follow all laboratory safety guidelines. DisposalPlease consult your current Flinn Scientific Catalog/Reference Manual for general guidelines and specific procedures, and review all federal, state and local regulations that may apply, before proceeding. Once completely cooled the paper clip may be recycled or thrown in the trash. The spouting bottle may be cleaned, dried, and stored for future use. Prelab PreparationSpouting Bottle
Procedure
Student Worksheet PDFTeacher Tips
Correlation to Next Generation Science Standards (NGSS)^{†}Science & Engineering PracticesAsking questions and defining problemsDeveloping and using models Planning and carrying out investigations Using mathematics and computational thinking Analyzing and interpreting data Disciplinary Core IdeasMSPS3.A: Definitions of EnergyMSPS3.B: Conservation of Energy and Energy Transfer HSPS3.A: Definitions of Energy HSPS3.B: Conservation of Energy and Energy Transfer Crosscutting ConceptsCause and effectScale, proportion, and quantity Systems and system models Performance ExpectationsMSPS41: Use mathematical representations to describe a simple model for waves that includes how the amplitude of a wave is related to the energy in a wave. Sample Data{12160_Data_Table_1}
Answers to QuestionsPredict the water flow pattern by drawing in the lines on the following diagram. {12160_Answers_Figure_1}
Discussion Questions and Calculations
DiscussionEvangelista Torricelli (1608–1647) was a contemporary of Galileo and is probably most famous for his development of the barometer. The unit of pressure—torr—was named in his honor. Torricelli also developed a theorem or law describing the mathematical relationship between the flow rate of fluid from a tank outlet and the height of the fluid above the outlet. The liquid flowing from an outlet in a tank has the same horizontal speed as an object falling freely from the level of the liquid’s surface to the level of the outlet. This relationship was later found to be a specific case of Bernoulli’s principle (Daniel Bernoulli, 1700–1782). The usual form of Bernoulli’s equation is shown in Equation 1. {12160_Discussion_Equation_1}
where
v is the velocity at a point
p is the pressure ρ is the density g is the acceleration of gravity (g = 9.81 m/s^{2}) h is the height above an arbitrary reference level or elevation. {12160_Discussion_Equation_2}
[Assume condition t is the water surface on the top of the bottle and condition b is the outlet at the bottom of the bottle (see Figure 6).]
{12160_Discussion_Figure_6}
At the top of the bottle the velocity is assumed to be 0. This reduces the equation to Equation 3.
{12160_Discussion_Equation_3}
At the bottom of the bottle the reference height is set to equal 0 so the equation further reduces to Equation 4.
{12160_Discussion_Equation_4}
Reducing the equation to simplest terms by eliminating p/ρ from both sides results in Equation 5.
{12160_Discussion_Equation_5}
Equation 5 can be used as is: gh = v^{2}/2, or it can be rearranged algebraically to solve for v, as Torricelli’s Law is commonly written, as shown by Equation 6.
{12160_Discussion_Equation_6}
From Equation 6 the velocity of the water flow from each opening of the bottle can be calculated. Note that this is the same speed that an object would have when falling from a height, h, from rest.There is a distinct pattern of water flow from the outlets in the bottle. This is because, as Galileo proposed and Newton proved, all objects fall toward the Earth at the same increasing rate (in a vacuum). That is, all objects will accelerate toward the Earth equally, regardless of their mass. In a vacuum, where there is no drag, or friction due to air, a heavy hammer will fall at exactly the same rate as a light feather. (This was demonstrated during the Apollo 15 moon landing, when David Scott dropped a hammer and feather at the same time, watched them hit the lunar surface at the same time, and then proudly announced that Galileo was correct!) At the surface of the Earth, the average acceleration toward the center of the Earth experienced by all objects is measured to be 9.8l m/s^{2} (32 ft/s^{2}). The vertical distance an object will fall under the influence of gravity in a given amount of time can be calculated using Equation 7. {12160_Discussion_Equation_7}
where
h_{o} is the falling height
g is the acceleration due to gravity t is the time {12160_Discussion_Equation_8}
Solving Equation 7 for t gives √2h_{o}/g and substituting for t in Equation 8 gives a final estimate of the distance the water should travel given a value of h_{o}, Equation 9.
{12160_Discussion_Equation_9}
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