Hydraulic Hot Water Bottle

Introduction

Pascal’s law applies to many aspects of our lives. An extremely important application of Pascal’s law occurs when a driver presses on a brake pedal to stop a car. Pascal’s law is also at work when a mechanic easily lifts a car using a hydraulic lift. Use a hot water bottle to demonstrate hydraulics and water pressure as well as Bernoulli’s principle.

Concepts

• Water pressure
• Pascal’s law
• Hydraulics
• Bernoulli’s principle

Materials

Safety Precautions

Although latex (in the hot water bottle) is considered nonhazardous, not all health aspects of this substance have been thoroughly investigated. Latex may be an allergen. Wet floors can be very slippery and dangerous. Clean up water spills immediately. Volunteers standing on the hot water bottle should stand next to a table or chair so they may balance themselves. The person holding the tubing should stand on a stable platform. Volunteers being lifted should stand next to a table or chair so they may balance themselves during the lifting process. Use a plastic pouring container to avoid the possibility of broken glass. The person holding the tubing should stand on a stable platform. Follow all laboratory safety guidelines.

Prelab Preparation

Part 1. Water Tower and Water Pressure

1. Fill the hot water bottle with approximately 1000 mL of tap water.
2. Screw the cap with the open nozzle onto the hot water bottle opening (see Figure 1).
   {12746_Preparation_Figure_1}
3. Attach one end of the Tygon^® tubing onto the nozzle on the cap.
4. Place the open end of the Tygon tubing into a 5-gallon bucket or into a sink.
5. Place the hot water bottle on a chair so that it is below the sink. If using a bucket, put the bucket on the chair and place the hot water bottle on the floor so that it is below the bucket.

Part 2. Hot Water Bottle Scale
(This may require two people.)

1. Remove the plunger from the 60-mL syringe.
2. Insert the tip of the syringe body into one end of the Tygon tubing.
3. Fill the hot water bottle with approximately 750 mL of tap water.
4. Screw the cap with the open nozzle onto the hot water bottle opening.
5. Attach the free end of the Tygon tubing onto the nozzle on the cap.
6. Place the syringe-body end of the Tygon tubing into a 5-gallon bucket or into a sink.
7. Place the hot water bottle on the floor next to the sink or bucket.
8. Lift the hot water bottle so it stands vertically with the nozzle end pointing up. Squeeze the bottom of the hot water bottle (the end opposite the nozzle) to expel the air inside the hot water bottle (see Figure 2). Continue squeezing on the bottle until water is forced into the Tygon tubing and no more air bubbles exit the bottle. Shake the bottle slightly to detach any air bubbles that may cling to the inside of the bottle.
   {12746_Preparation_Figure_2}
9. Continue to carefully squeeze the bottom of the hot water bottle to force the water through the entire tube.
10. Once the water has begun to exit the tubing and empty into the bucket or sink, pick up the syringe body and hold it vertically with the Tygon tubing hanging down.
11. Continue pressing on the hot water bottle to fill the body of the syringe with water (see Figure 2).
12. After the syringe body is approximately half-full, ease up on squeezing the hot water bottle so the water levels off at the midway point in the syringe body.
13. Inspect the syringe and tubing for any air bubbles. If there is a significant amount of air in the system, repeat steps 3–12. Small air bubbles in the system will not notably affect the results of the demonstration.
14. After inspecting the system for air bubbles, stop squeezing the hot water bottle and lay it flat on the table. The water will flow back into the hot water bottle and some water should remain in the tube near the opening to the bottle, but no air should enter the hot water bottle.

Part 3. Hot Water Bottle Hydraulic Jack

See Preparation section for Part 2 for steps 1–13.

14. After performing steps 1–13, inspect the tube for air bubbles, and then continue to squeeze the hot water bottle to completely fill the syringe body and until water begins to bulge over the top.
15. With the water bulging over the top of the syringe body, carefully insert the plunger (see Figure 3).
16. Inspect the syringe and tubing for any air bubbles. If there is a significant amount of air in the system, repeat steps 1–15. Small air bubbles in the system will not notably affect the results of the demonstration.
    {12746_Preparation_Figure_3}

Procedure

Part 1. Water Tower and Water Pressure

1. Ask students what the purpose of a water tower is. Instruct them to record their thoughts for Question 1 in Part 1 of the Hydraulic Hot Water Bottle Worksheet.
2. Have students gather around the bucket or sink so that they can all observe the open end of the Tygon tubing.
3. Simulate the function of a water tower.
4. Pick up the hot water bottle, hold it on the end opposite the cap and allow it to hang (see Figure 4). Students should observe the water flow into the bucket.
   {12746_Procedure_Figure_4}
5. Slowly raise and lower the “water tower” as students observe the water flow. It may be necessary to hold onto the end of the Tygon tubing so that it does not slip out of the bucket as the water flow increases. Instruct students to answer Question 2 of Part 1.
6. Lower the hot water bottle below the bottom of the bucket or sink. Instruct students to record their observations of the water flow for Question 3 of Part 1.
7. Ask a student to pick up the free end of the tubing out of the bucket and raise it above his or her head. Make sure the open end is pointing straight up.
8. Raise the hot water bottle again but keep it lower than the end of the Tygon tubing. Allow students to observe the water flow. Students should record their observations for Question 4 of Part 1.

Part 2. Hot Water Bottle Scale

1. Place the wood board on top of the hot water bottle. Do not cover the nozzle end of the hot water bottle (see Figure 5)
   {12746_Procedure_Figure_5_Board on empty hot water bottle}
2. Press down slightly on the board to push the water up the tube. There should not be significant amounts of air in the hot water bottle.
3. Select a small student volunteer to stand on the wood board.
4. Stand on a sturdy chair and hold the Tygon tubing straight and vertical (see Figure 6).
   {12746_Procedure_Figure_6}
5. Instruct the student volunteer to place a piece of tape on the tubing to mark the initial water level in the tube.
6. While holding the Tygon tubing straight and vertical, instruct the student volunteer to slowly and carefully stand on the wood board. Note: It is recommended the student press down on the board with one foot first to push some water up the tube. After the initial push, the volunteer can slowly begin applying his or her entire weight on the board. Make sure the student does not jump on the hot water bottle—this may cause it to rupture. Instruct the student to hold onto the nearby table for balance.
7. The water will rise in the Tygon tubing as the student stands on the board. Once the student becomes completely supported by the hot water bottle and the water in the tube has reached its peak, instruct the student to place another piece of tape on the Tygon tubing to mark the new height of the water.
8. Instruct the student to carefully step off the board and hot water bottle. The water will flow back into the hot water bottle.
9. Use a meter stick or tape measure to measure the difference between the final and initial water height. Students should record this measurement in Part 2 of the worksheet.
10. Have students calculate and record the weight of the student in Part 2 of the worksheet.

Part 3. Hot Water Bottle Hydraulic Jack

1. Place the filled hot water bottle flat on the floor near a tabletop.
2. Place the wood board on top of the hot water bottle. Do not cover the nozzle end of the hot water bottle (see Figure 5 in Part 2 of the Procedure).
3. Select a small student volunteer to stand on the wood board.
4. Instruct the student volunteer to carefully stand on the wood board. As the student stands on the board, press on the syringe plunger so that it does not pop out. Make sure the student does not jump on the hot water bottle—this may cause it to rupture. Instruct the student to hold onto the nearby table for balance, if necessary.
5. After the student becomes comfortably balanced on the wood board and hot water bottle, press down on the syringe plunger. When pressing the syringe plunger make sure to hold the Tygon tubing near the syringe connection with your free hand. Otherwise, the tubing may pop off the syringe and water would spill.
6. Instruct students to observe the distance the syringe plunger moves compared to the student on the board. Students should record their observations for Question 1 in Part 3 of the worksheet.
7. Release the syringe and allow the student’s weight to push the syringe plunger back up.
8. Use a ruler to measure the distance the top of the syringe plunger is from the top of the syringe body. Instruct students to record this distance in Part 3 of the worksheet.
9. Next, measure the initial height of the board from the floor. Have students record this distance in the appropriate blank on the worksheet.
10. Press the plunger all the way down. Measure the final distance the top of the plunger is from the top of the syringe body, and the final height of the board from the floor. Have students record these values on the worksheet.
11. Repeat step 7.
12. Select several students to push down on the plunger to feel the minimal effort needed to raise the student on the board.
13. After the demonstration, instruct the student on the board to carefully step off.

Part 4. Hot Water Bottle Hydraulic Jack (Alternate)

1. Set up the equipment as shown in Figures 5 and 6. Attach the Tygon tubing onto the nozzle on the hot water bottle plug. Push the tip of the syringe body into the other end of the tubing.
2. Adjust the board so that it does not cover the neck of the hot water bottle. It should be centered on the bottle (see Figured 5 and 6 in Part 2 of the Procedure).
3. Have a volunteer carefully stand on the board resting on the empty water bottle. Caution: To avoid puncturing the water bottle, do not jump or stomp on the board. Perform the demonstration near a table or chair to assist the volunteer's balance during the experiment.
4. Fill the plastic container with approximately 1000 mL of water. Show the water-filled container to the class and ask students if they believe 1000 mL of water will be able to lift the person on the board.
5. Carefully stand on a step-stool or chair.
6. Slowly pour the water into the syringe body (see Figure 7). Instruct students to observe what happens as the water flows into the hot water bottle!
   {12746_Procedure_Figure_7_Slowly pour water into the syringe body}
7. Have the volunteer on the board describe the feeling of being lifted.
8. Once the lift is complete, instruct the student to carefully step off the wood board.
9. Empty the water bottle completely before repeating the experiment with other volunteers. Caution students not to jump on the water bottle!
10. After performing this activity, discuss ideas about how the lifting occurs and have students answer the questions for Part 4 on the worksheet.

Student Worksheet PDF

12746_Student1.pdf

Teacher Tips

• Empty the hot water bottle and allow it to air dry before long-term storage. Do not store near acids or other corrosives.
• The hot water bottle is composed of rubber latex and may deteriorate over time. Inspect for cracks or nonelastic regions before using.
• The Discussion section for each demonstration may be copied for student use at the instructor’s discretion. Part 1 may be advanced for middle school or first-year physical science students. Students will need Equation 6 from Part 2 in order to calculate the weight of the student volunteer.
• In Part 1, a large, clear bucket will make it easier for students to see the water flow without the need to have them congregate closely around the bucket or sink.
• Use food dye to color the water and make it more visible for the students. Make sure to rinse the hot water bottle with water several times after the demonstration to clean out the dye from inside the bottle.
• For Part 2, select a small (less than 150 lb) student as a volunteer. This will limit the stress on the hot water bottle and also prevent the water from rising higher than 10 feet. Also, select a student who is not bashful about the class determining his or her weight.
• Use only 750 mL of water so the hot water bottle is not completely full. This will allow the bottle to lie flat on the floor and maximize the contact with the wood board.
• The syringe body at the end of the tubing will act as a reservoir to collect any water that may rise above the length of the tubing. If the water rises higher than 10 feet it will be necessary to select a smaller volunteer.
• The calculated weight of the individual will be significantly affected by the estimated area of the board in contact with the hot water bottle (see Discussion section). For more accurate results, measure the area of the board in contact with the hot water bottle.
• In Part 3, test the hydraulic press with just the wood board before performing the experiment with a volunteer. Check for any leaks or large air bubbles in the system.
• Use only 750 mL of water so the hot water bottle is not completely full. This will allow the bottle to lie flat on the floor and maximize the contact with the wood board.
• Select a small (less than 150 lb) student as a volunteer. This will limit the stress on the hot water bottle. Also, if work and mechanical advantage are going to be calculated, select a student who is not bashful about telling the class his or her weight.
• Consult the Discussion section and basic physical science or physics textbooks for the formulas to predict input and output forces and mechanical advantage. See also the Flinn Scientific Principles of Hydraulics Kit (Catalog No. AP6494) for a complete quantitative hydraulic system, or the Pascal’s Law—Student Laboratory Kit (Catalog No. AP6623) for an excellent student lab activity.In Part 4, test the hydraulic press with just the wood board before performing the experiment with a volunteer.
• The Part 4 demonstration works best with a very small student (less than 120 lbs).

Answers to Questions

Part 1. Water Tower and Water Pressure

1. What is the purpose of a water tower?

   A water tower stores water for a community. Water is stored at an elevated height so it can travel downward to the surrounding homes.

2. At what point during the lifting of the hot water bottle does water begin to flow out of the tube?

   The water begins to flow out of the hot water bottle as soon as the water bottle is raised above the end of the tube.

3. What happens when the water bottle is lowered below the bucket (or sink)?

   The water begins to flow in the reverse direction and back into the hot water bottle.

4. When the end of the plastic tube is raised above the hot water bottle, at what level does the water in the tube stay? Does the water continue to flow? Does the water level-off and reach an equilibrium height?

   The water in the tube stops flowing and then levels off at nearly the same height as the hot water bottle. When the hot water bottle is raised, the water level raises. When the hot water bottle is lowered, the water also decreases in height and remains at the same level as the hot water bottle.

Part 2. Hot Water Bottle Scale

Measured distance between initial water height and final water height:___112 cm___
Area of the board in contact with the hot water bottle: ___484 cm²___
Actual weight of student: ___115 lb___

1. Use Equation 6 to calculate the weight of the student. Hint: Watch units!
   {12746_Answers_Equation_1}
2. Compare the calculated weight to the actual weight. Describe methods that might improve the weight calculation.

   The water scale was close to the actual weight of the student, with about a 4% error. Improvements could have been made to holding the tubing straight and vertical. Also, measuring the area of the board actually in contact with the hot water bottle might improve the results.

Part 3. Hot Water Bottle Hydraulic Jack

1. Compare the distance the syringe plunger moves and the height that the student is lifted.

   The syringe plunger moves a much larger distance compared to how far the student is lifted. The change in height of the student is hardly noticeable, but the plunger moves several centimeters.

2. Initial length of plunger to the syringe body:___13.3 cm___
   Final length of plunger to the syringe body:___1.3 cm___
   Initial height of the board above the floor:___3.8 cm___
   Final height of the board above the floor:___4.1 cm___
   Ideal Mechanical Advantage of the hydraulic jack:___40___

   {12746_Answers_Equation_2}
3. Was more work done by the hydraulic lift than was performed by the person pushing the plunger?

   No, the same amount of work (excluding frictional forces) was used to push the plunger in as was required to lift the student. The smaller force on the plunger was used over a greater distance, compared to the larger force (the weight of the student) moving a very small distance.

4. What is a disadvantage of a hydraulic press?

   A disadvantage of a hydraulic press is that the heavy load does not move a great distance. A large movement of the effort is needed to raise the heavy output load only a few centimeters.

Part 4. Hot Water Bottle Hydraulic Jack (Alternate)

1. Describe what happens during this demonstration.

   The water is poured down the tube and flows into the hot water bottle. There is a lot of bubbling and gurgling as the water flows in and the air tries to flow out. The student on the board is slowly lifted. The student can actually feel himself rise slowly. The water has difficulty going down the tube. Sometimes the water flows down and sometimes with air flows up and out. After some time, all the water is poured down the tube. Most of the water enters the hot water bottle and lifts the student. Some water remains in the tube.

2. Develop a hypothesis that might explain the lifting power of the water.

   Any reasonable hypothesis should be accepted.

Discussion

Part 1. Water Tower and Water Pressure

Water towers are ubiquitous in nearly every town in the United States. In many cases they may be the tallest object for miles around. Many are decorated with a local school’s team mascot, the town’s name or even painted to look like a pumpkin. Other than displaying a school’s pride, or acting as a distinguishing landmark, the purpose of a water tower is to maintain a high water pressure in the local community without the continuous use of mechanical pumps.

The pressure associated with a static fluid can be derived from Bernoulli’s principle (Equation 1). Bernoulli’s equation describes why the pressure on a surface decreases as a fluid flows over it and is the basis for why airplanes fly and why baseballs curve.

where

P₁, P₂ is the external pressure at points 1 and 2, respectively
v_1,2 is the fluid velocity at points 1 and 2, respectively
h_1,2 is the height of points 1 and 2, respectively, above a reference point
ρ is the density of the fluid
g is the acceleration due to gravity

When the velocity (v₁ and v₂) of the fluid is zero, Equation 1 simplifies to Equation 2. where

P_h is the pressure at a given depth below the surface of a liquid
P_o is the external pressure at the surface of the liquid (usually just atmospheric pressure)
h is the depth beneath the surface of the liquid

The most remarkable result of Equation 2 is that the pressure at the bottom of a column of a liquid does not depend on the shape of the container holding the liquid, or the amount of liquid above the bottom—it only depends on the depth below the surface. Therefore, as the height of column of water is increased, the higher the pressure will be at the bottom. However, if a larger container of water was held at a lower elevation compared to a thin column of water, the thin column of water will result in a higher pressure at the bottom (see Figure 8). Water is stored in a water tower because the elevated water maintains a high pressure in the water pipes that travel out to the homes and businesses in the surrounding area. When a spigot is turned on in a home, however, the fluid is no longer static. The speed of the water exiting the spigot (or, in the case of Part 1, the tube opening) can be also determined using Bernoulli’s equation. Assume that the atmospheric pressure at the top of the water tower and the spigot level is the same since the water tower will be less than 50 meters tall. Therefore, P₁ and P₂ in Equation 1 cancel. A water tower contains a large reservoir of water, so as water flows out the spigot, the water in the tank will move considerably slower compared to the water exiting the spigot (v_tank < v_spigot). Therefore, v_tank can be ignored and Equation 1 reduces to Solving for v_spigot The speed of the fluid at the bottom of the water tower is proportional to the square root of the difference in height between the top of the water and the spigot height. The higher the tower, the faster the water will flow at the bottom. The increase in speed will be clearly visible as the hot water bottle is raised higher above the open end of the tube.

When the end of the tube is raised above the hot water bottle, the water reaches an equilibrium height inside the tube. This shows that water pressure in each column is balanced. The column of water supporting the reservoir of water in the hot water bottle does not force the water in the thin column to higher elevation. The water in each column stays at the same level because the pressure is only related to the height of the columns and not the amount of water (see Figure 9). Part 2. Hot Water Bottle Scale

In the second demonstration, the weight of an individual standing on a board can be calculated by measuring the change in elevation of the water in the tube.

From Bernoulli’s equation it was derived that the amount of pressure in a column of water depends only on the height of the column and not the amount of liquid above a certain point (Equation 2). When a student stands on the hot water bottle, the student will create a higher than atmospheric external pressure that will push the water up the tube until the pressure from the water balances the external pressure on the hot water bottle. The pressure (P_w) exerted by the individual on the board is equal to the weight (W) of the individual divided by the area (A) of the board in contact with the hot water bottle. Once the water in the tube reaches a level height, the column of water exerts the same pressure at the bottom as the pressure exerted by the individual on the board. The individual’s weight can then be calculated using the elevation change of the water in the column. Using Equation 2:

P_T is the total pressure on hot water bottle
P_o is the atmospheric exerted on the column of water
Δh is the change in height of the column of water

The total pressure on the hot water bottle includes both the pressure exerted by the individual standing on the board (P_w) as well as atmospheric pressure (P_o), (P_T = P_w + P_o). Substituting equations for P_T and P_w into Equation 5 and solving for W results in: Where, ρ is the density of water (ρ_w = 1.0 g/cm³) and g is the acceleration due to gravity constant (g = 9.81 m/s²). The area (A) in contact with the hot water bottle is estimated to be approximately 484 cm² (assuming maximum contact with the board).

Part 3. Hot Water Bottle Hydraulic Jack

Blaise Pascal (1623–1662) is well known as a mathematician. Pascal also had a strong interest in physical events and spent much of his time trying to explain the phenomena he witnessed in his experiments. He performed many experiments involving pressure in fluids. One of the most important principles he discovered became known as Pascal’s law or Pascal’s rule.

Pascal’s rule states that pressure applied anywhere to a fluid causes the pressure to be transmitted equally in all directions. This is the result of fluids being incompressible. A force applied at one end is transmitted throughout the entire fluid system.

Pressure is equal to a force per unit area (P = F/A). Therefore, if the pressure in a fluid is constant, then the larger the surface area the pressure is in contact with, the larger the force. A smaller surface area results in a smaller force. By arranging liquid columns of different sizes Pascal discovered that a relatively small force could lift a very heavy load. Pascal's law serves as the basis for the development of much of what is now known as hydraulics (see Figure 10). Hydraulics is important because it can provide a mechanical advantage. A mechanical advantage reduces the effort needed to lift a heavy load. The higher the mechanical advantage of a system, the higher the output force compared to the input force. Therefore, the higher the mechanical advantage, the easier it is to do the work. To calculate the mechanical advantage (MA) of a system, simply divide the output force by the input force (Equation 7). where

F_o is the output force
F_i is the input force

However, mechanical advantage does not give something for nothing. With a large mechanical advantage, it is easy to move a heavy load with a relatively smaller force. The trade-off is that the smaller applied force must be carried over a longer distance compared to the distance the heavy load moves. This is a result of the conservation of energy principle which states that the total energy input must equal the total energy output. A small force will move a large distance while the large load moves a small distance. The ideal mechanical advantage of a hydraulic system can be determined by dividing the distance the input force moves by the distance the output force moves (Equation 8). where

d_i is the input distance
d_o is the output distance

Part 4. Hot Water Bottle Hydraulic Jack (Alternate)

This demonstration relies on both the principles of hydraulics as well as inertia. As the water fills the hot water bottle, some air remains trapped in the bottle and helps to pressurize it. The hot water bottle does not truly work on the hydraulic principle because the system is open to the atmosphere and there is water and air in the system. It is an interesting activity that should generate excellent questions for experimentation.