Toricelli's Law Lab Report

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Introduction on Torricelli's Experiment

Discovered by Italian physicist and mathematician Evangelista Torricelli in 1643, Torricelli’s law is a theorem in fluid dynamics concerning the speed of the fluid flowing out of an opening, in relation to the height of the fluid above an opening. Torricelli was an important figure in science in which his contributions shined a new light in discoveries and inventions. He advanced as the Tuscan court mathematician and professor at the University of Florence. Torricelli invented the mercury barometer in 1643 and is also known for his work in optics and in fluid dynamics. Evangelista Torricelli found that water leaks out a small hole in the bottom of a container at a rate proportional to the square root of the depth of the water. Torricelli’s equation is derived from Bernoulli's principle.    

Purpose

Determining the relationship between the flow rate of the water coming out of a 2 litre bottle and the height above the opening.

Materials

• Compass
• Empty 2 Litre Bottle
• 100 mL Graduated Cylinder
• Ruler
• Scissors
• String
• Timer
• Calculator
• Water
• Tape
• Aluminum Tray

Procedure

1. Firstly the pop bottle was prepared for the experiment by taking the sharp end of the compass and cutting a hole that was about a centimetre in diameter.
2. Next, the amount of water below the hole was measured by filling the bottle up with water until it was right below the hole using a 100 mL graduated cylinder.
3. Then, the circumference of the pop bottle was measured by wrapping a piece of string around the bottle, cutting it off, and then measuring exactly how long the string was with a ruler. This number was recorded.
4. A piece of tape was put to cover the hole, and then 600 mL of water was poured into the bottle using a graduated cylinder for a more accurate measurement.
5. 600 mL was used as the first value for the experiment because the value had to be greater than the amount of water equal to the hole.
6. The bottle was then placed in an aluminum tray to prevent any water spilling anywhere.
7. A data table was made indicating the “Volume Lost over 5 Seconds (mL)”.
8. The procedure began with one person in charge setting up the timer at 5 seconds and the other person in charge of taking the tape off and on until the 5 seconds went up.
9. The first person started the timer and simultaneously, the other person took the tape off the bottle, and once the timer hit the 5 second mark, the tape was put back on.
10. The remaining water left in the bottle was found by pouring the rest into the graduated cylinder and then pouring it down the drain once measured.
11. Next, the volume of water lost over the 5 seconds was calculated by subtracting the amount of water left, from the total volume of the bottle which was 2 L.
12. This trial was done 2 more times with the same amount of water poured into the pop bottle- 600 mL.
13. The average of the trials was found by adding all the trials and dividing by three.
14. The steps were repeated 9 more times using increments of 100 mL until finally the last testing value was 1500 mL.

Diagram [pic 4]

How Error was Minimized

1. The type of liquid was kept constant in this laboratory by using water from the laboratory tap every trial throughout the experiment.
2. The temperature of the liquid and the air pressure acting on the pop bottle were kept constant by completing the experiment in the same room.
3. A 100 mL graduated cylinder was used in order to have accurate measurements of the water.
4. Took into account the uncertainty of every time water was poured into the bottle with the graduated cylinder, as well as the human reaction time.
5. Used 100 mL increment for every water volume difference in order to get the scope of the full range of values between 600 to 1500 mL. This allows for no trial to overlap another trial because 100 mL difference is a good amount to start with.
6. Performing three trials instead of one trial for every 100 mL increment for the second data table.
7. Used a period of 5.0 seconds for determining how much water leaks out in that time period because if we used a longer duration, the amount of water leaked out can overlap with the different trials too much. We also did not use a value less than 5.0 seconds because it would increase the obvious problem of the human reaction time. Human reaction time is around 0.2 seconds so using a time period of 1.0 second would mean that 20% of is uncertain.

Theory

Bernoulli's Principle

Torricelli’s law states that the speed of the fluid, v, leaking out of a hole at the bottom of the bottle filled to a depth of h is the same as the speed that the fluid would obtain in free fall from a height of h. This can be calculated using the equation V= √2gh, where g is the acceleration due to gravity. V= √2gh can be derived using Bernoulli’s principle.

Bernoulli’s principle is named after Daniel Bernoulli who established that when a fluid is moving at a faster velocity, there is a decrease in pressure or a decrease in the fluid’s potential energy. Similarly if the velocity is slower, the pressure and potential energy of the fluid is greater. The Bernoulli’s principle is derived from the idea of conservation of energy, and it is conservation of energy for flowing fluids. Applying the law of conservation of energy to Bernoulli’s principle, in a stable flow, the amount of energy is equal at all points of the streamline. This entails that the sum of internal, kinetic, and potential energy should remain persistent. Therefore, an increase in the velocity of a fluid implies that there will be an increase of its dynamic pressure and kinetic energy, and all together, there will be a decrease in the internal energy, potential energy, and static pressure.