lab 10

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Apr 3, 2024

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Lab 10:Under Pressure Torricelli’s Theorem Clayton McCall November 17 th 2023 Objective:
Create an experiment where you can find projectile range of a certain liquid with three bottles with different holes. Find the projectile range of each separate bottle to understand how it can be changed and how the three separate trials are different. Data Section Part 1: in the first part I put a hole in a 1-liter bottle near the top of the bottle filled it to the top and covered the hole with my finger. Then with the bottle filled I put it on a piece of paper I then marked where I put the bottle on the piece of paper and let my finger off the top of the hole to let the water flow. The water flowed on top of the paper, and I marked where the first drop fell. I then measured the distance from the bottle to where the water fell. I did this for three trials and recorded for the results. On the fourth trial I filled the bottle and twisted the cap on top of the bottle. This time when I let my finger off of the bottle the water did not flow. Data Table I Part I Measurements using Hole at the Top of a Bottle Trial Total Height of Bottle, H [m] (constant, record value as Height of hole above Flat Surface, h [m] Vertical Distance of water from top of bottle, y (H -h) Measure d Range, R [m] Calculated Range, R = 2 hy [m] % Difference between measured and calculated
Average) (constant , record value as Average) [m] (constant , record value as Average) Ranges (using averages) 1 .295 .24 .04 .155 .196 7.8% 2 .145 3 .13 Average .295 .24 .04 .143 .196 7.8% 4 (with cap on) Observation s With the cap on the bottle I have found that the water does not flow. Part 2: In part two I did the same thing that I did in the first trials except instead of having the hole at the top of the bottle it was closer to the middle of the bottle. In trial four again I filled the bottle to the top and released my finger off the hole. The same thing that happened in the first trial also happened in this trial and the water did not flow. To calculate the range in these trials I used the formula R=2√hy. The value of h in this formula represents how far the hole is from the bottom of the table which is .15 m. In this formula the value of y represents how far the top of the water is from the hole which in this case was .13 m. To solve this you plug in h and y R=2√.15x.13 and once you simplify you get the answer .279 m. Data Table 2 Part II Measurements using Hole near the Middle of a Bottle Trial Total Height of Bottle, H [m] Height of hole above Vertical Distance of water Measure d Range, R [m] Calculated Range, R = 2 hy % Difference between
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(constant, record value as Average) Flat Surface, h [m] (constant , record value as Average) from top of bottle, y (H -h) [m] (constant , record value as Average) [m] measured and calculated Ranges (using averages) 1 .295 .15 .13 .10 .279 22.3% 2 .105 3 .115 Average .295 .15 .13 .107 22.3% 4 (with cap on) Observation s With the cap on the bottle I have found that the water does not flow. Part 3: in part three I did the same process that I did in the first and second parts except this time the hole was closer to the bottom of the bottle. When I did the 4 th trial where the bottle was filled to the top and the cap was put on the bottle the same thing that happened in the first two trials also happened in this trial where the water did not flow. To find the percent difference of the measured and calculated range you use the formula: ( | measured value calculated value | measured value + calculated value 2 ) × 100 In this situation we will use the average value of the measured range as the measured value. Once you plug in the values you get. ( | .137 .178 | .137 + .178 2 ) × 100 Once you simplify the values you get the answer 6.5% difference.
Data Table 3 Part III Measurements using Hole near the Bottom of a Bottle Trial Total Height of Bottle, H [m] (constant, record value as Average) Height of hole above Flat Surface, h [m] (constant , record value as Average) Vertical Distance of water from top of bottle, y (H -h) [m] (constant , record value as Average) Measure d Range, R [m] Calculated Range, R = 2 hy [m] % Difference between measured and calculated Ranges (using averages) 1 .295 .0325 .245 .115 .178 6.5% 2 .165 3 .13 Average .295 .0325 .245 .137 .178 6.5% 4 (with cap on) Observation s With the cap on the bottle I have found that the water does not flow. Questions 1. Review the data in Data Tables 1, 2, and 3. Explain whether your data verified Torricelli’s Theorem within an acceptable % difference. I feel like in my 1 st and 3 rd parts my data was very accurate and proved the torricellis theorem. In my 2 nd part my data was inaccurate and I think the reason
for this was that I did not have the correct value for “y” which was the distance of the water from the hole. 2. The speed of water in a hose increases from 1.96 m/s to 25.5 m/s going from the hose to the nozzle. Using Equation 3, calculate the pressure in the hose, given that the absolute pressure in the nozzle is 1.01×10 5 N/m 2 (atmospheric, as it must be) and assuming level, frictionless flow. Show your calculations. P 1 + 1 2 ρv 1 2 + ρg h 1 = P 2 + 1 2 ρv 2 2 + ρg h 2 Equation 3 The first thing you do to find the pressure of the hose it to move p1 to one side of the equation with the rest on the other side of the equal sign. When you do this you get: p 1 = p 2 + 1 2 ρv 2 2 1 2 ρ v 1 2 = p 2 + 1 2 ρ ( v 2 2 v 1 2 ) After you move p1 to the other side of the equal sign you can plug in the values for pressure which is 1.01X10^5 v2 which is 25.5 and v1 which is 1.96. p 1 = 1.01 × 10 5 + 1 2 ( 10 3 ) ¿ ] p 1 = 4.24 × 10 5 Once you have plugged in the values you can simplify the answer to be 4.24x10^5. 3. A Siphon is used to drain fluid from a higher level reservoir to a lower level reservoir. If the drain is 6.75 m from the top of the higher level reservoir, what is the velocity of the fluid as it exits the drain? Show your calculation. V = 2 gh Equation 4 Finding the velocity of the fluid is very simple with this formula we know the height and we know the value of g to be 9.8. using these values we can plug them in to the formula and find the answer. V = 2 × 9.8 × 6.75 V = 11.5 Once you have plugged in the values to the formula you can simplify to find the answer that the velocity of the fluid out of the drain comes out to be 11.5 meters per second. 4. Explain your observation of the fluid flow when the cap was placed on the bottle, and you removed your finger from the hole. Was this the same for the holes in all 3 bottles?
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When the bottle had a cap tight on the bottle the water would not flow from the bottle when my hand was removed. This observation was the same for each different bottle 5. Explain your observation of the fluid flow when the cap was placed on the bottle, you removed your finger from the hole, and you squeezed the bottle. Was this the same for the holes in all 3 bottles? When I squeezed the bottle, the water would shoot out like a water gun with a lot of force shooting past the paper. This happened in each of the trials Conclusion: All in all, this lab was very enjoyable I loved using the separate bottles to better understand projectile range with liquid and how it works with Torricelli’s theorem. This lab was very enjoyable with the activity that is done in it. I feel like most of my values are accurate except for my values for my second part. I feel like in my second part my value for y which was the distance from the top of the water to the hole was inaccurate which made my calculated value inaccurate compared to my measured values. Other than my problem with the first part I enjoyed this lab very much. I am excited for my last lab and to learn what I can from it. References: Walker, J., Resnick, R., & Halliday, D. (2014). Fundamentals of physics . John Wiley & Sons, Inc.