Lab 2 Physics Pre Lab part 1

UIC Physics Department Physics 131 PreLab Page 1 of 2 NAME SECTION DATE P h y s i c s 1 3 1 – L a b # T i t l e P r e – l a b o r a t o r y A s s i g n m e n t Carefully read the entire lab manual for this lab and answer the following questions. 1 . Describe in your own words the overall goals of the lab. 2 . Identify the physics concepts that you will learn about or test in the lab. Ali Hernandez Wed 10 00am 11 15 23 6 Venturi meter Artificial Heart

UIC Physics Department Physics 131 PreLab Page 2 of 2 3 . Describe briefly what you will measure in the lab and make your predictions of the outcomes of the important measurements in the experiment. Your predictions do not need to be correct to earn credit on this part, but you should explain your reasoning. I n o r d e r t o r e c e i v e c r e d i t f o r t h i s p r e - l a b r e p o r t , y o u m u s t h a v e y o u r p r e - l a b c o m p l e t e d b e f o r e t h e l a b s e s s i o n b e g i n s , a n d s h o w i t t o y o u r T A s o t h e y c a n v e r i f y t h a t y o u h a v e d o n e i t . If your TA has not seen your pre-lab and confirmed that you have it completed at the beginning of your lab session, you will get a 0 for the pre-lab component of your lab report. As a record, p l e a s e h a v e y o u r T A s i g n y o u r c o m p l e t e d p r e - l a b r e p o r t b e l o w . If you have completed this electronically, and the TA cannot sign this document, write “Signature on last page of lab report” below, and have the TA write “Prelab Completed:” followed by their signature on the last page of your lab report. TA Signature:

UIC Physics Department Physics 131 Laboratory Manual Venturi Meter and Artificial Heart Page 2 of 7 In our experiments we will use a venturi meter ሺsee Figure 2ሻ as a pipe of varying cross-section and air as the fluid. There are two kind of venturi tubes used in this lab: short ሺ~ 9.5 inches in length with 2࠵? ଵ ൌ 16 mm and 2࠵? ଶ ൌ 8 mmሻ and long ሺ~ 13 inches in length with 2࠵? ଵ ൌ 12 mm and 2࠵? ଶ ൌ 8 mmሻ. If the air flows from the wide part of the venturi tube to the narrow part, the velocity of the air in section 2 will be higher than in section 1. Then, according to Eq. ሺ2ሻ, the pressure in section 2 will be lower than in section 1. By modeling the air flowing through the venturi meter as a steady flow of incompressible, nonviscous fluid, from Eqs. ሺ2ሻ and ሺ3ሻ it follows that the difference between the pressure in section 2 and the pressure in section 1, ∆࠵? ଵ,ଶ , must vary linearly with the air flow rate squared, i.e. ∆࠵? ଵ,ଶ ൌ ࠵?࠵?࠵?࠵?࠵? ൈ ࠵? ଶ ሺ4ሻ In the first part of the lab we will experimentally test this equation, i.e. whether ∆࠵? ଵ,ଶ is linearly dependent on ࠵? ଶ , as follows from Bernoulli’s Principle and the continuity equation. Part2. Artificial Heart As noted above, Bernoulli Principle ሺEq. ሺ2ሻ tells us that as pressure increases, velocity decreases and vice versa. Therefore, if someone has high blood pressure then the velocity of the blood in this person’s arteries will be smaller than normal, causing the heart to work harder since it will take longer for oxygenated blood to reach the extremities of the body. Now let's think about atherosclerosis or hardening of the arteries in case when the artery becomes constricted. This is analogous to decreasing the cross-sectional area of a pipe ሺsee Eq. ሺ3ሻሻ. Let’s predict what will happen to blood pressure and velocity. From the continuity equation ሺ3ሻ it follows that as the radius ሺor cross-sectional areaሻ decreases, the velocity in the pipe goes up to keep the flow rate constant. Then, according to Bernoulli's equation ሺ2ሻ this increase in velocity would lead to a pressure decrease. At first, this may seem counterintuitive since atherosclerosis increases the likelihood that the artery will burst, causing a heart attack or stroke. But the artery does not burst due to the blood pressure in the constriction, it bursts because of the pressure the plaque exerts on the arterial wall or because a completely blocked artery would create an increase in blood pressure in the chamber before the blockage, akin to filling up a water balloon until it burst. In the second part of the lab we will measure some physical properties of “blood” flow in an artificial body and see how Bernoulli’s Principle and the Continuity equation can be used to explain our observations. This artificial body consists of a “heart” that pumps “blood” into a system of arteries. Let’s remind ourselves of how our heart works. The heart consists of two sides, right and left. The right side takes the blood from the body through the veins and pumps it to the lungs, the left side takes the now oxygenated blood from the lungs and pumps it through the arteries into the body. Each side of an actual Figure 2

UIC Physics Department Physics 131 Laboratory Manual Venturi Meter and Artificial Heart Page 3 of 7 heart has two chambers and two one-way valves. The way the heart pumps is that the first chamber, the atrium expands filling with blood. As the atrium contracts the first one-way valve is opened and the blood enters the second chamber, the ventricle. The ventricle is expanding at this time, which also draws the blood into the chamber. Then the ventricle begins to contract closing the first one-way valve and opening the second, pumping the blood out of the heart ሺsee Figure 3ሻ. As our artificial body doesn’t have lungs, our artificial heart can be significantly simplified: it consists of just the left side. Also, our artificial heart doesn't include the left atrium, so the “blood” starts at the “left ventricle” ሺairline with air under pressure of ~18 psiሻ. From the “left ventricle” the “blood” is pushing into the “aorta”, the main piece of the venturi meter, through the “aortic” valve ሺPVC gray one way valveሻ. Then the “blood” flows into the system of arteries ሺoutlet and side connecting tubes in Figure 2ሻ, which may have different constrictions to model hardening of the arteries. Equipment Figure 4 shows initial setup of the apparatus used in this experiment which consists of venturi meter, flow meter and quad pressure sensor. Figure 3 Figure 4 subtracting do subtraction in kPa first then PA relative PA absolute Patm f Of IP Ypf 0.000012 D 2 slope AR A n 2

UIC Physics Department Physics 131 Laboratory Manual Venturi Meter and Artificial Heart Page 5 of 7 9. Close the gray valve of the apparatus, then click the “Record” button, wait for 5-10 seconds, then click “Stop”, and record the three sensor readings at ࠵? ൌ 0 L/min in Table 1. Note: These readings and ones you measured in step 4 must be the same within the error estimated in step 5. Data Analysis for Part 1 First, let’s convert the physical quantities you measured above in SI units, that is the flow rate from L/min to m 3 /s ሺ1 L/min ൌ 1.67  10  5 m 3 /sሻ and pressure from kPa to Pa ሺ1 kPa ൌ 1  10 3 Pa ሻ. 10. Convert the flow rate values listed in Table 1 to m 3 /s and record them in the same order in Table 2. 11. For each ࠵? calculate its ࠵? ଶ value and record in Table 2. To reduce errors due to the difference in pressure reading by the sensors in step 4, let’s convert the absolute ሺabsሻ pressures, ࠵? ௡,௔௕௦ , collected in Table 1 to pressures, ࠵? ௡,௥௘௟ , relative ሺrelሻ to the atmospheric pressure and at the same time, convert the pressures from kPa to Pa as ࠵? ௡,௥௘௟ ൌ ൫࠵? ௡,௔௕௦ െ ࠵? ௡,௔௧௠ ൯ ൈ 10 ଷ , where ࠵? is the sensor number ሺ1,2 or 3ሻ. Record these values in Table 2. 12. For each flow rate, calculate the absolute value of the pressure difference between the constriction ሺSection 2ሻ and the first chamber ሺSection 1ሻ, ∆࠵? ଵ,ଶ ൌ ห࠵? ଶ,௥௘௟ െ ࠵? ଵ,௥௘௟ ห and record the values in Table 2. 13. Repeat the same calculations for the absolute value of the pressure difference between the third ሺSection 3ሻ and the first chamber ሺSection 1ሻ, ∆࠵? ଵ,ଷ ൌ ห࠵? ଷ,௥௘௟ െ ࠵? ଵ,௥௘௟ ห and record these values in Table 2. 14. Copy the 2 nd and 6 th columns of Table 2 into LibreOffice Calc worksheet, plot ∆࠵? ଵ,ଶ vs ࠵? ଶ graph, and then apply LINESTሺሻ function to find the slope of the linear regression line, its uncertainty and the coefficient of determination. Record your results below: ࠵?࠵?࠵?࠵?࠵? ൌ ቀ ∆௉ భ,మ ொ మ ቁ ௦௟௢௣௘ ൌ ______________________  _____________ Pa  ሺm 3 /sሻ  2 R 2 ൌ ___________ ࠵? m 3 /s ࠵? ଶ ሺ m 3 /s ሻ 2 P 1,rel Pa P 2,rel Pa P 3,rel Pa ∆࠵? ଵ,ଶ Pa ∆࠵? ଵ,ଷ Pa Table 2. Experimental Results* * In the first two columns, use scientific notation for the numerical values and round them to two decimal places. No decimal places should be used for the rest 5 columns. 99.84 m my Prelative Paksolute Patmosphere 8 355 4 6.97225 7 4820 4470 4550 350 270 7.515 E 4 5.64755 7 4000 3680 3760 320 240 6.685 4 4 4622457 3140 2900 2970 240 170 5 8455 4 3.416405 7 2430 2250 2270 180 160 5 OIE 4 2.5100 E 7 1790 1650 1690 40 100 4 1755 4 1.743065 7 1200 1110 1150 90 50 3.34 4 1 2285057 770 720 750 50 20 2.5055 4 6.275025 420 400 400 20 20 1.67 4 2.78895 8 150 150 150 0 0 0.99

UIC Physics Department Physics 131 Laboratory Manual Venturi Meter and Artificial Heart Page 6 of 7 In the space to the right include a picture ሺscreenshotሻ of the ∆࠵? ଵ,ଶ vs ࠵? ଶ graph. 15. By combining Bernoulli’s Principle with continuity equation we can get the following expression for ∆௉ భ,మ ொ మ : ∆௉ భ,మ ொ మ ൌ ఘ ଶ ሺ ஺ భ మ ି஺ మ మ ஺ మ మ ஺ భ మ ሻ ൌ Slope ሺ5ሻ where ࠵? is the air density, and A 1 and A 2 are the cross-sectional areas of the wide and narrow sections of the venturi tube, respectively. 16. Use Eq. ሺ5ሻ to find the air density, then use the uncertainty in the slope you found above to estimate the experimental error in the air density and record both values below. ࠵? ൌ __________________  _____________ kg/m 3 Note: In this experiment the density of air can vary ሺfrom device to deviceሻ in the range of 1 – 3 kg/m 3 . Question 1. Does the numerical value of the air density you found make sense? Explain your reasoning. _________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________ Question 2. Do your experimental results support the Bernoulli’s Principle? Explain your reasoning. _________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________ Question 3. Sections 1 and 3 of the venturi meter have the same cross-sectional area. According to Bernoulli’s Principle when fluid flows from narrow section 2 to section 3 its velocity must decrease and the pressure in section 3 should recover to the same value as in section 1. Are your experimental results consistent with this prediction? If not, what could be reason for any discrepancy? Briefly describe your observations and conclusions below: _________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________ Note: It could be helpful to make a comparison using the values of ∆࠵? ଵ,ଶ and ∆࠵? ଵ,ଷ in table 2.