Lab 2 Physics Pre Lab part 1

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University of Illinois, Chicago *

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131

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Physics

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Dec 6, 2023

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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 1 of 7 Venturi Meter and Artificial Heart One of the most important laws in physics of fluid dynamics that is widely used in medicine is Bernoulli's equation. This equation ሺoften also called Bernoulli’s principleሻ describes the pressures and velocities of fluids in a pipe, which is widely used to model the processes/conditions affecting blood circulatory system in a body. The main purpose of this laboratory experiments is to give you some experience with fluid dynamics. Objectives  Understand Bernoulli’s principle and learn how to use devices such as venturi tube, flow meter and pressure sensor to measure fluid flow velocity and corresponding pressure.  Learn how Bernoulli’s principle and continuity equation can be applied to study the cardiovascular system in the human body. Introduction Part1. Bernoulli Principle Bernoulli's principle states that when an incompressible, smoothly flowing fluid gains speed, internal pressure in the fluid decreases, and vice versa. Ignoring changes in temperature and density, and energy dissipated by friction, Bernoulli's principle can be expressed as following: ࠵? ൅ ࠵?࠵?ℎ ൅ ଵ ଶ ࠵?࠵? ଶ ൌ ࠵?࠵?࠵?࠵?࠵?࠵?࠵?࠵? ሺ1ሻ where ࠵? is the density of the fluid, ࠵? is its speed, h is the elevation of the fluid ሺmeasured with respect to some reference pointሻ and ࠵? is the internal pressure of the fluid. Actually, Eq. ሺ1ሻ expresses conservation of energy for flowing fluids. When a fluid is at rest ሺ࠵? ൌ 0ሻ, Bernoulli's equation ሺ1ሻ reduces to ࠵? ൅ ࠵?࠵?ℎ ൌ ࠵?࠵?࠵?࠵?࠵?࠵?࠵?࠵? , which gives the increase in pressure with decreasing elevation ሺincreasing depthሻ in a motionless fluid. When a fluid is in motion, and if the fluid flow is horizontal ሺno change in elevationሻ, then Eq. ሺ1ሻ can be rewritten as ࠵? ൅ ଵ ଶ ࠵?࠵? ଶ ൌ ࠵?࠵?࠵?࠵?࠵?࠵?࠵?࠵? ሺ2ሻ In case of incompressible fluid, it moves in such a way that mass is conserved. It means that when a fluid is flowing in a tube of varying cross-section ሺFigure 1ሻ, the volumetric flow rate, ࠵? ൌ ࠵?࠵?, ሺwhere ࠵? is the cross-sectional area of the pipeሻ is the same everywhere in the tube, i.e. ࠵? ൌ ࠵? ଵ ൌ ࠵? ଵ ࠵? ଵ ൌ ࠵? ଶ ࠵? ଶ ൌ ࠵? ଶ ሺ3ሻ Eq. ሺ3ሻ is called the Continuity Equation for steady flow. In case of circular pipe with radii ࠵? ଵ and ࠵? ଶ , Eq. ሺ3ሻ can be written as ࠵? ଵ ଶ ࠵? ଵ ൌ ࠵? ଶ ଶ ࠵? ଶ . Figure 1

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

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