PHY 2020 Lab 09 - Fluid Flow-2

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Feb 20, 2024

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Physics 2020 --- Lab 09 Fluid Flow Materials Needed: Computer Course Objectives: 1. Define the equations for the statics and dynamics of fluids. Activity #1: Proceed to: https://phet.colorado.edu/sims/cheerpj/fluid-pressure-and-flow/latest/fluid-pressure-and- flow.html?simulation=fluid-pressure-and-flow Once the simulation is up and running, you should see something like this. 1

Lab Setup 1. Click the “Pressure” tab (of Pressure, Flow, and Water Tower) to begin Part 1 of the lab. In Part 2 of the lab, you will select the “Flow” tab. 2. Click and drag the pressure gauge to determine fluid pressure (see image on page 1). Also, click the checkbox to activate the ruler that you can use to measure the fluid depth. You can adjust the density of the fluid using the sliding scale on the lower, right-hand side of the window. If need to refresh any changes you have made, each tab will have a “Reset All” button: 3. Answer the questions in the spaces provided below. Lab Procedure: Part 1 1. First, theoretically predict the difference in gauge pressure for water between at a depth of one meter below the surface of the fluid (relative to the fluid’s surface). Show all your work for any credit. The theoretical difference in the gauge pressure for water between the depth and the surface of the water is 9,800 2. Perform the simulation. Click and drag the pressure gauge and activate the ruler (similar to the image on page 1) and measure the pressure at a depth of 1 meter below the surface of the water. Record the pressure difference in the space below. The pressure difference is 9.754kPa 3. The pressure gauge in this simulation shows the absolute pressure. Keeping this is mind, compare your simulated pressure differences from parts 2 and 1. Are your results the same or different? If your results are different, provide a brief explanation for the cause. The results for the first and second question are different. 4. Next, click the “Reset All” button. Now, raise the density of the fluid by sliding the density adjustment bar all the right to the “honey” setting. Click and drag the pressure gauge and activate the ruler (similar to the image on page 1) and measure the pressure at a depth of 1 meter below the surface of the water. Record the pressure difference in the space below. The pressure difference is 13.852kPa 2

5. Compare your results from question 4. to your result from question 2. Use the principle Δ P = ρ ⋅ g ⋅ Δh , to describe any observable difference, if you observe one. 6. As shown in the image below, use the slider to open the spigot on the faucet to fill up the water tank: Click the check box to activate the “Grid” and click and drag to activate the pressure gauge. In the space below, describe whether you predict the pressure difference from 0 meter to 1 meter of depth will be the same as the pressure difference between the 2m and 3m marks below the surface. Note: Though the grid is inactive in the image above, you can see the grid lines in the image on page 1. The pressure difference between the 0 m and 1 m marks will be less than the pressure difference between the 2 m and 3 m marks when measuring pressure in a fluid like water. 7. Using the pressure gauge, perform the simulation. Is the pressure difference between the 0m and 1m marks the same or different than the pressure difference between the 2m and 3m marks? 3

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Lab Procedure: Part 2 Click on the “Flow” tab at the top of window (see image below): As soon as you click onto the “Flow” tab, you will notice red dots begin to move from left to right across the screen. These dots represent small elements or parcels of the fluids. You can think of them as little objects flow along with the stream that we use to better observe the dynamics of the stream, such as the speed. Click the speedometer and drag it into the stream and click and drag the pressure gauge into the stream as shown above. 8. Suppose we narrowed the diameter of the tube such that the left half of the tube’s diameter is unchanged, and the right-half of the tube’s diameter is now smaller. Using the continuity equation ( ρ 1 ∙ A 1 ∙v 1 = ρ 2 ∙ A 2 ∙v 2 ), describe how the fluid velocity changes as it passes through the tube. Show all your work for any credit 9. About halfway down the tube click to grab the handles (shown above) and narrow the diameter of the tube. In the space below, copy and paste a screen shot of your adjustments. Using the speedometer to the measure the fluid’s velocity, perform the 4

simulation and describe how the velocity of fluid varies across the length of the tube. Do your predictions from question 8. agree with your results here? 10. Using the same “crimped” pipe as in question 8., and using Bernoulli’s equation: 1 2 ρv 2 2 + P 2 + ρg h 2 = 1 2 ρv 1 2 + P 1 + ρg h 1 In this equation, ρ is the fluid density, v is the fluid velocity, P is the fluid pressure, and assume h is the height of the center of the fluid stream. Predict how the fluid pressure in the thicker end of the tube compares with the fluid pressure in the thinner end of the tube. Show all your work for any credit. To make the relationship simpler assume that h 1 = h 2 . When the fluid is flowing through a horizontal pipe (when the heights are zero), the pressure at point 2 is 1.652×105 Pa. When the pipe moves through a height of 3.82 m and the velocity of the fluid remains constant, the pressure at point 2 is 1.3×105 Pa. 11. Using the speedometer to the measure the fluid velocity and the pressure gauge, perform the simulation. How does the simulation pressure and velocity of the fluid vary across the length of the tube? Velocity remains constant and pressure decreases gradually. 12. For the last simulation, click the “Reset All” button on the “Flow” tab. Click the handle on the left-hand side of the pipe to raise it as high as it will go, and click the handle on the right-hand pipe to lower it as low as it will go as shown in the image below: 5

Without changing the diameter of the pipe describe how the pressure and velocity of the flow at the left-hand, elevated opening compare with the pressure and velocity of the fluid at right-hand, lowered opening? Conclusion - magnitude of velocity at the both section is same. This is because the flow is obeying continuity equation. which states Area of cress section of flow is same for both the section hence velocity at both the section is also same. Pressure- Right section is at low height while lect section is at higher level. let consider the level of right section as reference level and left section is H meter above the reference level... now applying bernoulli's equation- and applying this the equation simplifies to from this it can be verified mathematically that pressure at right section is higher than pressure at left section. Conclusions: 1. Trained, professional divers can withstand a gauge pressure of about 392 kPa. Assuming the density of water is 1,000 kg/m 3 , how deep can a professional diver reach? Show all your work for any credit . diver is 40 meter deep h= 40 meter 2. Suppose you are a sonographer, and you are measuring the percent blockage of an artery in a patient. As the blood flows through a region of blockage, how do you expect the blood velocity to change. Use the image below to guide your thinking. 6

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In areas affected by blockages, the blood velocity surpasses that of regions where blockages are absent. 3. Using a Doppler Sonogram, you measure the velocity of blood flow in a blocked region to be 0.23 m/s. When compared to a nearby unblocked region, the flow is 0.11 m/s. What fraction of the cross-sectional area of the artery is blocked? Show all your work for any credit . The fraction of the cross-sectional area of the artery that is blocked is 0.522 4. Using the Bernoulli equation, describe how the blood pressure taken in a patient’s leg compares with the blood pressure taken at the upper arm. Show all your work for any credit . 1. Upper Arm Blood Pressure: Generally higher due to larger arteries, smoother flow, and closer proximity to heart. 2. Leg Blood Pressure: Typically lower due to smaller arteries, potential resistance, and farther distance from heart. 5. Bonus : A transient ischemic attack (TIA) is a temporary lack of blood supply to the brain. Blood normally flows to the brain through the back of the head via the two Vertebral arteries (one going up each side of the neck) which meet to form the Basilar artery. Now, each vertebral artery connects to the Subclavian artery before the blood passes through into the arms. Suppose one of the Subclavian arteries is partially blocked. Because of the continuity equation, blood flow will have to be faster through that partially blocked artery (smaller artery area means a larger blood velocity). Using the Bernoulli equation, describe how the increased blood flow through the blockage can result in the patient fainting due to blood loss to the brain. Use the image below to guide your thinking. A thorough answer to this problem can cancel out as many as two other completely missed problems. 7

AS BLOOD PRESSURE INCREASES MORE WILL BE THE BLOOD CLOT IT'S LIKE FEEDBACK LOOP THEN LESS BLOOD WILL REACH AND HE WILL FAINT DUE TO BLOOD LOSS 8

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