fluid dynamics

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Nov 24, 2024

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Lab 14 Worksheet Access the Fluid Pressure and Flow PhET simulation . Click on the image at the top of the page to access/play the simulation. This lab can be completed using either the CheerpJ or Java versions, though the CheerpJ version is easier to access. When the simulation launches, click on the “ Flow ” tab near the upper-left corner of the screen. You should see small red dots flowing through a pipe. Part 1 – Guided Exploration Use the simulation to answer the following questions: 1. Drag a velocity meter (labeled “Speed”) down to the uniform pipe. Measure the velocity in m/s of the water at several different positions within the pipe. How do the readings change as you move the sensor horizontally through the pipe? How do the readings change when you move the sensor vertically through the pipe? Be specific in your explanation. 2. Drag a pressure meter down to the uniform pipe. Measure the pressure in kPa of the water at several different positions within the pipe. How do the readings change as you move the sensor horizontally through the pipe? How do the readings change when you move the sensor vertically through the pipe? Be specific in your explanation. As the velocity meter is moved horizontally and vertically throughout the pipe, the velocity does not change. The pipe is uniform, hence, the velocity of the flow is constant throughout the horizontal movement as the depth of the pipe is consistent, such as in diameter. The same is shown in the vertical movement. As the pressure meter is dragged down the pipe in a horizontal manner, the pressure remained constant or relatively constant. The pipe, if the pipe is consistent throughout, the pressure reading will be relatively consistent. However, the pressure as the meter is dragged up and down, the pressure changes. At the top, the pressure goes down and going to the bottom, the pressure reading goes up. This pressure difference is due to hydrostatic pressure; this pressure difference is based on the depth of the water column above the sensor position. Picture 1 - Fluid Pressure and Flow Simulation

3. Do the pressure sensor readings report the gauge pressure or the absolute pressure? Explain. 4. Select the ruler tool and drag the ruler to the middle of the uniform pipe. Use the handlebars on the pipe to change the diameter of the middle of the pipe. Leave the rest of the pipe diameter unchanged. For each change in pipe diameter, measure the fluid velocity and pressure at points A and B as shown in the diagram below. Complete the table. Diameter A (m) Velocity A (m/s) Pressure A (kPa) Diameter B (m) Velocity B (m/s) Pressure B (kPa) 2.0 1.6 116.441 3.0 0.8 108.302 2.0 1.6 116.054 2.5 1.1 112.701 2.0 1.6 116.754 2.0 1.6 116.392 2.0 1.6 116.710 1.5 3.1 112.228 2.0 1.6 116.642 1.0 6.2 101.363 Point A Point B The pressure sensor report gauge pressure. The absolute pressure is the sum of the gauge pressure and atmospheric pressure and requires reliance of specific pressure ranges as a reference.

5. What is the effect on the velocity and pressure at point A if the pipe diameter at point B decreases? 6. What is the effect on the velocity and pressure at point B if the pipe diameter at point B decreases? Part 2 – Design and Conduct an Experiment 7. Design an experiment that will allow you to determine how the height difference between points A and B in the pipe will affect the velocities and the pressures. List your procedures below. Indicate the independent and dependent variables and include a few variables that must remain constant. When the diameter decreases at point B then, the velocity at that point increases slightly. The pressure, even at the decreased diameter, followed the similar pattern of hydrostatic pressure where at the top the pressure decreased than that compared to the top. The only difference was that in the point b range the numbers were slightly lower than that of point A. 1. set up a vertical pipe apparatus with two points, A and B, at different heights. 2. Measure and record the initial height difference between points A and B. 3. Measure the pressure and velocity at these points. 4. Gradually change the height difference between points b (the constant) and a by altering the position of point a to a higher or lower position 5. Repeat steps 1-4 for at least five data points. 6. Analyze the collected data of the height difference (independent variable) and the velocity and pressure (dependent variables). 7. Conclude and interpret. There is no change in velocity in both the horizontal and vertical direction at point A with a decrease in point B. This is also relatively the same regarding pressure, with only slight variation in a few decimal places, in both the horizontal and vertical directions; the pressures increase and decrease as expected due to the hydrostatic pressure as mentioned earlier in question number two.

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8. Perform your experiment. Create a properly labeled data table with at least five data points. Diameter A (m) Velocity A (m/s) Pressure A (kPa) Diameter B (m) Velocity B (m/s) Pressure B (kPa) 2 (initial) 1.6 110.290 2 1.6 120.290 2.5 1.1 109.953 2 1.6 120.288 3 0.7 112.351 2 1.6 119.914 3.5 0.5 109.547 2 1.6 120.765 4 0.4 113.632 2 1.6 120.234 9. What conclusions can you derive from your data? Be specific in your explanation. The relationship shows that the various heights, especially in diameter, affect the velocity more than the pressure. The velocity is larger in magnitude when the height is smaller such as in the initial height of two meters. However, the larger the height, such as four meters, the slower the velocity. Comparing the velocities, the initial heigh had a velocity of 1.6 m/s versus 0.4 m/s at the four-meter height. The velocity of b was made to be consistent in both velocity and pressure. For the pressure observation, the pressure increased at the bottom of the pipe and decreased at the top at both heights. The pressure variation is similar to that in the lab and only slight variation- this is also determined by the depth in the water itself that is being observed.