Demo lab1

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California State University, Long Beach *

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336

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Civil Engineering

Date

Apr 3, 2024

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pdf

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6

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California State University of Long Beach Civil Engineering Department CE 336: Fluid Mechanics Laboratory Lab No.1: Fluid Statics and Manometry Instructor: Khalid Rafique Group 4 Lab Section 1 By: Cindy Tran Experiment was performed: 2/12/24 Due Date: 3/11/24
Purpose The purpose of this experiment is to understand the mechanics of liquids under hydrostatic pressure by measuring static pressure with manometers as well as reading where the surface level of a liquid lies on a scale. Equipment Figure 1. F1-29 Armfield Apparatus
Figure 2. Diagram of the Experimental Setup A F1-29 apparatus as shown in Figure 1 was used for the entirety of the experiment. In Figure 2, the apparatus includes a vernier scale (1), a reservoir (2), a U-tube, 3 fixed tubes, and a manometer that can be adjusted to a different angle. Tables Liquid Level (mm) Eye at Liquid Level 276.5 Eye 100 mm Below Liquid Level 275 Eye 100 mm Above Liquid Level 278 Table 1. Liquid Level Measurement using a Level Scale
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Liquid Level (mm) Point Gauge 30.7 Hook Gauge Not collected Table 2. Liquid Level Measurement using a Vernier Scale Liquid Level (mm) At Reservoir 261.5 U-Tube 256 Fixed Tube 256 Inclined Tube at 60 degrees 308 Inclined Tube at 30 degrees Not readable Table 3. Free Surface Demonstration Level Change in Reservoir (mm) Level Change in U-Tube (mm) Apply Pressure 357 356 Reduce Pressure 172 164.5 Table 4. Pressure Change in Reservoir Level Change in Reservoir (mm) Level Change in U-Tube (mm) Connection w/ Reservoir 263 157 No Connection w/ Reservoir 261.5 295 Table 5. Pressure Change in the U-Tube Level Change in Legs (mm) Level Change in U-Tube (mm) Apply Pressure 180 251 Reduce Pressure 333 251 Table 6. Pressure Change in the Two Fixed Tubes Calculations 1) 𝐿 * 𝑠𝑖?Θ =
L= inclined height, h= vertical height 308 * 𝑠𝑖?(60) = 266. 7358 ?? 2) 𝑝 = γℎ = ρ𝑔ℎ 𝑝 = ρ𝑔𝐿 * 𝑠𝑖?Θ a) Reservoir: (997 kg/m³)(9.8 m/s²)(261.6*10^-3 m) = 2555.98896 Pa b) U-tube: (997 kg/m³)(9.8 m/s²)(256*10^-3 m) = 2501.2736 Pa c) Fixed tube: (997 kg/m³)(9.8 m/s²)(256*10^-3 m) = 2501.2736 Pa d) Inclined Tube at 60 deg: (997 kg/m³)(9.8 m/s²)(266.7358*10^-3 m)= 2606.1690 Pa Discussion Before beginning, it should be noted that the data set used in this report originated from the provided material “Raw Data Lab 1 - Fluid Statics & Manomentry” on Canvas so there may be errors that occurred in the lab that may not mentioned or information that was not provided outright. Questions: 1) What is parallax? Parallax is “the observed displacement of an object caused by the change of the observer's point of view” so the level of water appears to change depending on the angle someone views it. 2) How have the readings changed when you read the liquid level height below/above eye level? There seems to be a difference of 1.5 mm below or 2 mm above 276.5 mm in liquid level when viewing it 100 mm below/above liquid level respectively as shown in Table 1. Discussing Table 2, the point gauge data was given to be 30.7 mm while the hook gauge was not provided. 3) What is the advantage of using a point gauge and hook gauge? The purpose of the point gauge and hook gauge is to be able to have a more accurate reading of the water level as compared to just eyeing it since the gauge has a more exact ruler as well as being able to fine tune the instrument itself. 4) What were the liquid levels at the reservoir, U-tube, fixed tube, and inclined tube? The measurement given is in reference to depth from an unrecorded datum point so it is unknown as to what the actual measurement of the water level would be. The recorded water level at the reservoir was 261.5 mm. Compared to that, the U-tube and fixed tube had the same level at 256 mm while the inclined tube had a calculated vertical height of 266.73 mm. There was an equipment error where the reservoir has a consistent 4 mm datum difference from the fixed tube and U-tube as specified by the professor. 5) How has the liquid level changed using the U-tube and reservoir when you have applied pressure with connection/no-connection with the reservoir?
With connection to the reservoir, the water level in the U-tube drop has a change of 157mm. With no connection with the reservoir, the level actually rises in the U-tube by 295 mm. 6) What is the advantage of using an inclined manometer? The inclined tube should theoretically have a more accurate result as there is more graduation in an inclined reading than the horizontal reading but it is more susceptible to a human error in reading as the lines for the measurements are slanted and harder to read. The U-tube and fixed tube had the same result as there was no difference that would matter hydrostatically. Summary In observing the mechanics of liquids through manometers, it gave a better understanding on the effects of static pressure as well as hydrostatic pressure. A lot of the experiment involved reading the manometers of various tubes in various ways. Measuring by eye of the liquid level has some degree of human error involved which drops accuracy. Using the vernier and point/hook gauges increases accuracy because of the fine tuning knobs and a physical indicator of whether the needle is touching the surface level of the water, although it takes some time to set up as a result. U-tubes and fixed tubes seem to have the same level of accuracy but the U-tube differs from the fixed tube as it can also be used to calculate added pressure introduced into the system. The inclined tube is theoretically the most accurate way of measurement due to the increased amount of graduation used to describe the water level, but realistically there were some equipment errors that had changed the accuracy of the water level like datum height and actual angle of the inclined tubes. Inclined tubes in specific could adjust the amount of graduation depending on the angle so at an angle closer to the ground, there would be a much more accurate reading. The vertical height would stay the same as the mass in the tube would be conserved, even as it changed its angle. The reservoir seems to be the most resistant to pressure changes compared to the U-tubes and the fixed tube as the cross sectional area of the reservoir is much higher which means water in u-tubes and fixed tubes has to rise to a higher level to occupy the same volume since water is incompressible. References Gerhart, Philip M., et al. “3.6.1 Free Jets.” Munson, Young, and Okiishi’s Fundamentals of Fluid Mechanics , 8th ed., Wiley, Hoboken, NJ, 2016. Sultana. CE 336 Fluid Mechanics Laboratory . Long Beach, 2017.
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