Fluid-Mechanics-Lab-4-Memo

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New York University *

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Aerospace Engineering

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Apr 28, 2024

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Experiment 4: Pipe Flow Date: 4/10/2023 To: Professor Sven Haverkamp and Lab TA’s From: Joey Vivar, Lucas Botero, Charlie Calixto, David Kang, Will Lee Course: ME-UY 3311 Abstract The purpose of this experiment was to calibrate two different types of flow meters: a Venturi as well as a sharp-edged orifice plate. Copper tubes will be used to determine the flow velocities. The flow rate measurement was given through the rotameter, and the flow rate through four copper tubes with different diameters was measured. The flow properties calculations will be affected by the flow rate, the friction, and the roughness of the pipe wall. Two of the three tubes used are straight throughout its construction, a third tube will contain an elbow pipe section. Analyzing the construction of the pipe can allow us to derive the energy loss (or pressure drop) and flow rate given by the elements (elbows, values, pipes) and their specifications (diameter, length, fitting type). A portable piping system is used, a pump is driven and provides a consistent flow rate that can be measured on a rotameter and measuring tank; six large pipes are present, one will be connected to the manometer at a time, one will be connected per annular chamber. The height of the water is measured from an array of manometers; the difference between heights is denoted as the pressure drop throughout the pipe. The calculated head loss for tube 1 are 0.148 m, 0.170 m, 0.196 m for tube 2, and 0.385 m, 0.570 m, and 0.910 m, with 21.9%, 19.6%, and 18.6% percentage error respectively. The head loss for tube 2 for 0.4, 0.6, and 0.8 m^3/h are as follows: 0.385, 0.57, and 0.91 m, with 82%, 75%, and 74.5% percentage errors respectively. Data Elbow Pipes The following table represents the corresponding values as shown above for which includes the construction of an elbow pipe. Table 1: Tube 3 (Elbow Pipe) The following is the sample calculation for finding the equivalent length in the tube using the first row: 𝐿 ?𝑞 = 2𝐷∆𝑃 ρ?𝑉 2 2×0.02×8093.3 1000×0.0234×1.68 2 = 4. 9123 ?
The following is the plot o describe the relationship between the pressure drop and the horizontal distance as a function: Figure 1: Pressure vs Horizontal Distance Straight Pipes The following is the table for the volumetric flow rate, velocity, headloss, reynold’s number, Darcy-Weisbach, and Moody friction factor and the corresponding percent error per tube. The construction throughout these tubes remained straight throughout its construction. Table 2: Tube 1 and Tube 2 (Straight Pipes) The sample calc for the frictional factor using Darcy-Weisbach can be found by using the first pipe with a flow rate of 2 : ? 3 /ℎ
? = ℎ ? × 𝐷 𝐿 × 2? 𝑉 2 → 0. 148 × 0.026 2.2 × 2(9.81) (1.0464) 2 = 0. 0313 The friction factor was also found using Moody’s diagram for each of the tubes. Results and Discussion As stated above in table 1, the equivalent lengths for 4.912, 4.947, and 4.486 m respectively for the Q’s of 1.9, 2.0, and 2.1. The calculated head loss for tube 1 are 0.148 m, 0.170 m, 0.196 m for tube 2, and 0.385 m, 0.570 m, and 0.910 m, with 21.9%, 19.6%, and 18.6% percentage error respectively. The head loss for tube 2 for 0.4, 0.6, and 0.8 m^3/h are as follows: 0.385, 0.57, and 0.91 m, with 82%, 75%, and 74.5% percentage errors respectively. Due to the similarities of percentage error for each tube, it is assumed to be systematic error. Tube 1 has its associated Reynolds number ranging from 25866 to 31039 and tube 2 ranging from 8406 to 16813. For tube 1, the frictional factors via the Darcy-Weisbach equation and Moody’s chart range from 0.0288 to 0.0313 and 0.0235 to 0.0245 with tube 2 ranging from 0.1063 to 0.17999 and 0.0271 to 0.0324 respectively. For tube 3 the pressure drop ranges from 8093.3 Pa to 8829 with an associated Reynolds number ranging from 31945 to 35307. The respective friction factors via Moody's chart range from 0.0228 to 0.0234 with equivalent lengths from 4.4867 to 4.9471. Looking at all of the data, it is quite clear that every flow is turbulent, as seen from the Reynold's numbers of each tube. This is most likely due to the frictional factors mentioned in the section above. The flow is affected greatly by the friction, making the fluid particles bump into each other and create turbulence as they flow. In addition, there was the possibility of air bubbles inside the tubes as water passed through them, further increasing turbulence.
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