Lab_4-Partial_Report

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University of Illinois, Urbana Champaign *

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Course

335

Subject

Mechanical Engineering

Date

Dec 6, 2023

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pdf

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4

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Lab 4 Partial Report - Flow around a Bend in a Rectangular Duct Rahul Pillai | Section ABK | TAM 335 Objective: The objective of this experiment is to measure the resultant force applied by a curved rectangular duct to the air flowing within the duct. Additionally, this report validates the control-volume analysis based on the linear-momentum principle and calculates theoretical values for pressure coefficient using the free-vortex model. Theory: In this experiment the force F can be obtained using a control-volume analysis based on the principle of linear momentum. The forces can be calculated using the equations: 𝐹 ? = 𝜌𝑈 0 2 𝐴 𝐹 ? = (𝑝 0 + 𝜌𝑈 0 2 )𝐴 𝜌𝑈 0 2 = 2(𝑝 𝑏𝑜? − 𝑝 0 ) Another model used in this experiment is the free vortex model, which assumes that there is no external force on the fluid, causing each particle in the fluid to experience a constant acceleration for the proposed free-vortex velocity distribution, one can predict the radial dependence of the resulting pressure coefficient Cp by writing a Bernoulli equation between the entrance and any point along the radial plane. Cp can be calculated using the equation: 𝐶𝑝(𝑟) = 1 − 5203.42245251 𝑟 2 Results: Tables 1, 2, and 3 show the outer, inner, and radial pressures for flow rates 1, 2, and 3 respectively. This could be due to friction or shear stress that happens during the turn of the fluid. Figures 2, 3, and 4 in the appendix graph the coefficient of pressure vs. the radius for all three different box pressures. Additionally, Table 4 shows the calculated forces by the Integration method and control volume analysis. Discussion: Flow rates graphs figures 2, 3, and 4 clearly illustrate that the flow around the bend corresponds to a free vortex model. However, there seems to be a trend of the experimental data being smaller than the predicted value from the free vortex model. Additionally, The higher the flow rate, the more the experimental data adhered to the free vortex model Conclusions: 1. The flow around the bend followed a free vortex model 2. The higher the flow rate, the more the experimental data adhered to the free vortex model
Appendix Figure 1 Schematic of a 90° bend in the Rectangular Duct Figure 2 Coefficient of Pressure vs. Radius for Flow Rate 1 Figure 3 Coefficient of Pressure vs. Radius for Flow Rate 2
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