Lab_4-Partial_Report
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Dec 6, 2023
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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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cm3
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