Analysis of Poiseuille Flow In Rectangular Duct vs. Infinitely Large Flat Plates

Project Summary

My senior capstone design team needed to characterize the flow within our system in order to build a physical model visualizing Poiseuille flow between infinitely large flat plates.

The intended design was simplified into key geometric properties describing a system where a pump drives the movement of a water-glycerin mixture through pipes into a sealed rectangular pipe.
The inputs (our design needs) were defined to ensure incompressible, Newtonian, laminar fluid flow in a reasonable size range.
The outputs (in terms of velocity, volumetric flow rate, and pump delivery pressure) were calculated using fluid mechanics concepts.

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Since infinitely large flat plates are not possible to build and our maximum size range is something that can fit through doors, we needed to ensure that flow within a rectangular duct could approximate flow between infinite plates. Calculations were done for both scenarios and compared.
To ensure laminar flow, the Reynold’s number was set to a low value. This made the resulting velocity very low, which required the viscosity of the mixture to be adjusted with various proportions of water and glycerin.

MATLAB was used to document the analysis, allowing the capstone team to adjust the input parameters until a desired set of output parameters were achieved. This analysis drives all the key components of the design: the dimensions, the materials, and the pump.

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