BMES 444 Biofluid Modeling Assignment 2

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Drexel University *

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Mechanical Engineering

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Apr 3, 2024

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BMES 444 Biofluid Mechanics Version 20240227 Biofluid Modeling Assignment 2: Nondimensionalization and Fluid Rheology Academic Integrity Statement For this assignment, you may use any resources available to you, but you may not receive assistance from, nor give assistance to, any other individual (except from the instructor or course teaching assistant). In your submission, please include the following statement and your signature confirming the truth of the statement and your adherence to the Academic Integrity Policy of Drexel University. For this assignment, I make the following truthful statements: I have not received, nor will I receive, any assistance on this assignment from another individual, except for guidance provided by the instructor or the course teaching assistant I have not given, nor will I give, any assistance on this assignment to any other individual I have not discussed, nor will I discuss, this assignment with anyone except the instructor or course teaching assistant (until after the submission deadline) I will not plagiarize someone else’s work and submit it as my own I have read and understood Drexel University’s Academic Integrity Policy ( https://drexel.edu/studentlife/community_standards/code-of-conduct/academic- integrity-policy/ ), and have followed the policy as it pertains to this assignment I understand that acts of academic dishonesty will be reported to Student Conduct and will be penalized to the full extent allowed by Drexel University, including receiving a zero for this assignment or a failing grade for the entire course Signed, [your name and signature]
BMES 444 Biofluid Mechanics Version 20240227 Choose 1 of the following 2 activities and complete the described activity. Do not do both activities. When you have completed the activity, upload your submission as a PDF to the submission link on BB Learn. Activity 1: Nondimensionalization Scale models can be useful for estimating fluid behavior in the human body. Consider a situation where you have used a simple scale model to measure pressure drops in circular pipes. Your scale model system consisted of the following: Straight, circular pipe with diameter = 4 cm, length = 300 cm Fluid used for all testing was water at 20 o C Using this scale model, you have obtained the provided data (BMA2_option1_data.xlsx). In addition, you know that the pressure drop ΔP in a circular pipe depends on the length of the pipe L , the diameter of the pipe D , average flow velocity V , fluid density ρ , and fluid dynamic viscosity μ : ∆ P = f ( L,D ,V , ρ,μ ) Finally, you observe that pressure drop is directly proportional to the length of the pipe (which could be useful in simplifying the above relationship). Using the provided data set, please complete the following: a. (50 pts) Using the pressure drop data you obtained for your scale model system, estimate the pressure drop in the descending aorta of an adult human. b. (50 pts) Explain in detail your process for completing part a.
BMES 444 Biofluid Mechanics Version 20240227 Activity 2: Fluid Rheology Poly(ethylene glycol) (PEG) is frequently used as a biomaterial for tissue engineering. In some of these applications, PEG is spun into fibers to form fibrous scaffolds. The rheological properties of PEG solutions are very important to these spinning fabrication processes. I have provided viscometry data for a 5 wt% solution of PEG (BMA2_option2_data.xlsx). Using the provided data set, please complete the following: a. (50 pts) Using the provided apparent viscosity versus shear rate data, identify what rheological behavior(s) the fluid exhibits. In addition, if the fluid exhibits any of the following behaviors, determine the indicated quantity: a. Newtonian fluid – dynamic viscosity b. Bingham plastic or viscoplastic fluid – yield stress c. Power law fluid – n and K d. Herschel-Bulkley fluid – n , K , and yield stress e. If the fluid transitions from one behavior to another, determine the shear rate(s) over which the transition(s) occur b. (50 pts) Explain in detail your process for completing part a.
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