Physics 150 Studio 2.docx

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Feb 11, 2024
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University of Michigan, Department of Physics Physics 150, studio Fall Term 2021 Studio 2: Dimensional Analysis Group Name: MiCaE Section Number: 007 Group Member 1: Daniel Wu Group Member 2: Louis Probst Group Member 3: Carolyn Kalata Group Member 4: Sofia Mincy Group Member 5:
To edit this document for submission, just click "File" then "Make a copy." Share this with your group so everyone can edit. You can then fill it out and print to pdf - only one group member needs to do this. Submit the pdf to Canvas under Studio 2 (Submission). Learning Goals At the end of this studio, you should be able to: Determine dimensions of an unknown proportionality constant (in this case, viscosity) from information about its relationship to other (known) quantities Use dimensional analysis to determine the relationship between different quantities with known dimensions Use dimensional analysis and estimation to explain why small water droplets in clouds float but raindrops fall. Introduction Today, we're going to use dimensional analysis to investigate why clouds float and rain falls. To begin, we'll focus on the motion of a sphere through a fluid. Fluids have a property called viscosity that measures, in a sense, the "stickiness" of the fluid. Because of viscosity, a fluid will resist shear --that is, it will resist our efforts to pull layers of fluid in different directions. This resistance is similar to the way friction resists the motion of one surface against another.
Problem 1 We'll start by figuring out the units of viscosity. Consider an experiment where two layers of fluid, separated by a distance d, are sheared by moving one layer parallel to the other at a speed v . The experiment reveals that the fluid will resist shear with some force P per unit area. P is proportional to the velocity v and inversely proportional to the separation d . Viscosity ( μ ) is the constant of proportionality. In equation form, we have: Question. What are the units of viscosity? μ: (kg)/(m*s)
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