Ae311_fall_2011_hw_1 - Prof. Daniel J. Bodony AE311, Fall...

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Unformatted text preview: Prof. Daniel J. Bodony AE311, Fall 2011 HW #1 Due Friday, September 9th, 2011 Problem 1 Consider a stone of mass m falling from a height h from rest in a gravitational field with acceleration g . Use dimensional analysis to determine the dependency of the total time-to-fall, t , on m , h , and g . Does this result agree with your expectations? Problem 2 Consider a spherical object of diameter d falling from a height h in the presence of a gravitational field of acceleration g through a fluid. If the object is light enough we expect the drag force on the object to influence the total time t it takes to complete the fall. Assuming the object has density s , the fluid has density f and viscosity , determine the non-dimensional variables ( i.e. , the i s from the Buckhingham-Pi theorem). What are the meanings of these variables? Problem 3 When a fluid flows through a pipe, the pressure in the pipe drops due to frictional forces between the fluid and pipe walls. (We will study this in detail later.) We can use dimensional analysis to understand how the pressureand pipe walls....
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This note was uploaded on 01/26/2012 for the course MUS 130 taught by Professor Lee during the Fall '08 term at University of Illinois, Urbana Champaign.

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Ae311_fall_2011_hw_1 - Prof. Daniel J. Bodony AE311, Fall...

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