Problem 5: Dimensional Analysis Use the Buckingham Pi Theorem (Song, 2018, pages 219-221) to derive an equation for friction head loss, hr, as a function of gravitational acceleration, g, pipe diameter, D, pipe length, L, and average velocity, V=Q/A. Step 1-List the dimensional parameters (N, n₁, n₂, ...). Step 2-List the dimensions of all parameters in terms of primary dimensions. Step 3-Select a set of primary dimensions (MLT or FLT). Step 4-Select a set of repeating parameters. Step 5-Set up one or more dimensional equations in the form N= n*n2n3², then solve for the unknown exponents.
Problem 5: Dimensional Analysis Use the Buckingham Pi Theorem (Song, 2018, pages 219-221) to derive an equation for friction head loss, hr, as a function of gravitational acceleration, g, pipe diameter, D, pipe length, L, and average velocity, V=Q/A. Step 1-List the dimensional parameters (N, n₁, n₂, ...). Step 2-List the dimensions of all parameters in terms of primary dimensions. Step 3-Select a set of primary dimensions (MLT or FLT). Step 4-Select a set of repeating parameters. Step 5-Set up one or more dimensional equations in the form N= n*n2n3², then solve for the unknown exponents.
Engineering Fundamentals: An Introduction to Engineering (MindTap Course List)
5th Edition
ISBN:9781305084766
Author:Saeed Moaveni
Publisher:Saeed Moaveni
Chapter6: Fundamental Dimensions And Units
Section: Chapter Questions
Problem 49P
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