Problem 1:A thin rectangular plate has a width w and a height h. It is placed so that it is normal to a moving streamof fluid as shown in the figure. Assume the drag force D, that the fluid exerts on the plate is a function ofw and h, the fluid viscosity and density, μ and p, respectively, and the velocity V of the fluid approachingthe plate.+BEP.μWrite the general form of the drag function, meaning D =f(?,?,?) where the "?" are the parameters ofinterest. What are the dimensions of each of the parameters you determined? Use the Buckingham PiTheorem to determine all of the Pi Terms. Use the M-L-T system. Use w, V and p as your repeatingvariables. One you have developed your Terms, plug back in to prove that they are dimensionless.

Answered: Image /qna-images/answer/3207a367-281f-4526-ac0f-cc8a565a17cb.jpg

Problem 1: A thin rectangular plate has a width w and a height h. It is placed so that it is normal to a moving stream of fluid as shown in the figure. Assume the drag force D, that the fluid exerts on the plate is a function of w and h, the fluid viscosity and density, μ and p, respectively, and the velocity V of the fluid approaching the plate. P.μ Write the general form of the drag function, meaning D =f(?,?,?) where the "?" are the parameters of interest. What are the dimensions of each of the parameters you determined? Use the Buckingham Pi Theorem to determine all of the Pi Terms. Use the M-L-T system. Use w, V and p as your repeating variables. One you have developed your Pi Terms, plug back in to prove that they are dimensionless.

Problem 1: A thin rectangular plate has a width w and a height h. It is placed so that it is normal to a moving stream of fluid as shown in the figure. Assume the drag force D, that the fluid exerts on the plate is a function of w and h, the fluid viscosity and density, μ and p, respectively, and the velocity V of the fluid approaching the plate. P.μ Write the general form of the drag function, meaning D =f(?,?,?) where the "?" are the parameters of interest. What are the dimensions of each of the parameters you determined? Use the Buckingham Pi Theorem to determine all of the Pi Terms. Use the M-L-T system. Use w, V and p as your repeating variables. One you have developed your Pi Terms, plug back in to prove that they are dimensionless.

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Concept explainers

Properties of Fluids

The term fluid represents a type of substance that can easily change its shape under any external pressure/force and can flow. Fluids can acquire any shape in which it is stored and can resist normal stresses but cannot resist shear stress in rest condition. Whenever external shear stress is applied to fluids, it starts to flow. The fluids may be liquid or gas. Example- water, air, etc.

Question

Problem 1:
A thin rectangular plate has a width w and a height h. It is placed so that it is normal to a moving stream
of fluid as shown in the figure. Assume the drag force D, that the fluid exerts on the plate is a function of
w and h, the fluid viscosity and density, μ and p, respectively, and the velocity V of the fluid approaching
the plate.
+BE
P.μ
Write the general form of the drag function, meaning D =f(?,?,?) where the "?" are the parameters of
interest. What are the dimensions of each of the parameters you determined? Use the Buckingham Pi
Theorem to determine all of the Pi Terms. Use the M-L-T system. Use w, V and p as your repeating
variables. One you have developed your Terms, plug back in to prove that they are dimensionless.

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Step 1: Determining the given data

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Step 2: Finding general form of drag function

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Step 3: Finding dimensions of each term

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Step 4: Finding 1st pi term

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Step 5: Finding 2nd pi term

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Step 6: Finding 3rd pi term

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Step 7: Finding expression of drag force

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Step 8: Proving pi terms are dimensionless

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