A2) In order to solve the dimensional analysis problem involving shallow water wave as in Figure 2, Buckingham Pi Theorem has been used. h Figure 2 Through the observation that has been done, the wave speed © of waves on th surface of a liquid is a function of the depth (h), gravitational acceleration (9), flui density (p), and fluid viscosity (µ). By using this Buckingham PI Theorem: a) Analyze the above problem and show that the Froude Number (Fr) and Reynola Number (Re) are the relevant dimensionless parameters involve in this problem.
A2) In order to solve the dimensional analysis problem involving shallow water wave as in Figure 2, Buckingham Pi Theorem has been used. h Figure 2 Through the observation that has been done, the wave speed © of waves on th surface of a liquid is a function of the depth (h), gravitational acceleration (9), flui density (p), and fluid viscosity (µ). By using this Buckingham PI Theorem: a) Analyze the above problem and show that the Froude Number (Fr) and Reynola Number (Re) are the relevant dimensionless parameters involve in this problem.
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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Transcribed Image Text:A2) In order to solve the dimensional analysis problem involving shallow water waves
as in Figure 2, Buckingham Pi Theorem has been used.
h
Figure 2
Through the observation that has been done, the wave speed © of waves on the
surface of a liquid is a function of the depth (h), gravitational acceleration (g), fluid
density (p), and fluid viscosity (µ). By using this Buckingham Pi Theorem:
a) Analyze the above problem and show that the Froude Number (Fr) and Reynolds
Number (Re) are the relevant dimensionless parameters involve in this problem.
b) Manipulate your Pi (1) products to get the parameter into the following form:
pch
:= f(Re) where Re =
Fr =
c) If one additional primary variable parameter involve in this proolem such as,
temperature (T). Discuss on the Pi (m) products that can be produce and explain why
this dimensional analysis is very important in the experimental work.
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