
Elements Of Electromagnetics
7th Edition
ISBN: 9780190698614
Author: Sadiku, Matthew N. O.
Publisher: Oxford University Press
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Transcribed Image Text:1. An incompressible fluid of density p and viscosity µ flows through a long horizontal section of a round pipe of diameter
D. You would like to determine the shear stress on the walls of the tube (7) given an average velocity V. Assume some
constant average roughness height & along the inside wall of the pipe.
(a) Choosing μ, D, and p as your repeating parameters, develop a non-dimensional relationship between shear stress
and the other parameters.
Tw
Π2
PV2,
use
PVD
(b) Using different repeating parameters results in the following II groups: II₁ = 2, II₂ = 5, and II3 =
μ
these Pi groups for the rest of the problem. If you are attempting to model the shear stress on a proposed
new section of Water Tunnel #3 feeding New York City which must potentially supply 64.8 m³/s of water per
second. Given the future tunnel parameters given in the table, choose the experimental parameters left blank in
the table to ensure similarity, (make sure you show your work and prove that you have met the requirements for
similarity. Additionally, when choosing your working fluid, clearly denote the name of the fluid and it's properties.
).
Parameter
Velocity
ρ
μ
D
€
Prototype
1.5 m/s
1000 kg/m³
1.0x10-3kg/ms
7.3 m
0.25 mm
Experiment
0.0045 mm
(c) Explain your working fluid choice. Use engineering arguments, i.e. cite rational design concerns (physical proper-
ties, cost, corrosiveness, toxicity,...)
(d) If your experiment measures a shear stress of 1000.0 N/m², what do you predict the shear stress on the walls of
Tunnel #3 to be?
(e) What is the meaning of each of these Pi groups. I.e. describe in words what are they the ratios of.
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