유체역학 6판 조광래 외2명 솔루션(1-3)

소개

유체역학 6판 조광래 외2명 솔루션(1-3)

목차

Chapter 1 • Introduction

Chapter 2 • Pressure Distribution
in a Fluid

Chapter 3 • Integral Relations
for a Control Volume

본문내용

Chapter 3 • Integral Relations
for a Control Volume
3.1 Discuss Newton’s second law (the linear momentum relation) in these three forms:
( )
system
m d m d d
dt dt
ρ υ
⎛ ⎞
Σ = Σ = Σ = ⎜ ⎟
⎜ ⎟
⎝ ⎠
F a F V F ∫ V
Solution: These questions are just to get the students thinking about the basic laws of
mechanics. They are valid and equivalent for constant-mass systems, and we can make
use of all of them in certain fluids problems, e.g. the #1 form for small elements, #2 form
for rocket propulsion, but the #3 form is control-volume related and thus the most
popular in this chapter.
3.2 Consider the angular-momentum relation in the form
O ( )
system
d d
dt
ρ υ
⎡ ⎤
Σ = ⎢ × ⎥
⎢⎣ ⎥⎦
M ∫ r V
What does r mean in this relation? Is this relation valid in both solid and fluid
mechanics? Is it related to the linear-momentum equation (Prob. 3.1)? In what manner?
Solution: These questions are just to get the students thinking about angular
momentum versus linear momentum. One might forget that r is the position vector from
the moment-center O to the elements ρ dυ where momentum is being summed. Perhaps
rO is a better notation.

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