유체역학 및 열전달 Chapter 5. Basic Equations of Fluid Flow (7)

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유체역학 및 열전달

Chapter 5. Basic Equations of Fluid Flow (7)

부산대학교 화공생명공학부 현 규 (Kyu Hyun)

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Macroscopic Momentum Balances

(거시적 운동량 수지)

(Rate of momentum accumulation)

=(Rate of momentum entering) – (Rate of momentum leaving) + (Sum of forces acting on the system)

- (4.16)

å

+ -

= M &

_a

M &

_b

F

0

- (4.46)

• Momentum correction factor :

평균유속과 사용할때와 다르기 때문

-Momentum flux

V

m &

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Macroscopic Momentum Balances

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Macroscopic Momentum Balances

g w

b b a

a

S p S F F

p

F = - + -

å

Pressure x area

Net force of wall of channel on fluid

-Component of force of gravity - (+ for upward direction)

g w

b b a

a a

a b

b

V V p S p S F F

m ^& ( b - b ) = - + -

-Equation of motion(Momentum Balance) = Force Balance

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Layer flow with free surface (1)

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Layer flow with free surface (2)

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Mechanical Energy Equation (Bernoulli equation)

• 유체가 흘러가기 위해서는 에너지가 필요하다. 따라서 유체역학과 에너지에

대한 방정식이 필요하다.

• In physics, energy is a quantity that is often understood as the ability to perform work.

• This quantity can be assigned to any particle, object, or system of objects as a consequence of its physical state.

• During a 1961 lecture for undergraduate students at the California Institute of Technology, Richard Feynman, a celebrated physics teacher and Nobel

Laureate, said this about the concept of energy:

• There is a fact, or if you wish, a law, governing all natural phenomena that are known to date. There is no known exception to this law—it is exact so far as we know. The law is called the conservation of energy.

• It states that there is a certain quantity, which we call energy, that does not change in manifold changes which nature undergoes. That is a most abstract idea, because it is a mathematical principle; it says that there is a numerical quantity which does not change when something happens. It is not a description of a mechanism, or anything concrete;

it is just a strange fact that we can calculate some number and when we finish

watching nature go through her tricks and calculate the number again, it is the same.

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Mechanical Energy Equation (Bernoulli equation)

• Energy is a scalar physical quantity. In the International System of Units (SI), energy is measured in joules, but in some fields other units such as kilowatt- hours and kilocalories are also used. Different forms of energy include

•

kinetic,

•

potential,

•

thermal,

•

gravitational,

•

sound,

•

elastic and electromagnetic energy.

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Mechanical Energy Equation (Bernoulli equation)

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Mechanical Energy Equation (Bernoulli equation)

• Consider a volume element of a stream tube

2 0

2

= +

+ r f

r / ) cos

( ug

dx u dP dx

u u d

1 0

2

2 = +

+

\ dx

g dZ dx

dP dx

u d

r )

/ (

2 2

b b

b a

a

u

p gZ gZ u

p + + = + +

r r

-Bernoulli equation without friction -Eq. (4.67)

2 0

2

÷÷ = ø ö çç è

æ + +

\ u P gZ

dx d

r

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Bernoulli equation

2 2

b b

b a

a

u

p gZ gZ u

p + + = + +

r r

-Daniel Bernoulli

-Daniel Bernoulli was a Swiss

mathematician and physicist and was one of the many prominent mathematicians in the Bernoulli family. He is particularly

remembered for his applications of mathematics to mechanics,

especially fluid mechanics, and for his pioneering work in probability and statistics. His name is

commemorated in the Bernoulli principle, a particular example of the conservation of energy, which describes the mathematics of the mechanismunderlying the

operation of two important

technologies of the 20th century: the carburetor and the airplane wing.

-Published in 1738

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Mechanical Energy Equation (Bernoulli equation)

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Mechanical Energy Equation (Bernoulli equation)

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Mechanical Energy Equation (Bernoulli equation)

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Mechanical Energy Equation (Bernoulli equation)

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Mechanical Energy Equation (Bernoulli equation) I

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Mechanical Energy Equation (Bernoulli equation) II

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Shear stress and skin friction in Pipes (전단 응력 및 표면

마찰) (1) –

^{page 98}

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마찰) (2)

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마찰) (3)

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마찰) (4)

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마찰) (5)

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마찰) (6)

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마찰) (7)

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마찰) (8)

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마찰) (9)

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Turbulent Flow in Pipes and Channels (1)

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The friction factor Chart (1)

k / D

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The friction factor Chart (2)

n ppm

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Total friction for “real” pipe

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Friction loss from sudden expansion of cross section

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Friction loss from sudden contraction of cross section

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Friction loss

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Minimizing expansion and contraction losses

유체역학 및 열전달 Chapter 5. Basic Equations of Fluid Flow (7)