부산대학교현규유체역학및열전달 1

유체역학및열전달

Chapter 5. Basic Equations of Fluid Flow (7)

부산대학교 화공생명공학부현 규 (Kyu Hyun)

부산대학교현규

Macroscopic Momentum Balances (거시적운동량수지)

(Rate of momentum accumulation)=(Rate of momentum entering) – (Rate of momentum leaving)

+ (Sum of forces acting on the system)- (4.16)

å+-= FMM ba&&0 - (4.46)

• Momentum correction factor : 평균유속과 사용할때와 다르기 때문

-Momentum flux

Vm&

유체역학및열전달 2

부산대학교현규

Macroscopic Momentum Balances (거시적운동량수지)

유체역학및열전달 3

부산대학교현규

Macroscopic Momentum Balances (거시적운동량수지)

gwbbaa FFSpSpF -+-=åPressure x area

Net force of wall of channel on fluid

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

gwbbaaaabb FFSpSpVVm -+-=- )( bb&

-Equation of motion(Momentum Balance) = Force Balance

유체역학및열전달 4

부산대학교현규

Layer flow with free surface (1)

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부산대학교현규

Layer flow with free surface (2)

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부산대학교현규

Mechanical Energy Equation (Bernoulli equation)

유체역학및열전달 7

• 유체가 흘러가기 위해서는 에너지가 필요하다. 따라서 유체역학과 에너지에대한 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. —The Feynman Lectures on Physics

부산대학교현규

Mechanical Energy Equation (Bernoulli equation)

유체역학및열전달 8

• 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.

부산대학교현규

Mechanical Energy Equation (Bernoulli equation)

유체역학및열전달 9

부산대학교현규

Mechanical Energy Equation (Bernoulli equation)

• Consider a volume element of a stream tube

022

=++ frr cos)/( ugdxdPu

dxudu

0122

=++\dxdZg

dxdP

dxud

r)/(

22

22b

bba

aa ugZpugZp

++=++rr

-Bernoulli equation without friction

-Eq. (4.67)

유체역학및열전달 10

02

2

=÷÷ø

öççè

æ++\ gZPu

dxd

r

부산대학교현규

Bernoulli equation

22

22b

bba

aa ugZpugZp

++=++rr

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-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 mechanism underlying the operation of two important technologies of the 20th century: the carburetor and the airplane wing.

-Published in 1738

부산대학교현규

Mechanical Energy Equation (Bernoulli equation)

유체역학및열전달 12

부산대학교현규

Mechanical Energy Equation (Bernoulli equation)

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부산대학교현규

Mechanical Energy Equation (Bernoulli equation)

유체역학및열전달 14

부산대학교현규

Mechanical Energy Equation (Bernoulli equation)

유체역학및열전달 15

부산대학교현규

Mechanical Energy Equation (Bernoulli equation) I

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부산대학교현규

Mechanical Energy Equation (Bernoulli equation) II

유체역학및열전달 17

부산대학교현규

Shear stress and skin friction in Pipes (전단응력및표면마찰) (1) – page 98

유체역학및열전달 18

부산대학교현규

Shear stress and skin friction in Pipes (전단응력및표면마찰) (2)

유체역학및열전달 19

부산대학교현규

Shear stress and skin friction in Pipes (전단응력및표면마찰) (3)

유체역학및열전달 20

부산대학교현규

Shear stress and skin friction in Pipes (전단응력및표면마찰) (4)

유체역학및열전달 21

부산대학교현규

Shear stress and skin friction in Pipes (전단응력및표면마찰) (5)

유체역학및열전달 22

부산대학교현규

Shear stress and skin friction in Pipes (전단응력및표면마찰) (6)

유체역학및열전달 23

부산대학교현규

Shear stress and skin friction in Pipes (전단응력및표면마찰) (7)

유체역학및열전달 24

부산대학교현규

Shear stress and skin friction in Pipes (전단응력및표면마찰) (8)

유체역학및열전달 25

부산대학교현규

Shear stress and skin friction in Pipes (전단응력및표면마찰) (9)

유체역학및열전달 26

부산대학교현규

Turbulent Flow in Pipes and Channels (1)

유체역학및열전달 27

부산대학교현규

Turbulent Flow in Pipes and Channels (2)

유체역학및열전달 28

부산대학교현규

Turbulent Flow in Pipes and Channels (3)

유체역학및열전달 29

부산대학교현규

The friction factor Chart (1)

k / D

유체역학및열전달 30

부산대학교현규

The friction factor Chart (2)

ppmn

유체역학및열전달 31

부산대학교현규

Total friction for “real” pipe

유체역학및열전달 32

부산대학교현규

Friction loss from sudden expansion of cross section

유체역학및열전달 33

부산대학교현규

Friction loss from sudden contraction of cross section

유체역학및열전달 34

부산대학교현규

Friction loss

유체역학및열전달 35

부산대학교현규

Minimizing expansion and contraction losses

유체역학및열전달 36