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# 华工流体力学复习提纲

Chapter 2 Fluid flow 流体流动 fluid statics and its application Nature of fluids ? Density 密度 Incompressible fluid 不可压缩流体 Compressible fluid 可压缩流体 Pressure 压强(压力) Independent of direction Unit SI制：N/m2或Pa， mmHg， mH2O ? Pg = Pabs – Patm ? Pv = Patm - Pabs
?

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Hydrostatic equilibrium

Pb ? Pa ? ?g ?Z a ? Zb ?
pa

?

? gza ?

pb

?

? gzb

Limitation: 适用：静止、连续的同种不可压缩性流体； Incompressible fluid、 Continuous fluid hydrostatic equation application 应用 U tube manometer U形压差计的计算式

?

?
? ?

Solution: 图(a) ?p=Rg(ρm-ρ)； 图(b) ?p=Rg(ρm-ρ空)=Rgρm；

?p=Rg(ρm-ρE)
?p=Rgρm-hgρ。

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Chapter3 Fluid-flow phenomena

Ideal fluid 理想流体 Has zero viscosity Potential flow has two characteristics: ? Irrigational flow ? There is no friction loss
?

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Newtonian fluid

du ? ?? dy
the proportionality constant

μ

For gas, it increases with temperature For liquid, it decreases with temperature
1Pa· =10 P（泊） =1000 cP ( 厘 泊) S

Laminar and turbulent flow 滞流和湍流
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Laminar flow 层流/滞流 fluid flows in parallel straight lines. without lateral mixing

Turbulent flow 湍流 fluid moves erratically in form of crosscurrents and eddies
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Reynolds number

Re ?

d?u

?

● Re ≤ 2100, flow is laminar flow 滞流
Re ≥ 4000, flow is turbulence 湍流

● 2100< Re<4000 , a transition flow 过渡流

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Flow in boundary layers

Laminar and turbulent flow in boundary layers

Boundary-layer formation in straight tubes

Boundary-layer separation and wake formation 边界层的分离

Chapter 4 basic equations of fluid flow
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Mass balance 连续性方程

? m ? V? ? ua Sa ?a ? ub Sb ?b ? uS? ? const
incompressible fluid, flow through the station a and b

V ? ua

?
4

d ? ub
2 a

?
4

d

2 b

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Mechanical energy balance

2 b

Pa

u Pb u ? gZa ? ? W ? ? gZb ? ? h f ? 2 ? 2
2 a 2 b

2 a

J/kg

Pa u P u b ? Za ? ? ? Zb ? ?g 2 g ?g 2g
2 2 ua ub Pa ? Z a ?g ? ? ? Pb ? Z b ?g ? ? 2 2

m

pa

For incompressible flow (不可压缩流体.) 2. Without friction loss 3. For unit．．．

Chap5

Incompressible flow in pipes

and channels

Shear stress and skin friction in pipes
L u2 L u2 hf ? ?4f ?? ? d 2 d 2 ?p

λ =4f

Flow in noncircular channel

Velocity distribution in a pipe

?w 2 2 ?rw ? r ? ur ? 2?rw
?r ? ur ? 1? ? ? ?r ? u ma

x ? w?
2

?w u max ? rw 2?

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Hagen-Poiseuille equation
?p rw rw ?pd 2 u? ? ?L 2 4? 32??L

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Laminar flow in pipes 层流流动 Turbulent flow in pipes 湍流流动

64 ?? Re

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friction factor and friction coefficient chart

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Friction from changes in velocity or direction 局部阻力计算
u2 h fe ? K e 2
u------小管平均流速

Friction loss from sudden expansion of cross section Friction loss from sudden contraction of cross section Effect of fittings and valves
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Pipe Flow Systems 管路计算
Single Pipes 简单管路

Multiple Pipes Systems 复杂管路

Chapter 6 flow past immersed bodies
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Terminal velocity

laminar 层流区(Stokes区) ：
ut ? g ?? p ? ? ?d 18?
2 p

Re p ?

d put ?

?

Rep≤1

Transition (过渡区)：Allen ′ law
turbulent
(湍流区)

：Newton ′ law

Separation equipments Gravity settling processes
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gravity settling chamber Centrifugal settling processes

cyclone separator
Critical diameter

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Filtration

discontinuous pressure filters Principles of cake filtration Constant-pressure filtration

dV A ?p ? dt ?rv (V ? Vm )
2

【7-66】

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Filtration equation of constant pressure

2?pA V ? 2VVm ? t ?rv
2 2

V ? 2VVm ? KA t
2 2

【7-70】

Continuous filtration

K? V ?A n

【7-74】

Washing filter cakes
dV KA2 ? dt 2(V ? V )e
therefore

KA ? dV ? ? dV ? ? ? ?? ? ? ? dt ? w ? dt ? E 2(V ? Ve )
2

【7-75】

Chapter8 transportation and metering of fluids
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Power requirement power supplied to the pump drive from an external source

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Suction lift and cavitation

no liquid can be drawn when cavitation occurs

air bound

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Suction lift
2 pa ? p2 u2 Hg ? ? ? hf ?g 2g

To avoid cavitation, the pressure in station 2 must
2 p1 ? pv u2 Hg ? ? NPSH ? ? hf ?g 2g

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Centrifugal pump theory
?H ? ? k ? BQ

Effects of speed and impeller size change

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characteristic curve

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Centrifugal-pump characteristics
to increase speed

to decrease speed

characteristic curve

?

2

H ? K ? BQ

System curve

system curve

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Operating point

Operating point

system curve

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Operating point change
to increase speed

to decrease speed

Operational point

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Operation in parallel and in series of centrifugal pump

in parallel in series

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Measurement of flowing fluids
Venturi meter

ub ?

Cv 1? ?
4

2? pa ? pb ?

?

(8-34)

Orifice meter

uo ?

Co 1? ?
4

2? pa ? pb ?

?

Area meters: Rot meters Calibration Installation Direction of flow through modification

Picot tube

measure the local velocity

uo ?

2? ps ? po ?

?

(8-48)

Chapter 10
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Heat Transfer

Conduction

dq dt ? ?k dA dx
Direction of heat flow

(10-2)

conductivity

Convection Newton’s law of cooling
?

q ? h(t s ? t f ) A
Coefficient depends on the flow patterns the thermal properties of the fluid

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Radiation The energy emitted is proportional to the fourth power of the absolute temperature.

Wb ? ?T

4

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heat transfer through flat slab heat transfer through cylinder

Compound resistance in series

total temperature drop

overall thermal resistance

Chap11 Principles of heat flow in fluids
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Countercurrent and parallel-current flows

parallel

Single-pass shell-and-tube condenser
Temp of condensing vapor T

C Temperature o

Δt1

Δt

Δt2

Length of tube m

?

Energy balances

q=mhCph (Th1-Th2)= mcCpc (tc2 - tc1)

(11-6)

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Overall heat-transfer coefficient

1 dA dA dA ? ? ? U hi dAi kdAm ho dAo
Special cases of the overall coefficient

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Average temperature of fluid stream

Where

?t2 ? ?t1 ?tm ? ?t2 ln ?t1

Chap12 Heat transfer to fluids without phase change
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Heat transfer by forced convection in turbulent flow

hi d 0.8 n Nu ? ? 0.023 Re Pr k

(12-30)

Chap13 Heat transfer to fluids with phase change
Heat transfer from condensing vapors Dropwise and film-type condensation
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? r ? 2 gk 3 ? ? ? 0.725 ? ? ? ? do ?t ?
Horizontal tubes vertical tubes
noncondensing gas

1 4

(13-14)

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Pool boiling of saturated liquid
natural convection Nucleate boiling. film boiling