me2135e fluid mechanics formula sheeta0066078x lin shaodun page

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ME2135E Fluid

Mechanics Formula

sheetA0066078X

Lin Shaodun Page2

of 4

Minimum pumpingloss:

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 √

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 ⁄ 

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HydrodynamicsBearing-Inclined

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 ⁄  

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Hydrodynamics

Bearing-Rayleighstep

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  ⁄)

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Flat Plate Boundary

Layer Flow Rex

=5x105

Re

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Laminar(BlasiusSolution)

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2.59

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Turbulent (1/7

Power Lower vel.profile )

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1.29

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For laminar flows H

varies between 2 and3, 

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 (normal: 1.5~2) 

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 Blasius Solution:

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√ 

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Boundary Layer with

transition

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√ 

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 Attached Flow Pointof separation

Separated flow:

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Pressure decreases inthe flow direction,

acceleratethe lower part

of boundary layer,

Result in

thinner boundary layerthan the case

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 Pressure increases in theflow direction,

decelerate thelower part

of boundary layer, and

cause some

fluid particles adjacentto the wall to be brought

to rest.

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Navier-StokesEquation

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ME2135E Fluid

Mechanics FormulasheetA0066078X

Lin Shaodun Page3

of 4

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Steady Parallel Flowthough a straight

channel width=2b

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Stream function:CCW 

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Positive, CW 

Negative, Volume

flow: 

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 Incompressible flow:

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∮

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∯

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 Velocity Potential

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 Differential

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Stream FunctionsFlowType

Flow Pattern

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 Stream Function

VelocityPotential

Flow Type FlowPattern

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Stream Function

Velocity Potential

ParallelFlow

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Source andUniform flow(Half Rankine)

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 Stagnation Pt

:

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UniformObliqueFlow

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Sink / Sourcepair

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 ⁄  

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 Sourceor Sink 

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 Sink / Sourcepair in

Uniformflow (Full Rankine)

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 PointVortex

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 Doublet

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Vortex-Source

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A Doublet inUniformflow(Flow over cylinder)

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,

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Flow with circulation

round acircular cylinder inuniformflow

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1110010

tan2tan2

x x y yq x x y yq yu

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 21211202000

22y y x x x xq y y x x

x xquu

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For source and sink at

general coordinates

(x0

,y

0) and (x

1

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,y1

)

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ME2135E Fluid

Mechanics Formula

sheetA0066078X

Lin Shaodun Page4

of 4

Sample Q&A1. NSequation:

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2 liquid with diff.

, same

, no mixing, no

pressure grad. Plate

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moving at U

horizontal, gap =h+hANS: 

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2. NS question:

liquid flow onslantplate , zero shear at

interface, with gravity

g, liquid thickness=h,

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flow direction as x

axis.ANS: 

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3. NS question:liquid flow vertically

within 2 fixed plates,under gravity g

(direction

 –  z), liquid

thickness=h.ANS: 

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4. NS question:liquid flow within 2

plates,one fixed,another moves

upwardsin velocity U,

under gravity g,liquid thickness=h

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  ANS: 

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5. NS question:

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Couette flow,

pressure gradient at xdirection. Liquid

thickness=hANS: 

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 6. Stream function:

Flow past a cylinderwith its axis

perpendicular to thedirection of flow.ANS: 

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 ANS: 

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7. Stream function:A vortex with wall.

ANS: 

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8. Boundary layer:Skin friction.

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+

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9. Stream function:

Two sink Q at x=±

1 and one source NQ

at 0,0ANS: 

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