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ME2135E Fluid

Mechanics Formula

sheetA0066078X

Lin Shaodun Page2

of 4

Minimum pumpingloss:



√



⁄



HydrodynamicsBearing-Inclined



⁄



Hydrodynamics

Bearing-Rayleighstep



⁄)



Flat Plate Boundary

Layer Flow Rex

=5x105

Re



Laminar(BlasiusSolution)



2.59



Turbulent (1/7

Power Lower vel.profile )



1.29



For laminar flows H

varies between 2 and3,



(normal: 1.5~2)



Blasius Solution:



√



Boundary Layer with

transition



√



Attached Flow Pointof separation

Separated flow:



Pressure decreases inthe flow direction,

acceleratethe lower part

of boundary layer,

Result in

thinner boundary layerthan the case



Pressure increases in theflow direction,

decelerate thelower part

of boundary layer, and

cause some

fluid particles adjacentto the wall to be brought

to rest.



Navier-StokesEquation



ME2135E Fluid

Mechanics FormulasheetA0066078X

Lin Shaodun Page3

of 4



Steady Parallel Flowthough a straight

channel width=2b



Stream function:CCW



Positive, CW

Negative, Volume

flow:



Incompressible flow:



∮



∯



Velocity Potential



Differential



Stream FunctionsFlowType

Flow Pattern



Stream Function

VelocityPotential

Flow Type FlowPattern



Stream Function

Velocity Potential

ParallelFlow



Source andUniform flow(Half Rankine)



Stagnation Pt

:



UniformObliqueFlow



Sink / Sourcepair



⁄



Sourceor Sink



Sink / Sourcepair in

Uniformflow (Full Rankine)



PointVortex



Doublet



Vortex-Source



A Doublet inUniformflow(Flow over cylinder)



,



Flow with circulation

round acircular cylinder inuniformflow



1110010

tan2tan2

x x y yq x x y yq yu



21211202000

22y y x x x xq y y x x

x xquu



For source and sink at

general coordinates

(x0

,y

0) and (x

1



,y1

)



ME2135E Fluid

Mechanics Formula

sheetA0066078X

Lin Shaodun Page4

of 4

Sample Q&A1. NSequation:



2 liquid with diff.

, same

, no mixing, no

pressure grad. Plate



moving at U

horizontal, gap =h+hANS:



2. NS question:

liquid flow onslantplate , zero shear at

interface, with gravity

g, liquid thickness=h,



flow direction as x

axis.ANS:



3. NS question:liquid flow vertically

within 2 fixed plates,under gravity g

(direction

– z), liquid

thickness=h.ANS:



4. NS question:liquid flow within 2

plates,one fixed,another moves

upwardsin velocity U,

under gravity g,liquid thickness=h



ANS:



5. NS question:



Couette flow,

pressure gradient at xdirection. Liquid

thickness=hANS:



6. Stream function:

Flow past a cylinderwith its axis

perpendicular to thedirection of flow.ANS:



ANS:



7. Stream function:A vortex with wall.

ANS:



8. Boundary layer:Skin friction.



+



9. Stream function:

Two sink Q at x=±

1 and one source NQ

at 0,0ANS:

me2135e fluid mechanics formula sheeta0066078x lin shaodun page

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