ME2135E Fluid Mechanics
Formula sheet
Centrifugal Pump Power
Head
Head
Eff
Eff
Head
( ) ( ) () () () ⁄ ⁄ ⁄ ⁄ ⁄( ) ⁄ ⁄ Capacity
Head
Power
Coeff
Coeff
Coeff
Axial Pump Power
Head
°
: Absolute Blade velocity Flow velocity relative to blade Absolute flow velocity Normal component of Tangential component of
Inlet velocity triangle
V=V n
ur1
ub1
Outlet velocity triangle
V 2
V t2 t2
Cavitation
ur2 V n2 n2
ub2
∑ ∑ Cavitation index:
Hydrostatic Bearing
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ME2135E Fluid Mechanics
Formula sheet
⁄ √ ⁄ ] [ ̅ ⁄ ⁄ ⁄ | Minimum pumping loss:
Hydrodynamics Bearing-Inclined
Hydrodynamics Bearing-Rayleigh step
(⁄ ⁄) Flat Plate Boundary Layer Flow
Rex =5x105
⁄ ⁄ ⁄ ⁄ ⁄ ⁄ ⁄ ⁄ ⁄ ⁄ ⁄ ⁄ ⁄ ⁄ Re
Laminar (Blasius
2.59
Solution)
Turbulent (1/7 Power
1.29
Lower vel. profile )
For laminar flows H varies between 2 and 3,
(normal: 1.5~2)
Blasius Solution:
√
Boundary Layer with transition
⁄⁄ ⁄⁄ ⁄ √
Attached Flow
Point of separation
Pressure decreases in the flow direction, accelerate
Pressure increases in the flow direction, decelerate the
the lower part of boundary layer, Result in thinner
lower part of boundary layer, and cause s ome fluid
boundary layer than the case
Separated flow:
particles adjacent to the wall to be brought to rest.
Navier-Stokes Equation
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ME2135E Fluid Mechanics
Formula sheet
Steady Parallel Flow though a straight channel width=2b
∮ ∯ ⃗ ̂ ̂
Stream function: CCWPositive, CWNegative, Volume flow:
Incompressible flow:
Velocity Potential
Differential
Stream Functions Flow Type
Flow Pattern
Parallel Flow
Uniform Oblique Flow
Point Vortex
VortexSource
Flow with circulation round a circular cylinder in uniform flow
u0 y
q
2
tan
Velocity Potential
Flow Type
Source and Uniform flow
(Half Rankine)
Source or Sink
Stream Function
Sink / Source pair in Uniform flow (Full Rankine)
Doublet
A Doublet in Uniform flow (Flow over cylinder)
Stream Function
Velocity Potential
: ⁄ Stagnation Pt
,
y0 q 1 y y1 tan x x x x 2 0 1
1 y
Sink / Source pair
Flow Pattern
u
u0
x x x x q 2 x x y y 2 x x y y q
0
1
2
0
2
0
2
1
2
1
For source and sink at general coordinates (x 0 ,y 0 ) and (x 1 ,y 1 )
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ME2135E Fluid Mechanics
Formula sheet
Sample Q&A
| ∫
1. NS equation: 2 liquid with diff.
ANS:
, same
, no mixing, no pressure grad. Plate moving at U horizontal, gap =h+h
2. NS question: liquid flow on slant plate , 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.
4. NS question: liquid flow within 2 plates, one fixed, another moves upwards in velocity U, under gravity g, l iquid thickness=h ANS: 5. NS question: Couette flow, pressure gradient at x direction. Liquid thickness=h ∫ ANS: 6. Stream function: Flow past a cylinder with its axis perpendicular to the direction of flow. ° [ ] 7. Stream function: A vortex with wall. ANS:
ANS:
ANS:
ANS:
[ ] 8. Boundary layer: Skin friction.
⁄ ⁄ ⁄ ⁄ ⁄ * + 9. Stream function: Two sink Q at x= ±1 and one source NQ at 0,0 ANS:
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