MBL_Int(1).pdf of mbl fliid mechanicsm of

mBL fluids

1. ME 2201 Fluid Mechanics
Semester 5
4/26/2023 ME 2201 1

2. Module V-Incompressible Viscid Flows: Momentum
Boundary Layers
4/26/2023 2ME 2201
•Internal Flows (flow bounded on all sides)
•PhysicalConcepts
•PoiseuilleFlowandCouetteFlow
•PipeFlowsandFrictionFactor

3. Boundary Layer Theory:
4/26/2023 3
•BL is the thin layer of viscous moving fluid in the immediate vicinity of a
bounding surface (usually termed ‘Wall’).
•Thickness of BL, ??????, is the region of significant viscous flow effects
•MostImpeffectofBLisNoSlipCondition
�=�
??????????????????
@??????=0;
��
�??????
=0
@??????=�;�=0
ME 2201

4. Boundary Layer Theory:
4/26/2023 4
Flow in a pipe is
Laminar when Re < 2100
Turbulent when Re > 4200
For practical purposes, the critical
value for flow transition is taken to be
Re
crit= 2300
Laminar Flow
Analytical/Numerical
Solutions
Transition Flow
No data
No correlations
Turbulent Flow
Data/Correlations
No Analytical Solution
Eddies/Vortices
ME 2201

5. 4/26/2023 5ME 2201
Ignored for analysisAnalytical Solutions
Hydrodynamic Entrance Length

6. Poiseuille Flow
4/26/2023 6ME 2201
L >> a
Assumptions:
1.Newtonian and incompressible flow
2.Steady and parallel flow (v=0;
??????
????????????
=0)
3.2D (&#3627408484;=
??????
????????????
=0)

7. Poiseuille Flow
4/26/2023 7ME 2201
??????&#3627408477;
??????&#3627408485;
=??????
??????
2
&#3627408482;
??????&#3627408486;
2
@&#3627408486;=±ℎ;&#3627408482;=0
@&#3627408486;=0;
&#3627408465;&#3627408482;
&#3627408465;&#3627408486;
=0
steady No gravity
in horizontal
direction
2DparallelContinuity 2DContinuity
Applying double integration to governing equation

8. Couette Flow
4/26/2023 8ME 2201
Assumptions:
1.Newtonian and incompressible flow
2.Parallel and Steady flow (v=0;
??????
????????????
=0)
3.2D (&#3627408484;=
??????
????????????
=0)
4.p = constant
steady No gravity
in horizontal
direction
2Dparallel 2DContinuityP= constContinuity

9. Couette Flow
0=??????
??????
2
&#3627408482;
??????&#3627408486;
2
@&#3627408486;=+ℎ;&#3627408482;=??????
@&#3627408486;=−ℎ;&#3627408482;=0
Applying double integration to governing equation
Applying BC
Shear Stress Volume Flow rate
&#3627408452;=න
−ℎ
ℎ
&#3627408482;&#3627408473;&#3627408465;&#3627408486;
Depth &#3627408473;in &#3627408487;−&#3627408465;????????????
4/26/2023 ME 2201 9

10. Poiseuille Flow –Cont’d
4/26/2023 10ME 2201

11. Couette Flow
4/26/2023 11ME 307 ME 2201
Twoimmisciblefluidsarecontainedbetweeninfiniteparallelplates.
Theplatesareseparatedbydistance2h,andthetwofluidlayersare
ofequalthicknessh:thedynamicviscosityoftheupperfluidisthree
timesthatofthelowerfluid.Ifthelowerplateisstationaryandthe
upperplatemovesatconstantspeedU=6.1m/s,whatisthevelocity
attheinterface?Assumelaminarflows,andthatthepressure
gradientinthedirectionofflowiszero.

12. Poiseuille Flow –Pipe
4/26/2023 12ME 2201
Continuity in cylindrical coordinates
&#3627408487;−&#3627408474;&#3627408476;&#3627408474;&#3627408466;&#3627408475;&#3627408481;&#3627408482;&#3627408474;in cylindrical coordinates
Assumptions:
1.Newtonian and incompressible flow
2.Parallel flow (&#3627408483;
??????=0)
3.Steady flow (
??????
????????????
=0)
4.2D (&#3627408483;
??????=
??????
????????????
=0)
[2] [4]
[Fully developed
flow]
[3]
[2] [4] [continuity]
[4] [continuity]
[horizontal
direction]
Integrating twice

13. Poiseuille Flow –Pipe
Hagen-Poiseuille
Equation

14. Poiseuille Flow –Pipe
4/26/2023 14ME 2201

15. Friction Factor–Pipe
4/26/2023 15ME 2201
??????
1>??????
2
&#3627408466;=&#3627408482;+
??????
2
2
+??????&#3627408487;
Rate of change
within CV
Energy flux
passing thru. CS
Mass flow rateEnthalpyTotal energy

16. 4/26/2023 ME 2201 16
Introducing correction factor that helps
convert local velocity to average velocity
Resubstituting
Re-arranging
Heat
Transfer
Change in
thermal energy
Head form
Energy form

17. 4/26/2023 17ME 2201

18. 4/26/2023 18ME 2201
For const area and const elevation
For Laminar Flow:
For turbulent Flow:

19. 4/26/2023 19ME 2201
Int Flow -Minor Loss

20. 4/26/2023 20ME 2201
Int Flow -Minor Loss

21. Int Flow –Head Loss, Pipe Flow Problems
4/26/2023 21ME 2201

22. 4/26/2023 22ME 2201

23. Int Flow –Head Loss, Pipe Flow Problems
4/26/2023 23ME 2201

24. 4/26/2023 24ME 2201

25. Int Flow –Head Loss, Pipe Flow Problems
4/26/2023 25ME 2201