Successfully reported this slideshow.
We use your LinkedIn profile and activity data to personalize ads and to show you more relevant ads. You can change your ad preferences anytime.
Basic Fluid Dynamics
Momentum <ul><li>P = mv </li></ul>
Viscosity <ul><li>Resistance to flow; momentum diffusion </li></ul><ul><li>Low viscosity: Air </li></ul><ul><li>High visco...
Reynolds Number <ul><li>The Reynolds Number ( Re ) is a non-dimensional number that reflects the balance between viscous a...
Poiseuille Flow <ul><li>In a slit or pipe, the velocities at the walls are 0 (no-slip boundaries) and the velocity reaches...
Poiseuille Flow S.GOKALTUN Florida International University
Entry Length Effects Tritton, D.J. Physical Fluid Dynamics, 2 nd  Ed. Oxford University Press, Oxford. 519 pp.
Re << 1 (Stokes Flow) Tritton, D.J. Physical Fluid Dynamics, 2 nd  Ed. Oxford University Press, Oxford. 519 pp.
Eddies and Cylinder Wakes Re = 41 Tritton, D.J. Physical Fluid Dynamics, 2 nd  Ed. Oxford University Press, Oxford. 519 pp...
Eddies and Cylinder Wakes S.Gokaltun Florida International University Streamlines for flow around a circular cylinder at 9...
Eddies and Cylinder Wakes Streamlines for flow around a circular cylinder at 40  ≤ Re ≤ 5 0.(g=0.0001, L=300 lu, D=100 lu)...
Separation Tritton, D.J. Physical Fluid Dynamics, 2 nd  Ed. Oxford University Press, Oxford. 519 pp.
Laplace Law <ul><li>There is a pressure difference between the inside and outside of bubbles and drops </li></ul><ul><li>T...
Laplace Law P in P out r  P =   /r  ->    =   P/r, which is linear in 1/r (a.k.a. curvature)
Young-Laplace Law <ul><li>With solid surfaces, in addition to the fluid1/fluid2 interface – where the interaction is given...
Young-Laplace Law <ul><li>Zero contact angle means perfect wetting; </li></ul><ul><li> P =   cos   /r </li></ul>
Upcoming SlideShare
Loading in …5
×

05

616 views

Published on

Published in: Technology, Education
  • Be the first to comment

05

  1. 1. Basic Fluid Dynamics
  2. 2. Momentum <ul><li>P = mv </li></ul>
  3. 3. Viscosity <ul><li>Resistance to flow; momentum diffusion </li></ul><ul><li>Low viscosity: Air </li></ul><ul><li>High viscosity: Honey </li></ul><ul><li>Kinematic viscosity </li></ul>
  4. 4. Reynolds Number <ul><li>The Reynolds Number ( Re ) is a non-dimensional number that reflects the balance between viscous and inertial forces and hence relates to flow instability (i.e., the onset of turbulence) </li></ul><ul><li>Re = v L/  </li></ul><ul><li>L is a characteristic length in the system </li></ul><ul><li>Dominance of viscous force leads to laminar flow (low velocity, high viscosity, confined fluid) </li></ul><ul><li>Dominance of inertial force leads to turbulent flow (high velocity, low viscosity, unconfined fluid) </li></ul>
  5. 5. Poiseuille Flow <ul><li>In a slit or pipe, the velocities at the walls are 0 (no-slip boundaries) and the velocity reaches its maximum in the middle </li></ul><ul><li>The velocity profile in a slit is parabolic and given by: </li></ul>x = 0 x = a u(x) <ul><li>G can be gravitational acceleration or (linear) pressure gradient (P in – P out )/L </li></ul>
  6. 6. Poiseuille Flow S.GOKALTUN Florida International University
  7. 7. Entry Length Effects Tritton, D.J. Physical Fluid Dynamics, 2 nd Ed. Oxford University Press, Oxford. 519 pp.
  8. 8. Re << 1 (Stokes Flow) Tritton, D.J. Physical Fluid Dynamics, 2 nd Ed. Oxford University Press, Oxford. 519 pp.
  9. 9. Eddies and Cylinder Wakes Re = 41 Tritton, D.J. Physical Fluid Dynamics, 2 nd Ed. Oxford University Press, Oxford. 519 pp. Re = 30 Re = 40 Re = 47 Re = 55 Re = 67 Re = 100
  10. 10. Eddies and Cylinder Wakes S.Gokaltun Florida International University Streamlines for flow around a circular cylinder at 9 ≤ Re ≤ 10.(g=0.00001, L=300 lu, D=100 lu)
  11. 11. Eddies and Cylinder Wakes Streamlines for flow around a circular cylinder at 40 ≤ Re ≤ 5 0.(g=0.0001, L=300 lu, D=100 lu) ( Photograph by Sadatoshi Taneda. Taneda 1956a, J. Phys. Soc. Jpn., 11, 302-307. ) S.Gokaltun Florida International University
  12. 12. Separation Tritton, D.J. Physical Fluid Dynamics, 2 nd Ed. Oxford University Press, Oxford. 519 pp.
  13. 13. Laplace Law <ul><li>There is a pressure difference between the inside and outside of bubbles and drops </li></ul><ul><li>The pressure is always higher on the inside of a bubble or drop (concave side) – just as in a balloon </li></ul><ul><li>The pressure difference depends on the radius of curvature and the surface tension for the fluid pair of interest:  P =  /r </li></ul>
  14. 14. Laplace Law P in P out r  P =  /r ->  =  P/r, which is linear in 1/r (a.k.a. curvature)
  15. 15. Young-Laplace Law <ul><li>With solid surfaces, in addition to the fluid1/fluid2 interface – where the interaction is given by the interfacial tension    -- we have interfaces between each fluid and the surface  S1  and  S2 </li></ul><ul><li>Often one of the fluids preferentially ‘wets’ the surface </li></ul><ul><li>This phenomenon is captured by the contact angle </li></ul><ul><li>cos  = (  S2 -  S1   </li></ul>
  16. 16. Young-Laplace Law <ul><li>Zero contact angle means perfect wetting; </li></ul><ul><li> P =  cos  /r </li></ul>

×