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CE 230-Engineering Fluid Mechanics

CE 230-Engineering Fluid Mechanics. Fluid flow. Flowing fluids. Static versus flowing fluid Objectives of the part of course Basic concepts and definitions. Types of flow. Steady versus unsteady Uniform versus no uniform 1-D versus multi-D Laminar versus turbulent.

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CE 230-Engineering Fluid Mechanics

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  1. CE 230-Engineering Fluid Mechanics Fluid flow

  2. Flowing fluids • Static versus flowing fluid • Objectives of the part of course • Basic concepts and definitions

  3. Types of flow • Steady versus unsteady • Uniform versus no uniform • 1-D versus multi-D • Laminar versus turbulent

  4. Development of flow pattern • Why not solve problem? • Flow visualization analog and experimental methods • Streamlines, streaklines and pathlines

  5. Pathlines

  6. Uniform flow

  7. Non-uniform flow

  8. Velocity distribution in a pipe- laminar vs turbulent flow

  9. Volume flow rate, Q • Q = ΔV/ Δt = dV/dt • Calculating Q if velocity is constant • Q=∫ v.dA • Mass flow rate

  10. Example 5.3 Find flow rate and average velocity in the pipe (R=5 cm), if the velocity distribution is given by: Note that U [cm/s] r [cm]

  11. Example 5.3 Find flow rate and average velocity in the 5 m wide channel. Given: d = 2 m and maximum velocity = 3 m/s.

  12. Example Find flow rate and average velocity in the triangular channel. Given: maximum velocity = 6 ft/s.

  13. Material derivative and Acceleration • Total acceleration • Local acceleration • Convective acceleration

  14. Example (p 4-26) Determine local, convective and total accelaration at x=0.5L and t= 3 s

  15. BERNOULLI EQUATION

  16. Derivation of Euler’s equation Consider a cylindrical fluid element being accelerated in direction l and neglect viscous effects Use equilibrium equation Σ F = m a

  17. Derivation of Euler’s equation

  18. Let’s take l along a stream line call s (i.e. flow along a streamline) But Therefore

  19. Assume steady flow and drop subscript But last term is Substituting back, dividing by γ (assuing incompressible fluid) and integrating wrt s we get

  20. Bernoulli equation One form of BE is Note assumptions made No losses Flow along streamline Steady flow incompressible

  21. 4.44 Consider water jet shown. Calculate h, if the water velocity as it exists the nozzle is 20 ft/s

  22. 4.103 Find pressure at A if h=15 m and V=6 m/s

  23. Estimate exit velocity and minimum pressure L H

  24. Stagnation tube

  25. Find flow rate of water given pipe diameter at 2 =10 cm pipe diameter at 1 =30 cm 5 m 60 cm Hg

  26. 4.64 Find V and Q

  27. 5.76 Find manometer deflection

  28. Pitot tube

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