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- 6. 6 Characterization of flow based on Reynolds number Osborne Reynolds (a British engineer) conducted a flow experiment, i.e. by injecting dye into pipe flow to classify the types of flow. Turbulent Near laminar Dr. Indrajeet Sahu Fluid Mechanics VCE
- 7. 7 Three types of flow: Laminar flow Transitional flow Reynolds number Re is the ratio of the inertia force on an element of fluid to the viscous force. VD Re VD Re < 2300 Re > 4000 2300 < Re < 4000 where V = average velocity, D = diameter of pipe, = fluid density, = dynamic viscosity, and = kinematic viscosity Re is dimensionless. Turbulent flow Reynolds number is one of the important dimensionless number used in the dimensional analysis in fluid mechanics and hydraulics. Dr. Indrajeet Sahu Fluid Mechanics VCE
- 8. 8 The transition from laminar to turbulent flow depends on the geometry, surface roughness, flow velocity, surface temperature, and type of fluid. The flow regime depends mainly on the ratio of inertial forces to viscous forces (Reynolds number). Dr. Indrajeet Sahu Fluid Mechanics VCE
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- 10. 10 Example 4.1 Determine the range of average velocity of flow for which the flow would be in the transitional region if an oil of S.G. = 0.89 and dynamic viscosity = 0.1 Ns/m2 is flowing in a 2-in pipe. Solution: For transitional flow, When Re = 2000, When Re = 4000, 4000 Re 2000 VD Re D V Re 0254 0 2 890 1 0 000 2 . . V m/s 424 4. V 0254 0 2 890 1 0 000 4 . . V m/s 847 8. V Therefore, for the flow to be in transitional state, the average velocity V should be between 4.424 m/s and 8.847 m/s. Dr. Indrajeet Sahu Fluid Mechanics VCE
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- 13. 13 Hydrodynamic entrance region: The region from the pipe inlet to the point at which the boundary layer merges at the centerline. Hydrodynamic entry length Lh: The length of this region. Hydrodynamically developing flow: Flow in the entrance region. This is the region where the velocity profile develops. Hydrodynamically fully developed region: The region beyond the entrance region in which the velocity profile is fully developed and remains unchanged. Fully developed: When both the velocity profile and the normalized temperature profile remain unchanged. Hydrodynamically fully developed In the fully developed flow region of a pipe, the velocity profile does not change downstream, and thus the wall shear stress remains constant as well. Dr. Indrajeet Sahu Fluid Mechanics VCE
- 14. 14 The variation of wall shear stress in the flow direction for flow in a pipe from the entrance region into the fully developed region. The pressure drop is higher in the entrance regions of a pipe, and the effect of the entrance region is always to increase the average friction factor for the entire pipe. Dr. Indrajeet Sahu Fluid Mechanics VCE
- 15. 15 Entry Lengths The hydrodynamic entry length is usually taken to be the distance from the pipe entrance to where the wall shear stress (and thus the friction factor) reaches within about 2 percent of the fully developed value. hydrodynamic entry length for laminar flow hydrodynamic entry length for turbulent flow hydrodynamic entry length for turbulent flow, an approximation Dr. Indrajeet Sahu Fluid Mechanics VCE
- 16. 16 LAMINAR FLOW IN PIPES We consider steady, laminar, incompressible flow of a fluid with constant properties in the fully developed region of a straight circular pipe. In fully developed laminar flow, each fluid particle moves at a constant axial velocity along a streamline and the velocity profile u(r) remains unchanged in the flow direction. Free-body diagram of a ring-shaped differential fluid element of radius r, thickness dr, and length dx oriented coaxially with a horizontal pipe in fully developed laminar flow. There is no motion in the radial direction, and thus the velocity component in the direction normal to the pipe axis is everywhere zero. There is no acceleration since the flow is steady and fully developed. Dr. Indrajeet Sahu Fluid Mechanics VCE
- 17. 17 Boundary conditions Maximum velocity at centerline Velocity profile Dr. Indrajeet Sahu Fluid Mechanics VCE
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- 20. 20 Dracy-Weisbach Equation Dr. Indrajeet Sahu Fluid Mechanics VCE
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- 49. 49 Dr. Indrajeet Sahu Fluid Mechanics VCE V 2 Take Velocity and
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