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# Laminar flow, turbulent flow and Reynold’s number

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1. Laminar flow, turbulent flow and Reynold’s number Chan Wei Lim Zhong Hui Tan Hong You M4

2. Laminar flow • Also known as streamline flow • Occurs when the fluid flows in parallel layers, with no disruption between the layers • The opposite of turbulent flow (rough)

3. Laminar flow • In fluid dynamics (scientific study of properties of moving fluids), laminar flow is: • A flow regime characterized by high momentum diffusion, low momentum convection, pressure and velocity independent from time. *momentum diffusion refers to the spread of momentum (diffusion) between particles of substances, usually liquids

4. Laminar flow Turbulent Flow • Laminar flow over a flat and horizontal surface can be pictured as consisting of parallel and thin layers • Layers slide over each other, thus the name ‘streamline’ or smooth. • The paths are regular and there are no fluctuations Laminar Flow

5. Laminar flow • 3 Conditions • fluid moves slowly • viscosity is relatively high • flow channel is relatively small • Blood flow through capillaries is laminar flow, as it satisfies the 3 conditions • Most type of fluid flow is turbulent • There is poor transfer of heat energy!

6. Turbulent flow • Usually occurs when the liquid is moving fast • The flow is ‘chaotic’ and there are irregular fluctuations • Includes: • Low momentum diffusion • high momentum convection • rapid variation of pressure and velocity of the fluid • Good way to transfer thermal energy

7. Turbulent Flow • The speed of the fluid at a point is continuously undergoing changes in both magnitude and direction.

8. Examples of turbulence • Oceanic and atmospheric layers and ocean currents • External flow of air/water over vehicles such as cars/ships/submarines • In racing cars, e.g. leading car causes understeer at fast corners • Turbulence during air-plane’s flight • Most of terrestrial atmospheric circulation • Flow of most liquids through pipes

9. Reynold’s number • A dimensionless number in fluid mechanics • Dynamic Pressure : Shearing Stress • Thus, it quantifies the relative importance of these two types of forces for given flow conditions. • Arises when performing analysis of fluid dynamics • Can be used to determine dynamic similitude in such cases. Concept used in the testing of models, e.g. testing miniature airplanes/submarines

10. Dynamic Pressure + Shearing Stress • Dynamic Pressure • The pressure of a fluid which results from its motion • Formula: • Shearing Stress • Measure of the force of friction from a fluid acting on a body in the path of that fluid • Formula: Fluid Density Weight Density of Water Fluid Velocity Water Surface Slope Average water depth

11. Reynold’s numberFlow in a pipe or liquid • p is the density of the fluid • V is the mean fluid velocity • D is the diameter • Q is the volumetric flow rate Dynamic Pressure • μ  is the dynamic viscosity of the fluid • v is the kinematic velocity of the fluid • A is the pipe cross-sectional area. Shearing Stress

12. Reynold’s number • The Reynold’s number can be used to determine if a flow is laminar, transient or turbulent • Laminar when Re < 2300 • Turbulent when Re > 4000 • Transient when 2300 < Re < 4000

13. Acknowledgements • http://www.geo.wvu.edu/~jtoro/geol101/streams/laminar%20flow.jpg • http://www.britannica.com/EBchecked/topic/328742/laminar-flow • http://en.wikipedia.org/wiki/Laminar_flow • http://www.answers.com/topic/laminar-flow • http://www.cosmosmagazine.com/files/imagecache/feature/files/20071217_physics.jpg • http://en.wikipedia.org/wiki/Turbulent_flow#Examples_of_turbulence

14. Acknowledgements • http://anordinarymom.files.wordpress.com/2008/11/airplane-turbulence-copy.gif • http://www.engineeringtoolbox.com/reynolds-number-d_237.html • http://en.wikipedia.org/wiki/Dynamic_similitude • http://www.engineeringtoolbox.com/reynolds-number-d_237.html