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

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)

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

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

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!

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

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

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

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

Dynamic Pressure + Shearing Stress 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

Reynold’s number Flow 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

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 Spermatozoa 1×10−4 Blood flow in brain 1×102 Blood flow in aorta 1×103

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

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