# Fluid Mechanics Applications/B07: application of laminar and turbulent flow

Liquid or gas flow through pipes or ducts is commonly used in heating and cooling applications and fluid distribution networks. The fluid in such applications is usually forced to flow by a fan or pump through a flow section. So that there are two types of flow in pipe that is laminar and turbulent flow so it have many application in different field

## Laminar and Turbulent Flow
##### laminar flow

When the fluid is moving slowest, get a well-defined streak-line. so Where the fluid moves slowly in layers in a pipe, without much mixing among the layers. This flow situation is called laminar flow

##### turbulent flow

When the fluid is moving faster, get an irregular streak-line which blurs and spreads the dye out. The streak-line also fluctuates randomly with time.so where considerable mixing occurs, velocities are high. This flow is called turbulent flow.

##### Example

If you have been around smokers, you probably noticed that the cigarette smoke rises in a smooth plume for the first few centimeters and then starts fluctuating randomly in all directions as it continues its rise. Other plumes behave similarly in below figure The flow regime in the first case is said to be laminar, characterized by smooth streamlines and highly ordered motion, and turbulent in the second case, where it is characterized by velocity fluctuations and highly disordered motion.

## Reynolds Number

the flow regime depends mainly on the ratio of inertial forces to viscous forces in the fluid. This ratio is called the Reynolds number. the flow is primarily determined by reynolds number:
$R_{e}={{\rho vD} \over \mu }$
where
$\rho$→density
$D$→diameter of pipe
$v$→fluid velocity
$\mu$→viscosity
so that the reynolds number in laminar flow should be less than 2000 also we should know the reynolds number in turbulent flow should be greater than 4000

## Application of laminar and turbulent flow
### Flow in blood vessel
##### Laminar flow

Laminar flow is the normal condition for blood flow throughout most of the circulatory system. It is characterized by concentric layers of blood moving in parallel down the length of a blood vessel. The highest velocity (Vmax) is found in the center of the vessel. The lowest velocity (V=0) is found along the vessel wall. The flow profile is parabolic once laminar flow is fully developed. This occurs in long, straight blood vessels, under steady flow conditions. One practical implication of parabolic, laminar flow is that when flow velocity is measured using a Doppler flowmeter, the velocity value represents the average velocity of a cross-section of the vessel, not the maximal velocity found in the center of the flow stream.

##### Turbulent flow

Generally in the body, blood flow is laminar. However, under conditions of high flow, particularly in the ascending aorta, laminar flow can be disrupted and become turbulent. When this occurs, blood does not flow linearly and smoothly in adjacent layers, but instead the flow can be described as being chaotic.The Turbulent flow also occurs in large arteries at branch points, in diseased and narrowed (stenotic) arteries (see figure below). Turbulence increases the energy required to drive blood flow because turbulence increases the loss of energy in the form of friction, which generates heat. Turbulence does not begin to occur until the velocity of flow becomes high enough that the flow lamina break apart. Therefore, as blood flow velocity increases in a blood vessel or across a heart valve, there is not a gradual increase in turbulence. Instead, turbulence occurs when a critical Reynolds number (Re) is exceeded.

## References

* ↑ http://www.uio.no/studier/emner/matnat/math/MEK4450/h11/undervisningsmateriale/modul-5/Pipeflow_intro.pdf
* ↑ http://www.cvphysiology.com/Hemodynamics/H006.htm
* ↑ http://www.cvphysiology.com/Hemodynamics/H007.htm