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  • Calculate Reynolds number.
  • Use the Reynolds number for a system to determine whether it is laminar or turbulent.

Sometimes we can predict if flow will be laminar or turbulent. We know that flow in a very smooth tube or around a smooth, streamlined object will be laminar at low velocity. We also know that at high velocity, even flow in a smooth tube or around a smooth object will experience turbulence. In between, it is more difficult to predict. In fact, at intermediate velocities, flow may oscillate back and forth indefinitely between laminar and turbulent.

An occlusion, or narrowing, of an artery, such as shown in [link] , is likely to cause turbulence because of the irregularity of the blockage, as well as the complexity of blood as a fluid. Turbulence in the circulatory system is noisy and can sometimes be detected with a stethoscope, such as when measuring diastolic pressure in the upper arm’s partially collapsed brachial artery. These turbulent sounds, at the onset of blood flow when the cuff pressure becomes sufficiently small, are called Korotkoff sounds . Aneurysms, or ballooning of arteries, create significant turbulence and can sometimes be detected with a stethoscope. Heart murmurs, consistent with their name, are sounds produced by turbulent flow around damaged and insufficiently closed heart valves. Ultrasound can also be used to detect turbulence as a medical indicator in a process analogous to Doppler-shift radar used to detect storms.

Figure shows a rectangular section of a blood vessel. The blood flow is shown toward right. The blood vessel is shown to be broader at one end and narrow toward the opposite end. The flow is shown to be laminar as shown by horizontal parallel lines. The velocity is v one in the broader section of blood vessel. The junction where the tube narrows the velocity is v two. The lines of flow are shown to bend. The regions where the blood vessels are narrow, the flow is shown to be turbulent as shown to by curling arrows. The velocity is given by v three toward right. The length of the arrows depicting the velocities represent that v three is greater than v two greater than v one.
Flow is laminar in the large part of this blood vessel and turbulent in the part narrowed by plaque, where velocity is high. In the transition region, the flow can oscillate chaotically between laminar and turbulent flow.

An indicator called the Reynolds number     N R size 12{N rSub { size 8{R} } } {} can reveal whether flow is laminar or turbulent. For flow in a tube of uniform diameter, the Reynolds number is defined as

N R = 2 ρ vr η (flow in tube), size 12{N rSub { size 8{R} } = { {2ρ ital "vr"} over {η} } } {}

where ρ size 12{ρ} {} is the fluid density, v size 12{v} {} its speed, η size 12{η} {} its viscosity, and r size 12{r} {} the tube radius. The Reynolds number is a unitless quantity. Experiments have revealed that N R size 12{N rSub { size 8{R} } } {} is related to the onset of turbulence. For N R size 12{N rSub { size 8{R} } } {} below about 2000, flow is laminar. For N R size 12{N rSub { size 8{R} } } {} above about 3000, flow is turbulent. For values of N R size 12{N rSub { size 8{R} } } {} between about 2000 and 3000, flow is unstable—that is, it can be laminar, but small obstructions and surface roughness can make it turbulent, and it may oscillate randomly between being laminar and turbulent. The blood flow through most of the body is a quiet, laminar flow. The exception is in the aorta, where the speed of the blood flow rises above a critical value of 35 m/s and becomes turbulent.

Is this flow laminar or turbulent?

Calculate the Reynolds number for flow in the needle considered in Example 12.8 to verify the assumption that the flow is laminar. Assume that the density of the saline solution is 1025 kg/ m 3 .

Strategy

We have all of the information needed, except the fluid speed v size 12{v} {} , which can be calculated from v ¯ = Q / A = 1.70 m/s size 12{ {overline {v}} =Q/A=1 "." "70"" m/s"} {} (verification of this is in this chapter’s Problems and Exercises).

Solution

Entering the known values into N R = 2 ρ vr η size 12{N rSub { size 8{R} } = { {2ρ ital "vr"} over {η} } } {} gives

N R = 2 ρ vr η = 2 ( 1025 kg/m 3 ) ( 1.70 m/s ) ( 0.150 × 10 3 m ) 1 . 00 × 10 3 N s/m 2 = 523 .

Discussion

Since N R size 12{N rSub { size 8{R} } } {} is well below 2000, the flow should indeed be laminar.

Questions & Answers

Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
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Adin
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Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
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Damian Reply
absolutely yes
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it is a goid question and i want to know the answer as well
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characteristics of micro business
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Anassong
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
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SUYASH Reply
for screen printed electrodes ?
SUYASH
What is lattice structure?
s. Reply
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
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On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
Sanket Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, Introduction to physics for vanguard high school (derived from college physics). OpenStax CNX. Oct 15, 2014 Download for free at http://legacy.cnx.org/content/col11715/1.1
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