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F S = 6 πRηv . size 12{F rSub { size 8{S} } =6πRηv} {}
Part a of the figure shows a sphere moving in a fluid. The fluid lines are shown to move toward the left. The viscous force on the sphere is also toward the left given by F v as shown by the arrow. The flow is shown as laminar as shown by linear bending lines. Part b of the figure shows a sphere moving with higher speed in a fluid. The fluid lines are shown to move toward the left. The viscous force on the sphere is also toward the left given by F v prime as shown by the arrow. The flow is shown as laminar above and below the sphere shown by linear lines of flow and turbulent on left of the sphere shown by curly lines of flow. Part c of the figure shows a sphere still moving with higher speed in a fluid. The fluid lines are shown to move toward the left at the edges of flow away from the sphere. The viscous force on the sphere is also toward the left given by F v double prime as shown by the arrow. The flow is turbulent all around the sphere as shown by curly lines of flow. The viscous drag F v double prime is shown to be still greater by longer length of arrows.
(a) Motion of this sphere to the right is equivalent to fluid flow to the left. Here the flow is laminar with N R size 12{ { {N}} sup { ' } rSub { size 8{R} } } {} less than 1. There is a force, called viscous drag F V size 12{F rSub { size 8{V} } } {} , to the left on the ball due to the fluid’s viscosity. (b) At a higher speed, the flow becomes partially turbulent, creating a wake starting where the flow lines separate from the surface. Pressure in the wake is less than in front of the sphere, because fluid speed is less, creating a net force to the left F V size 12{ { {F}} sup { ' } rSub { size 8{V} } } {} that is significantly greater than for laminar flow. Here N R size 12{ { {N}} sup { ' } rSub { size 8{R} } } {} is greater than 10. (c) At much higher speeds, where N R size 12{ { {N}} sup { ' } rSub { size 8{R} } } {} is greater than 10 6 size 12{"10" rSup { size 8{6} } } {} , flow becomes turbulent everywhere on the surface and behind the sphere. Drag increases dramatically.

An interesting consequence of the increase in F V size 12{F rSub { size 8{V} } } {} with speed is that an object falling through a fluid will not continue to accelerate indefinitely (as it would if we neglect air resistance, for example). Instead, viscous drag increases, slowing acceleration, until a critical speed, called the terminal speed    , is reached and the acceleration of the object becomes zero. Once this happens, the object continues to fall at constant speed (the terminal speed). This is the case for particles of sand falling in the ocean, cells falling in a centrifuge, and sky divers falling through the air. [link] shows some of the factors that affect terminal speed. There is a viscous drag on the object that depends on the viscosity of the fluid and the size of the object. But there is also a buoyant force that depends on the density of the object relative to the fluid. Terminal speed will be greatest for low-viscosity fluids and objects with high densities and small sizes. Thus a skydiver falls more slowly with outspread limbs than when they are in a pike position—head first with hands at their side and legs together.

Take-home experiment: don’t lose your marbles

By measuring the terminal speed of a slowly moving sphere in a viscous fluid, one can find the viscosity of that fluid (at that temperature). It can be difficult to find small ball bearings around the house, but a small marble will do. Gather two or three fluids (syrup, motor oil, honey, olive oil, etc.) and a thick, tall clear glass or vase. Drop the marble into the center of the fluid and time its fall (after letting it drop a little to reach its terminal speed). Compare your values for the terminal speed and see if they are inversely proportional to the viscosities as listed in [link] . Does it make a difference if the marble is dropped near the side of the glass?

Knowledge of terminal speed is useful for estimating sedimentation rates of small particles. We know from watching mud settle out of dirty water that sedimentation is usually a slow process. Centrifuges are used to speed sedimentation by creating accelerated frames in which gravitational acceleration is replaced by centripetal acceleration, which can be much greater, increasing the terminal speed.

The figure shows the forces acting on an oval shaped object falling through a viscous fluid. An enlarged view of the object is shown toward the left to analyze the forces in detail. The weight of the object w acts vertically downward. The viscous drag F v and buoyant force F b acts vertically upward. The length of the object is given by L. The density of the object is given by rho obj and density of the fluid by rho fl.
There are three forces acting on an object falling through a viscous fluid: its weight w size 12{w} {} , the viscous drag F V size 12{F rSub { size 8{V} } } {} , and the buoyant force F B size 12{F rSub { size 8{B} } } {} .

Section summary

  • When an object moves in a fluid, there is a different form of the Reynolds number N R = ρ vL η (object in fluid), size 12{ { {N}} sup { ' } rSub { size 8{R} } = { {ρ ital "vL"} over {η} } } {} which indicates whether flow is laminar or turbulent.
  • For N R size 12{ { {N}} sup { ' } rSub { size 8{R} } } {} less than about one, flow is laminar.
  • For N R size 12{ { {N}} sup { ' } rSub { size 8{R} } } {} greater than 10 6 size 12{"10" rSup { size 8{6} } } {} , flow is entirely turbulent.

Conceptual questions

What direction will a helium balloon move inside a car that is slowing down—toward the front or back? Explain your answer.

Will identical raindrops fall more rapidly in 5º C size 12{5 rSup { size 12{ circ } } C} {} air or 25º C size 12{"25" rSup { size 12{ circ } } C} {} air, neglecting any differences in air density? Explain your answer.

If you took two marbles of different sizes, what would you expect to observe about the relative magnitudes of their terminal velocities?

Questions & Answers

how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
Maciej
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s. Reply
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Devang Reply
are you nano engineer ?
s.
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
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
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s.
how to fabricate graphene ink ?
SUYASH Reply
for screen printed electrodes ?
SUYASH
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s. Reply
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
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what's the easiest and fastest way to the synthesize AgNP?
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Cied
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I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
I'm interested in nanotube
Uday
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
what is nano technology
Sravani Reply
what is system testing?
AMJAD
preparation of nanomaterial
Victor Reply
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
Himanshu Reply
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AMJAD
what is system testing
AMJAD
what is the application of nanotechnology?
Stotaw
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
Azam
anybody can imagine what will be happen after 100 years from now in nano tech world
Prasenjit
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
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name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
Prasenjit
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silver nanoparticles could handle the job?
Damian
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I'm interested in Nanotube
Uday
this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
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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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