<< Chapter < Page Chapter >> Page >

The circulatory system provides many examples of Poiseuille’s law in action—with blood flow regulated by changes in vessel size and blood pressure. Blood vessels are not rigid but elastic. Adjustments to blood flow are primarily made by varying the size of the vessels, since the resistance is so sensitive to the radius. During vigorous exercise, blood vessels are selectively dilated to important muscles and organs and blood pressure increases. This creates both greater overall blood flow and increased flow to specific areas. Conversely, decreases in vessel radii, perhaps from plaques in the arteries, can greatly reduce blood flow. If a vessel’s radius is reduced by only 5% (to 0.95 of its original value), the flow rate is reduced to about ( 0 . 95 ) 4 = 0 . 81 size 12{ \( 0 "." "95" \) rSup { size 8{4} } =0 "." "81"} {} of its original value. A 19% decrease in flow is caused by a 5% decrease in radius. The body may compensate by increasing blood pressure by 19%, but this presents hazards to the heart and any vessel that has weakened walls. Another example comes from automobile engine oil. If you have a car with an oil pressure gauge, you may notice that oil pressure is high when the engine is cold. Motor oil has greater viscosity when cold than when warm, and so pressure must be greater to pump the same amount of cold oil.

The figure shows a section of a cylindrical tube of length l. The two end cross section are shown to have pressure P two and P one respectively. The radius of the cylindrical tube is given by r. The direction of flow is shown by horizontal arrows toward right end of the tube. The flow rate is marked as Q.
Poiseuille’s law applies to laminar flow of an incompressible fluid of viscosity η size 12{η} {} through a tube of length l size 12{l} {} and radius r size 12{r} {} . The direction of flow is from greater to lower pressure. Flow rate Q size 12{Q} {} is directly proportional to the pressure difference P 2 P 1 size 12{P rSub { size 8{2} } - P rSub { size 8{1} } } {} , and inversely proportional to the length l size 12{l} {} of the tube and viscosity η size 12{η} {} of the fluid. Flow rate increases with r 4 size 12{r rSup { size 8{4} } } {} , the fourth power of the radius.

What pressure produces this flow rate?

An intravenous (IV) system is supplying saline solution to a patient at the rate of 0 . 120 cm 3 /s size 12{0 "." "120"``"cm" rSup { size 8{3} } "/s"} {} through a needle of radius 0.150 mm and length 2.50 cm. What pressure is needed at the entrance of the needle to cause this flow, assuming the viscosity of the saline solution to be the same as that of water? The gauge pressure of the blood in the patient’s vein is 8.00 mm Hg. (Assume that the temperature is 20ºC .)

Strategy

Assuming laminar flow, Poiseuille’s law applies. This is given by

Q = ( P 2 P 1 ) π r 4 8 η l , size 12{Q= { { \( P rSub { size 8{2} } - P rSub { size 8{1} } \) π`r rSup { size 8{4} } } over {8ηl} } } {}

where P 2 size 12{P rSub { size 8{2} } } {} is the pressure at the entrance of the needle and P 1 size 12{P rSub { size 8{1} } } {} is the pressure in the vein. The only unknown is P 2 size 12{P rSub { size 8{2} } } {} .

Solution

Solving for P 2 size 12{P rSub { size 8{2} } } {} yields

P 2 = 8 η l πr 4 Q + P 1 . size 12{P rSub { size 8{2} } = { {8ηl} over {πr rSup { size 8{4} } } } Q+P rSub { size 8{1} } } {}

P 1 size 12{P rSub { size 8{1} } } {} is given as 8.00 mm Hg, which converts to 1 . 066 × 10 3 N/m 2 size 12{1 "." "066" times "10" rSup { size 8{3} } `"N/m" rSup { size 8{2} } } {} . Substituting this and the other known values yields

P 2 = 8 ( 1 . 00 × 10 3 N s/m 2 ) ( 2 . 50 × 10 2 m ) π ( 0 . 150 × 10 3 m ) 4 ( 1 . 20 × 10 7 m 3 /s ) + 1 . 066 × 10 3 N/m 2 = 1 . 62 × 10 4 N/m 2 .

Discussion

This pressure could be supplied by an IV bottle with the surface of the saline solution 1.61 m above the entrance to the needle (this is left for you to solve in this chapter’s Problems and Exercises), assuming that there is negligible pressure drop in the tubing leading to the needle.

Flow and resistance as causes of pressure drops

You may have noticed that water pressure in your home might be lower than normal on hot summer days when there is more use. This pressure drop occurs in the water main before it reaches your home. Let us consider flow through the water main as illustrated in [link] . We can understand why the pressure P 1 size 12{P rSub { size 8{1} } } {} to the home drops during times of heavy use by rearranging

Questions & Answers

I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
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
why?
Adin
what school?
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.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
Daniel
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
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
How can I make nanorobot?
Lily
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply
Practice Key Terms 5

Get the best Algebra and trigonometry course in your pocket!





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
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Introduction to physics for vanguard high school (derived from college physics)' conversation and receive update notifications?

Ask