1. Home
  2. College physics
  3. Fluid dynamics and its biological
  4. Viscosity and laminar flow;

12.4 Viscosity and laminar flow; poiseuille’s law  (Page 4/12)

<< Chapter < Page
  College physics     Page 4 / 12
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.

Got questions? Get instant answers now!

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

it is the relatively stable flow of income
Chidubem Reply
what is circular flow of income
Divine Reply
branches of macroeconomics
SHEDRACK Reply
what is Flexible exchang rate?
poudel Reply
is gdp a reliable measurement of wealth
Atega Reply
introduction to econometrics
Husseini Reply
Hi
mostafa
hi
LEMLEM
hello
Sammol
hi
Mahesh
bi
Ruqayat
hi
Ruqayat
Hi fellas
Nyawa
hey
Sammol
hi
God
hello
Jahara
Good morning
Jorge
hi
abubakar
hi
Nmesoma
hi
Mahesh
Hi
Tom
Why is unemployment rate never zero at full employment?
Priyanka Reply
bcoz of existence of frictional unemployment in our economy.
Umashankar
what is flexible exchang rate?
poudel
due to existence of the pple with disabilities
Abdulraufu
the demand of a good rises, causing the demand for another good to fall
Rushawn Reply
is it possible to leave every good at the same level
Joseph
I don't think so. because check it, if the demand for chicken increases, people will no longer consume fish like they used to causing a fall in the demand for fish
Anuolu
is not really possible to let the value of a goods to be same at the same time.....
Salome
Suppose the inflation rate is 6%, does it mean that all the goods you purchase will cost 6% more than previous year? Provide with reasoning.
Geetha Reply
Not necessarily. To measure the inflation rate economists normally use an averaged price index of a basket of certain goods. So if you purchase goods included in the basket, you will notice that you pay 6% more, otherwise not necessarily.
Waeth
discus major problems of macroeconomics
Alii Reply
what is the problem of macroeconomics
Yoal
Economic growth Stable prices and low unemployment
Ephraim
explain inflationcause and itis degre
Miresa Reply
what is inflation
Getu
increase in general price levels
WEETO
Good day How do I calculate this question: C= 100+5yd G= 2000 T= 2000 I(planned)=200. Suppose the actual output is 3000. What is the level of planned expenditures at this level of output?
Chisomo Reply
how to calculate actual output?
Chisomo
how to calculate the equilibrium income
Beshir
Criteria for determining money supply
Thapase Reply
who we can define macroeconomics in one line
Muhammad
Aggregate demand
Mohammed
C=k100 +9y and i=k50.calculate the equilibrium level of output
Mercy Reply
Hi
Isiaka
Hi
Geli
hy
Man
👋
Bahunda
hy how are you?
Man
ys
Amisha
how are you guys
Sekou
f9 guys
Amisha
how are you guys
Sekou
ys am also fine
Amisha
fine and you guys
Geli
from Nepal
Amisha
nawalparasi district from belatari
Amisha
nd u
Amisha
I am Camara from Guinea west Africa... happy to meet you guys here
Sekou
ma management ho
Amisha
ahile becheclor ho
Amisha
hjr ktm bta ho ani k kaam grnu hunxa tw
Amisha
belatari
Amisha
1st year ho
Amisha
nd u
Amisha
ahh
Amisha
kaha biratnagar
Amisha
ys
Amisha
kina k vo
Amisha
money as unit of account means what?
Kalombe
A unit of account is something that can be used to value goods and services and make calculations
Jim
all of you please speak in English I can't understand you're language
Muhammad
I want to know how can we define macroeconomics in one line
Muhammad
it must be .9 or 0.9 no Mpc is greater than 1 Y=100+.9Y+50 Y-.9Y=150 0.1Y/0.1=150/0.1 Y=1500
Kalombe
Mercy is it clear?😋
Kalombe
hi can someone help me on this question If a negative shocks shifts the IS curve to the left, what type of policy do you suggest so as to stabilize the level of output? discuss your answer using appropriate graph.
Galge Reply
if interest rate is increased this will will reduce the level of income shifting the curve to the left ◀️
Kalombe
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply
<< Chapter < Page Page > Chapter >>
Practice Key Terms 5

Read also:

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, College physics. OpenStax CNX. Jul 27, 2015 Download for free at http://legacy.cnx.org/content/col11406/1.9
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'College physics' conversation and receive update notifications?

Ask