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The arterioles (small arteries) leading to an organ, constrict in order to decrease flow to the organ. To shut down an organ, blood flow is reduced naturally to 1.00% of its original value. By what factor did the radii of the arterioles constrict? Penguins do this when they stand on ice to reduce the blood flow to their feet.


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Angioplasty is a technique in which arteries partially blocked with plaque are dilated to increase blood flow. By what factor must the radius of an artery be increased in order to increase blood flow by a factor of 10?

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(a) Suppose a blood vessel’s radius is decreased to 90.0% of its original value by plaque deposits and the body compensates by increasing the pressure difference along the vessel to keep the flow rate constant. By what factor must the pressure difference increase? (b) If turbulence is created by the obstruction, what additional effect would it have on the flow rate?

(a) 1.52

(b) Turbulence will decrease the flow rate of the blood, which would require an even larger increase in the pressure difference, leading to higher blood pressure.

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A spherical particle falling at a terminal speed in a liquid must have the gravitational force balanced by the drag force and the buoyant force. The buoyant force is equal to the weight of the displaced fluid, while the drag force is assumed to be given by Stokes Law, F s = 6 π r η v size 12{F rSub { size 8{s} } =6πrηv} {} . Show that the terminal speed is given by

v = 2 R 2 g 9 η ρ s ρ 1 , size 12{v= { {2R rSup { size 8{2} } g} over {9η} } left (ρ rSub { size 8{s} } - ρ rSub { size 8{1} } right )} {}

where R size 12{R} {} is the radius of the sphere, ρ s size 12{ρ rSub { size 8{s} } } {} is its density, and ρ 1 size 12{ρ rSub { size 8{1} } } {} is the density of the fluid and η size 12{η} {} the coefficient of viscosity.

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Using the equation of the previous problem, find the viscosity of motor oil in which a steel ball of radius 0.8 mm falls with a terminal speed of 4.32 cm/s. The densities of the ball and the oil are 7.86 and 0.88 g/mL, respectively.

225 mPa s size 12{"225"`"mPa" cdot s} {}
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A skydiver will reach a terminal velocity when the air drag equals their weight. For a skydiver with high speed and a large body, turbulence is a factor. The drag force then is approximately proportional to the square of the velocity. Taking the drag force to be F D = 1 2 ρ Av 2 size 12{F rSub { size 8{D} } = { { size 8{1} } over { size 8{2} } } ρ ital "Av" rSup { size 8{2} } } {} and setting this equal to the person’s weight, find the terminal speed for a person falling “spread eagle.” Find both a formula and a number for v t size 12{v rSub { size 8{t} } } {} , with assumptions as to size.

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A layer of oil 1.50 mm thick is placed between two microscope slides. Researchers find that a force of 5 . 50 × 10 4 N size 12{5 "." "50" times "10" rSup { size 8{ - 4} } `N} {} is required to glide one over the other at a speed of 1.00 cm/s when their contact area is 6 . 00 cm 2 size 12{6 "." "00"`"cm" rSup { size 8{2} } } {} . What is the oil’s viscosity? What type of oil might it be?

0 . 138 Pa s, size 12{0 "." "138 Pa" cdot s} {}


Olive oil.

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(a) Verify that a 19.0% decrease in laminar flow through a tube is caused by a 5.00% decrease in radius, assuming that all other factors remain constant, as stated in the text. (b) What increase in flow is obtained from a 5.00% increase in radius, again assuming all other factors remain constant?

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[link] dealt with the flow of saline solution in an IV system. (a) Verify that a pressure of 1 . 62 × 10 4 N/m 2 size 12{1 "." "62" times "10" rSup { size 8{4} } `"N/m" rSup { size 8{2} } } {} is created at a depth of 1.61 m in a saline solution, assuming its density to be that of sea water. (b) Calculate the new flow rate if the height of the saline solution is decreased to 1.50 m. (c) At what height would the direction of flow be reversed? (This reversal can be a problem when patients stand up.)

(a) 1 . 62 × 10 4 N/m 2 size 12{1 "." "62" times "10" rSup { size 8{"4 "} } "N/m" rSup { size 8{2} } } {}

(b) 0 . 111 cm 3 /s size 12{0 "." "111 cm" rSup { size 8{3} } "/s"} {}

(c)10.6 cm

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When physicians diagnose arterial blockages, they quote the reduction in flow rate. If the flow rate in an artery has been reduced to 10.0% of its normal value by a blood clot and the average pressure difference has increased by 20.0%, by what factor has the clot reduced the radius of the artery?

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During a marathon race, a runner’s blood flow increases to 10.0 times her resting rate. Her blood’s viscosity has dropped to 95.0% of its normal value, and the blood pressure difference across the circulatory system has increased by 50.0%. By what factor has the average radii of her blood vessels increased?


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Water supplied to a house by a water main has a pressure of 3 . 00 × 10 5 N/m 2 size 12{3 "." "00" times "10" rSup { size 8{5} } `"N/m" rSup { size 8{2} } } {} early on a summer day when neighborhood use is low. This pressure produces a flow of 20.0 L/min through a garden hose. Later in the day, pressure at the exit of the water main and entrance to the house drops, and a flow of only 8.00 L/min is obtained through the same hose. (a) What pressure is now being supplied to the house, assuming resistance is constant? (b) By what factor did the flow rate in the water main increase in order to cause this decrease in delivered pressure? The pressure at the entrance of the water main is 5 . 00 × 10 5 N/m 2 size 12{5 "." "00" times "10" rSup { size 8{5} } `"N/m" rSup { size 8{2} } } {} , and the original flow rate was 200 L/min. (c) How many more users are there, assuming each would consume 20.0 L/min in the morning?

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An oil gusher shoots crude oil 25.0 m into the air through a pipe with a 0.100-m diameter. Neglecting air resistance but not the resistance of the pipe, and assuming laminar flow, calculate the gauge pressure at the entrance of the 50.0-m-long vertical pipe. Take the density of the oil to be 900 kg/m 3 size 12{"900"`"kg/m" rSup { size 8{3} } } {} and its viscosity to be 1 . 00 ( N/m 2 ) s size 12{1 "." "00"` \( "N/m" rSup { size 8{2} } \) cdot s} {} (or 1.00 Pa s size 12{1 "." "00"`"Pa" cdot s} {} ). Note that you must take into account the pressure due to the 50.0-m column of oil in the pipe.

2 . 95 × 10 6 N/m 2 size 12{2 "." "21" times "10" rSup { size 8{6} } " N/m" rSup { size 8{2} } } {} (gauge pressure)

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Concrete is pumped from a cement mixer to the place it is being laid, instead of being carried in wheelbarrows. The flow rate is 200.0 L/min through a 50.0-m-long, 8.00-cm-diameter hose, and the pressure at the pump is 8 . 00 × 10 6 N/m 2 size 12{8 "." "00" times "10" rSup { size 8{6} } `"N/m" rSup { size 8{2} } } {} . (a) Calculate the resistance of the hose. (b) What is the viscosity of the concrete, assuming the flow is laminar? (c) How much power is being supplied, assuming the point of use is at the same level as the pump? You may neglect the power supplied to increase the concrete’s velocity.

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Construct Your Own Problem

Consider a coronary artery constricted by arteriosclerosis. Construct a problem in which you calculate the amount by which the diameter of the artery is decreased, based on an assessment of the decrease in flow rate.

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Consider a river that spreads out in a delta region on its way to the sea. Construct a problem in which you calculate the average speed at which water moves in the delta region, based on the speed at which it was moving up river. Among the things to consider are the size and flow rate of the river before it spreads out and its size once it has spread out. You can construct the problem for the river spreading out into one large river or into multiple smaller rivers.

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Questions & Answers

full meaning of GPS system
Anaele Reply
how to prove that Newton's law of universal gravitation F = GmM ______ R²
Kaka Reply
sir dose it apply to the human system
Olubukola Reply
prove that the centrimental force Fc= M1V² _________ r
Kaka Reply
prove that centripetal force Fc = MV² ______ r
how lesers can transmit information
mitul Reply
griffts bridge derivative
Ganesh Reply
below me
please explain; when a glass rod is rubbed with silk, it becomes positive and the silk becomes negative- yet both attracts dust. does dust have third types of charge that is attracted to both positive and negative
Timothy Reply
what is a conductor
below me
why below you
no....I said below me ...... nothing below .....ok?
dust particles contains both positive and negative charge particles
corona charge can verify
when pressure increases the temperature remain what?
Ibrahim Reply
what is frequency
Mbionyi Reply
define precision briefly
Sujitha Reply
CT scanners do not detect details smaller than about 0.5 mm. Is this limitation due to the wavelength of x rays? Explain.
hope this helps
what's critical angle
Mahmud Reply
The Critical Angle Derivation So the critical angle is defined as the angle of incidence that provides an angle of refraction of 90-degrees. Make particular note that the critical angle is an angle of incidence value. For the water-air boundary, the critical angle is 48.6-degrees.
dude.....next time Google it
okay whatever
pls who can give the definition of relative density?
the ratio of the density of a substance to the density of a standard, usually water for a liquid or solid, and air for a gas.
What is momentum
aliyu Reply
mass ×velocity
it is the product of mass ×velocity of an object
how do I highlight a sentence]p? I select the sentence but get options like copy or web search but no highlight. tks. src
Sean Reply
then you can edit your work anyway you want
Wat is the relationship between Instataneous velocity
Oyinlusi Reply
Instantaneous velocity is defined as the rate of change of position for a time interval which is almost equal to zero
Practice Key Terms 5

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Source:  OpenStax, College physics. OpenStax CNX. Jul 27, 2015 Download for free at http://legacy.cnx.org/content/col11406/1.9
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