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Take-home experiment: inhalation

Under the conditions of normal activity, an adult inhales about 1 L of air during each inhalation. With the aid of a watch, determine the time for one of your own inhalations by timing several breaths and dividing the total length by the number of breaths. Calculate the average flow rate Q size 12{Q} {} of air traveling through the trachea during each inhalation.

The topic of chaos has become quite popular over the last few decades. A system is defined to be chaotic when its behavior is so sensitive to some factor that it is extremely difficult to predict. The field of chaos is the study of chaotic behavior. A good example of chaotic behavior is the flow of a fluid with a Reynolds number between 2000 and 3000. Whether or not the flow is turbulent is difficult, but not impossible, to predict—the difficulty lies in the extremely sensitive dependence on factors like roughness and obstructions on the nature of the flow. A tiny variation in one factor has an exaggerated (or nonlinear) effect on the flow. Phenomena as disparate as turbulence, the orbit of Pluto, and the onset of irregular heartbeats are chaotic and can be analyzed with similar techniques.

Section summary

  • The Reynolds number N R size 12{N rSub { size 8{R} } } {} can reveal whether flow is laminar or turbulent. It is
    N R = 2 ρ vr η . size 12{N rSub { size 8{R} } = { {2ρ ital "vr"} over {η} } } {}
  • 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 2000 and 3000, it may be either or both.

Conceptual questions

Doppler ultrasound can be used to measure the speed of blood in the body. If there is a partial constriction of an artery, where would you expect blood speed to be greatest, at or nearby the constriction? What are the two distinct causes of higher resistance in the constriction?

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Sink drains often have a device such as that shown in [link] to help speed the flow of water. How does this work?

Shows a picture of a small ring shaped section of a cylinder. It is shown to be partitioned in to four equal portions.
You will find devices such as this in many drains. They significantly increase flow rate.
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Some ceiling fans have decorative wicker reeds on their blades. Discuss whether these fans are as quiet and efficient as those with smooth blades.

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Problems&Exercises

Verify that the flow of oil is laminar (barely) for an oil gusher that shoots crude oil 25.0 m into the air through a pipe with a 0.100-m diameter. The vertical pipe is 50 m long. 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 ).

N R = 1.99 × 10 2 <2000

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Show that the Reynolds number N R size 12{N rSub { size 8{R} } } {} is unitless by substituting units for all the quantities in its definition and cancelling.

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Calculate the Reynolds numbers for the flow of water through (a) a nozzle with a radius of 0.250 cm and (b) a garden hose with a radius of 0.900 cm, when the nozzle is attached to the hose. The flow rate through hose and nozzle is 0.500 L/s. Can the flow in either possibly be laminar?

(a) nozzle: 1 . 27 × 10 5 size 12{1 "." "27" times "10" rSup { size 8{5} } } {} , not laminar

(b) hose: 3 . 51 × 10 4 size 12{1 "." "27" times "10" rSup { size 8{5} } } {} , not laminar.

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A fire hose has an inside diameter of 6.40 cm. Suppose such a hose carries a flow of 40.0 L/s starting at a gauge pressure of 1 . 62 × 10 6 N/m 2 size 12{1 "." "62" times "10" rSup { size 8{6} } `"N/m" rSup { size 8{2} } } {} . The hose goes 10.0 m up a ladder to a nozzle having an inside diameter of 3.00 cm. Calculate the Reynolds numbers for flow in the fire hose and nozzle to show that the flow in each must be turbulent.

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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 . Verify that the flow of concrete is laminar taking concrete’s viscosity to be 48.0 ( N/ m 2 ) · s , and given its density is 2300 kg/ m 3 .

2.54<<2000, laminar.

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At what flow rate might turbulence begin to develop in a water main with a 0.200-m diameter? Assume a 20º C size 12{"20" rSup { size 12{ circ } } C} {} temperature.

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What is the greatest average speed of blood flow at 37º C in an artery of radius 2.00 mm if the flow is to remain laminar? What is the corresponding flow rate? Take the density of blood to be 1025 kg / m 3 .

1.02 m/s

1.28 × 10 –2 L/s

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In Take-Home Experiment: Inhalation , we measured the average flow rate Q size 12{Q} {} of air traveling through the trachea during each inhalation. Now calculate the average air speed in meters per second through your trachea during each inhalation. The radius of the trachea in adult humans is approximately 10 2 m size 12{"10" rSup { size 8{ - 2} } `m} {} . From the data above, calculate the Reynolds number for the air flow in the trachea during inhalation. Do you expect the air flow to be laminar or turbulent?

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Gasoline is piped underground from refineries to major users. The flow rate is 3 . 00 × 10 –2 m 3 /s size 12{3 "." "00" times "10" rSup { size 8{2} } `m rSup { size 8{3} } "/s"} {} (about 500 gal/min), the viscosity of gasoline is 1.00 × 10 –3 ( N/m 2 ) s size 12{1 "." "00" times "10" rSup { size 8{5} } ` \( "N/m" rSup { size 8{2} } \) cdot s} {} , and its density is 680 kg/m 3 size 12{"680"`"kg/m" rSup { size 8{3} } } {} . (a) What minimum diameter must the pipe have if the Reynolds number is to be less than 2000? (b) What pressure difference must be maintained along each kilometer of the pipe to maintain this flow rate?

(a) ≥ 13.0 m

(b) 2 . 68 × 10 6 N/m 2 size 12{2 "." "68" times "10" rSup { size 8{ - 6} } " N/m" rSup { size 8{2} } } {}

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Assuming that blood is an ideal fluid, calculate the critical flow rate at which turbulence is a certainty in the aorta. Take the diameter of the aorta to be 2.50 cm. (Turbulence will actually occur at lower average flow rates, because blood is not an ideal fluid. Furthermore, since blood flow pulses, turbulence may occur during only the high-velocity part of each heartbeat.)

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Unreasonable Results

A fairly large garden hose has an internal radius of 0.600 cm and a length of 23.0 m. The nozzleless horizontal hose is attached to a faucet, and it delivers 50.0 L/s. (a) What water pressure is supplied by the faucet? (b) What is unreasonable about this pressure? (c) What is unreasonable about the premise? (d) What is the Reynolds number for the given flow? (Take the viscosity of water as 1.005 × 10 –3 ( N / m 2 ) s .)

(a) 23.7 atm or 344 lb/ in 2

(b) The pressure is much too high.

(c) The assumed flow rate is very high for a garden hose.

(d) 5.27 × 10 6 size 12{5 "." "27" times "10" rSup { size 8{6} } } {} >>3000, turbulent, contrary to the assumption of laminar flow when using this equation.

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Questions & Answers

2 how heat loss is prevented in a vacuum flask
Abdullah Reply
what is science
Helen
logical reasoning for a particular phenomenon.
Ajay
I don't know anything about it 😔. I'm sorry, please forgive 😔
Adarsh
due to non in contact mean no conduction and no convection bec of non conducting base and walls and also their is a grape between the layer like to take the example of thermo flask
Abdul
dimensions v²=u²+2at
Lagben Reply
what if time is not given in finding the average velocity?
Alan Reply
the magnetic circuit of a certain of the flux paths in each of the long and short sides being 25cm and 20cm reprectielectrove. there is an air gap of 2mm long in one the long sides if a flux density of 0.8weber/m is to produce in the magnet of 1500 turns..
Daniel Reply
How do you calculate precision
Sacky Reply
what module is that?
Fillemon
Chemisty 1A?
Fillemon
No it has something to do with measurements bro... What we did today in class
Sacky
Tah bra honestly I didn't understand a thing in that class..when re your Tutorials?
Fillemon
Friday bro... But the topics we did are in this app... Just try to master them quickly before the test dates... Are you done with the Maths sheet
Sacky
I eat ass
Anderson
I'll work on the maths sheet tomorrow bra @Sacky Malyenge but I'll try mastering them
Fillemon
I'll eat your mom's ass with a side of tendies
Anderson
@Fillemon Nanwaapo
Anderson
lol, hush
Emi
There are very large numbers of charged particles in most objects. Why, then, don’t most objects exhibit static electricity?
Bilkisu Reply
Because there's an equal number of negative and positive charges... objects are neutral in nature
NELSON
when a ball rolls on a smooth level ground,the motion of its centre is?
Mary Reply
what is electro magnetic field?
Mary
electromagnetic field is a special type of field been produced by electric charges..!!! like the word electro from Electricity and the word magnetic from Magnetism.. so it is more of a join field..!!!
NELSON
Electromagnetic field is caused by moving electric charge
Muhammad
when a ball rolls on a smooth level ground,the motion of its centre is?
Mumeh
what's the relationship btw displacement and position
Declan Reply
displacement is the change of position 8======✊=D 💦💦
Anderson
what is the meaning of elasticity
Pele Reply
is the ability of a material to or any object to expand to a limit point
king
this is about kinematics you bonk
Emi
what does emf/R mean
Eze Reply
What is work
Wisdom Reply
work is the product of force and perpendicular distance
DAVID
Pls explain simple harmonic motion
Olaiya Reply
Any to and from motion of a fluid or any elastic object
Sacky
a current of 5.5mA is flowing through a 3.3k resistor.compute th p.d developed across the resistor
Clifford Reply
A p.d of 24 volts exist across a 15 OHM'S resistor.calculate the current flowing the resistor
Clifford
a current of 5.5mA is flowing through a 3.3kOHM'S resistor.compute th p.d developed across the resistor
Clifford
solve it please
Festus
the so unit power is the watt(w)/joul/second (w1)/s
Jibo Reply
Really
Lawal
what is time
Jibo Reply
a measure of the duration of an event
Raymond
density
Masente
Practice Key Terms 1

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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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