# 12.5 The onset of turbulence  (Page 2/3)

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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 $Q$ 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 ${N}_{\text{R}}$ can reveal whether flow is laminar or turbulent. It is
${N}_{\text{R}}=\frac{2\rho \text{vr}}{\eta }.$
• For ${N}_{\text{R}}$ below about 2000, flow is laminar. For ${N}_{\text{R}}$ above about 3000, flow is turbulent. For values of ${N}_{\text{R}}$ 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?

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

Some ceiling fans have decorative wicker reeds on their blades. Discuss whether these fans are as quiet and efficient as those with smooth blades.

## 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 $\text{900 kg}{\text{/m}}^{3}$ and its viscosity to be $1.00\phantom{\rule{0.25em}{0ex}}\left({\text{N/m}}^{2}\right)\cdot \text{s}$ (or $1.00 Pa\cdot \text{s}$ ).

${N}_{\text{R}}=1.99×{10}^{2}<2000$

Show that the Reynolds number ${N}_{\text{R}}$ is unitless by substituting units for all the quantities in its definition and cancelling.

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: $1\text{.}\text{27}×{\text{10}}^{5}$ , not laminar

(b) hose: $3\text{.}\text{51}×{\text{10}}^{4}$ , not laminar.

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 $1\text{.}\text{62}×{\text{10}}^{6}\phantom{\rule{0.25em}{0ex}}{\text{N/m}}^{2}$ . 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.

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 $8\text{.}\text{00}×{\text{10}}^{6}\phantom{\rule{0.25em}{0ex}}{\text{N/m}}^{2}$ . Verify that the flow of concrete is laminar taking concrete’s viscosity to be $48.0\phantom{\rule{0.25em}{0ex}}\left(\text{N/}{\text{m}}^{2}\right)·\text{s}$ , and given its density is $2300 kg/{\text{m}}^{3}$ .

2.54<<2000, laminar.

At what flow rate might turbulence begin to develop in a water main with a 0.200-m diameter? Assume a $\text{20º C}$ temperature.

What is the greatest average speed of blood flow at $\text{37º C}$ 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 $1025 kg/{\text{m}}^{3}$ .

1.02 m/s

$1.28×{\text{10}}^{–2}\phantom{\rule{0.25em}{0ex}}\text{L/s}$

In Take-Home Experiment: Inhalation , we measured the average flow rate $Q$ 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 ${\text{10}}^{-2}\phantom{\rule{0.25em}{0ex}}\text{m}$ . 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?

Gasoline is piped underground from refineries to major users. The flow rate is $3\text{.}\text{00}×{\text{10}}^{–2}\phantom{\rule{0.25em}{0ex}}{\text{m}}^{3}\text{/s}$ (about 500 gal/min), the viscosity of gasoline is $1.00×{\text{10}}^{–3}\phantom{\rule{0.25em}{0ex}}\left({\text{N/m}}^{2}\right)\cdot \text{s}$ , and its density is $\text{680}\phantom{\rule{0.25em}{0ex}}{\text{kg/m}}^{3}$ . (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) $\text{≥ 13.0 m}$

(b) $2\text{.}\text{68}×{\text{10}}^{-6}\phantom{\rule{0.25em}{0ex}}{\text{N/m}}^{2}$

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.)

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 $1.005×{10}^{–3}\phantom{\rule{0.25em}{0ex}}\left(\text{N}/{m}^{2}\right)\cdot \text{s}$ .)

(a) 23.7 atm or $\text{344 lb/}{\text{in}}^{2}$

(b) The pressure is much too high.

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

(d) $5.27×{\text{10}}^{6}$ >>3000, turbulent, contrary to the assumption of laminar flow when using this equation.

What are the two major system units in the world
What is physical quantities
Jizel
Who is the father of physics
Newton.Geliliyo and Einstein is called father of physics
Neha
Newtin
Jizel
Einstein
Jizel
what is wave
a wave is a distirbance that transmits energy from one place ro another within or without a medium
Vincent
wave is the transfer of energy from one medium to another without the transfer of particles
ZIFAC
wave is a disturbance which transfer energy from one medium to another without causing any permanent displacement by itself
Joyfulsounds
wave is a disturbance or oscillation that travel through space and matter,accompanied by a transfer of energy
Ridwan
A wave is any disturbances in an elastic medium which carries energy from one point to another through a medium
abdul
what is harmonic motion
Nozyani
is a restoring force
Joyfulsounds
a wave is a disturbance and there are trasfer energy from one medium to another and travel through any space without the trasfer of particles.
Neha
a wave is a disturbance that travels or carries energy from one point to another through a medium
Wisdom
A moving disturbance in the level of a body water, undulation
Jizel
what is thermodynamics
what is thermodynamics
Charity
thermodynamics is a heat and energy significant physics
Neha
Relating to the conversation of heat into other forms of energy
Jizel
Are the antimatters of Hadrons also Hadrons?!Does the same rule apply to Leptons?
yes. Hadrons are the elementary particles that take part in stong, electromagnetic and weak interactions. Infact only Hadrons are involved in Strong interactions and when an anti-particle of any hadron is produced, it would be a hadron-conservations laws. Leptons are involved in weak int and follow
Lalita
what is physics
physic is a pure science that deal with behavior of matter,energy & how it related to other physical properties
Ridwan
Owk. But am are Art student.
Hussaini
What happens when an aeroplanes window is opened at cruise altitude?
what is the minimum speed for any object to travel in time?
as per theory of relativity, minimum speed will be the speed of light
Mr.
what is physics
it is just a branch of science which deals with the reasons behind the daily activities taking place everyday in our lives. it clearly states the reason in the form of laws.
sandhya
?
lkpostpost2000@yahoo
like Newton's laws , Kepler's laws etc....
sandhya
physics is the study of motion or moving things. Usually the moving things are normal items like vars or planets but sometimes it's electricity or heat that moves.
Jake
physics is one of the most significant diciplines of natural science which describe the nature and its matter
Neha
I would describe it as the science that is interested in the fundamental laws of nature. For example, what is light, what is sound, what is electricity/magentism, what forces are at work on a specific body. The knowledge of the world around us makes it possible to fly, have cell phones, GPS, etc.
Robyn
what happens when an aeroplane takes off?
it flies
Mr.
the lift generated by the wing overcome the weight of the plane(in Newton)and a net force of upward is created
Phebilia
it is a direct application of Magnus effect (which helps in throwing curve balls) the wings of plane are made in such a way that the net flow of air is more below them rather than on their upper side. So when the plane accelerates, the flaps produce the upward lift when enough velocity is obtained
Mr.
then due to lower pressure on upper part of wings helps producing an additional lift because air flows from areaof lower to the area of higher pressure
Mr.
The engines located under the wings generate thrust .. in relation thrust is a force ... which ovwrcomes or becomes greater than the weight of the plane.. remember weight is a force Weight = m x g-2 So therefore F(thrust) becomes greater than F(weight) Even if by 1Newton the plane starts lifting o
Theophilus
what happens when a ship moves
Williams
What is the sign of an acceleration that reduces the magnitude of a negative velocity? Of a positive velocity?
If it reduces the magnitude of the velocity, the acceleration sign is the opposite compared to the velocity.
Nicolas
yes
Williams
what is accerelation
an objects tendency to speed up over time
RayRay
acceleration is the change in velocity over the change in time it would be written delta-v over delta-t.
Shii
the change in velocity V over a period of time T.
Matthew
Delta means "change in"...not period of
Shii
just kidding. it all works mathematically
Shii
except doesn't time really only change if the instantaneous speeds vary...?
Shii
and I assume we are all talking average acceleration
Shii
Hey shiii 😀
the rate of change of velocity is callaed acceleration
Amna
a=delta v/delta t
Amna
the rate of change in velocity with respect to time is acceleration
Nana
nana you r right
Indrajit
good
oguji
what is meant by lost volt
Lost volt. Lol. It is the electrical energy lost due to the nature or the envirommental conditions (temperature and pressure) that affect the cable across which the potential difference is measured.
Theophilus
What is physics?
physics is brance science concerned with nature and properties of matter and energy
George
sure
Okpara
yah....
kashif
physics is study of the natural phenomenon on the basis of certain laws and principles. it's like watching a game of chess and trying to understand its rules how it's played.
Ajit
awesome
Okpara
physics is study of nature and it's law
AMRITA
physics is a branch of science that deals with the study of matter ,properties of matter and energy
Lote
Branch of science (study) of matter, motion and energy
Theophilus
what is a double-slit experiment?Explain.
when you pass a wave of any kind ie sound water light ect you get an interface pattern forming on a screen behind it, where the peaks and troughs add and cancel out due to the diffraction caused by a wave traveling through the slits
Luke
double slit experiment was done by YOUNG. And it's to give out monochromatic coherent, if an incoherent wave is passing through it. And then the waves form interference fringes. The screen placed in front of the double slit is preferably a film and then in the middle where "p=0" a brighter color
navid
is formed and then the constructive interferences occur at 0 (which is the brightest band)... then a sequence of bright band (constructive interference) and dark band (destructive interference) happens and the further from the central band the lower the intensity of bright band(constructive interfe
navid
what is photoelectric effect
the emission of electrons in some materials when light of suitable frequency falls on them
Hardeyyemih
The phenomenon that involves the emission of electrons (photoelectrons) when light of appropriate wavelength and frequency is incident on the surface of a metal.
ibrahim