# 14.7 Viscosity and turbulence  (Page 6/14)

 Page 6 / 14

## Summary

• Laminar flow is characterized by smooth flow of the fluid in layers that do not mix.
• Turbulence is characterized by eddies and swirls that mix layers of fluid together.
• Fluid viscosity $\eta$ is due to friction within a fluid.
• Flow is proportional to pressure difference and inversely proportional to resistance:
$Q=\frac{p-2{p}_{1}}{R}.$
• The pressure drop caused by flow and resistance is given by ${p}_{2}–{p}_{1}=RQ$ .
• The Reynolds number ${N}_{\text{R}}$ can reveal whether flow is laminar or turbulent. It is ${N}_{\text{R}}=\frac{2\rho vr}{\eta }$ .
• 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.

## Key equations

 Density of a sample at constant density $\rho =\frac{m}{V}$ Pressure $p=\frac{F}{A}$ Pressure at a depth h in a fluid of constant density $p={p}_{0}+\rho gh$ Change of pressure with height in a constant-density fluid $\frac{dp}{dy}=\text{−}\rho g$ Absolute pressure ${p}_{\text{abs}}={p}_{\text{g}}+{p}_{\text{atm}}$ Pascal’s principle $\frac{{F}_{1}}{{A}_{1}}=\frac{{F}_{2}}{{A}_{2}}$ Volume flow rate $Q=\frac{dV}{dt}$ Continuity equation (constant density) ${A}_{1}{v}_{1}={A}_{2}{v}_{2}$ Continuity equation (general form) ${\rho }_{1}{A}_{1}{v}_{1}={\rho }_{2}{A}_{2}{v}_{2}$ Bernoulli’s equation $p+\frac{1}{2}\rho {v}^{2}+\rho gy=\text{constant}$ Viscosity $\eta =\frac{FL}{vA}$ Poiseuille’s law for resistance $R=\frac{8\eta l}{\pi {r}^{4}}$ Poiseuille’s law $Q=\frac{\left({p}_{2}-{p}_{1}\right)\pi {r}^{4}}{8\eta l}$

## Conceptual questions

Explain why the viscosity of a liquid decreases with temperature, that is, how might an increase in temperature reduce the effects of cohesive forces in a liquid? Also explain why the viscosity of a gas increases with temperature, that is, how does increased gas temperature create more collisions between atoms and molecules?

When paddling a canoe upstream, it is wisest to travel as near to the shore as possible. When canoeing downstream, it is generally better to stay near the middle. Explain why.

The water in the center of the stream is moving faster than the water near the shore due to resistance between the water and the shore and between the layers of fluid. There is also probably more turbulence near the shore, which will also slow the water down. When paddling up stream, the water pushes against the canoe, so it is better to stay near the shore to minimize the force pushing against the canoe. When moving downstream, the water pushes the canoe, increasing its velocity, so it is better to stay in the middle of the stream to maximize this effect.

Plumbing usually includes air-filled tubes near water faucets (see the following figure). Explain why they are needed and how they work.

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 after the constriction? What are the two distinct causes of higher resistance in the constriction?

You would expect the speed to be slower after the obstruction. Resistance is increased due to the reduction in size of the opening, and turbulence will be created because of the obstruction, both of which will clause the fluid to slow down.

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

## Problems

(a) Calculate the retarding force due to the viscosity of the air layer between a cart and a level air track given the following information: air temperature is $20\phantom{\rule{0.2em}{0ex}}\text{°C}$ , the cart is moving at 0.400 m/s, its surface area is $2.50\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-2}\phantom{\rule{0.2em}{0ex}}{\text{m}}^{2},$ and the thickness of the air layer is $6.00\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-5}\text{m}$ . (b) What is the ratio of this force to the weight of the 0.300-kg cart?

a. $3.02\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{\text{−}3}\phantom{\rule{0.2em}{0ex}}\text{N}$ ; b. $1.03\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{\text{−}3}$

what is quantam
quantum is a division of mechanics
Baje
what is friction
a force act by surface between two bodies whose are always oppose the relative motion .....
Raghav
when two rough bodies are placed in contact and try to slip each other ... than a force act them and it's ippse the relative motion between them
Raghav
thats friction force and roughnes of both bodies is define friction of surface
Raghav
what is a progressive wave
What is the wake for therapist
can u like explain your question with clear detail
Chikamso
who would teach me vectors?
what's chemistry
branch of science dt deals with the study of physical properties of matter and it's particulate nature
Josiah
Good
Daniel
actually
Nathz
Y acctually do u hav ur way of defining it? just bring ur iwn idear
Daniel
well, it deals with the weight of substances and reaction behind them as well as the behavior
Josiah
buh hope Esther, we've answered ur question
Josiah
what's ohms law
CHIJIOKE
ohms law states that, the current flowing through an electric circuit is directly proportional to the potential difference, provided temperature and pressure are kept constant
Josiah
what is sound
James
ohms law states that the resistance of a material is directly proportional to the potential difference between two points on that material, if temperature and other physical conditions become constant
Chikamso
How do I access the MCQ
As I think the best is, first select the easiest questions for you .and then you can answer the remaining questions.
lasitha
I mean I'm unable to view it
Abraham
when I click on it, it doesn't respond
Abraham
ohhh,try again and again ,It will be showed
lasitha
okay
Abraham
what is centripetal force
هي قوة ناتجة من الحركة الدائرية ويكون اتجاهها إلى المركز دائماً
meaning of vector quantity
vector quantity is any quantity that has both magnitude in terms of number (units) and direction in terms of viewing the quantity from an origin using angles (degree) or (NEWS) method
LEWIS
vector quantity is physical quantity has magnitude and direction
vector is a quantity that is use in measuring size of physical properties and their direction
Bitrus
what difference and similarities between work,force,energy and power?
Anes
power
mehreen
power
saba
enery is the ability to do work. work is job done, force is a pull or push. power has to do with potential. they belong to different categories which include heat energy, electricity.
Andrew
force refers to a push or pull... energy refers to work done while power is work done per unit time
Shane
mathematically express angular velocity and angular acceleration
it depends on the direction. an angular velocity will be linear and angular acceleration will be an angle of elevation.
Andrew
The sonic range finder discussed in the preceding question often needs to be calibrated. During the calibration, the software asks for the room temperature. Why do you suppose the room temperature is required?
Suppose a bat uses sound echoes to locate its insect prey, 3.00 m away. (See [link] .) (a) Calculate the echo times for temperatures of 5.00°C5.00°C and 35.0°C.35.0°C. (b) What percent uncertainty does this cause for the bat in locating the insect? (c) Discuss the significance of this uncertainty an
Shaina
give a reason why musicians commonly bring their wind instruments to room temperature before playing them.
Shaina
The ear canal resonates like a tube closed at one end. (See [link]Figure 17_03_HumEar[/link].) If ear canals range in length from 1.80 to 2.60 cm in an average population, what is the range of fundamental resonant frequencies? Take air temperature to be 37.0°C,37.0°C, which is the same as body tempe
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By what fraction will the frequencies produced by a wind instrument change when air temperature goes from 10.0°C10.0°C to 30.0°C30.0°C ? That is, find the ratio of the frequencies at those temperatures.
Shaina
what are vector quantity
Quantities that has both magnitude and direction
NNAEMEKA
what is lenses
Rhoda
vector quantities are those physical quantites which have magnitude as well as direction and obey the laws of vector algebra.
Huzaif
electric current has both magnitude and direction but it doesn't obey the laws of vector algebra, hence it is not a vector quantity.
Huzaif
what is momentum
Momentum=mv
Nana
what is dimension