Skip to main content

♦️Revision Notes on Flow of Liquids and Viscosity♦️(2/3)➖➖➖➖➖➖➖➖➖➖➖➖➖➖➖➖

♦️Revision Notes on Flow of Liquids and Viscosity♦️(2/3)
➖➖➖➖➖➖➖➖➖➖➖➖➖➖➖➖

Viscosity:- Viscosity is the property of fluids by virtue of which they tend to destroy any relative motion between their layers.

Velocity gradient:- Velocity gradient is defined as the rate of change of velocity with respect to distance.

(a) Velocity gradient = dv/dr
(b) Dimension of velocity gradient = [dv/dr] = [T-1]
(c) Direction of velocity gradient is perpendicular to the direction of flow, directed in the direction of increasing velocity.
(d) Average velocity gradient:- Average velocity gradient is the difference between velocities of two layers separated a unit distance apart.

Average velocity gradient = Δv/Δr

Newton’s law of viscosity:-

In accordance to Newton’s law of viscosity, the viscous drag force depends upon the nature of fluid along with following factors:-

(a) F∝A (common area of two layers)

(b) F∝dv/dr (velocity gradient)

(c) So, F =ηA (dv/dr)

Here η is called coefficient of viscosity of fluid.

Coefficient of viscosity of fluid (ηv) or fugitive elasticity:-

ηv = shear stress/velocity gradient = (F/A)/(dv/dr)

Modulus of rigidity(ηr):-

ηr = shear stress/shear strain = (F/A)/(θ) = (F/A)/(dx/dr)

Here, θ = dx/dr = displacement gradient

Coefficient of viscosity (Absolute viscosity or Dynamic viscosity):-

F= ηA (dv/dr) if A = 1, dv = 1, dr =1, F = η

Co-efficient of viscosity of a fluid is defined as the tangential force per unit area which is required to maintain (or resist) a unit relative velocity between two layers a unit distance apart.

Or

Co-efficient of viscosity of a fluid is defined as the tangential force per unit area which is required to maintain a unit velocity gradient between its layers.

Unit of η:-

S.I:- η = 1 deca poise = 1 N sec/m2

Co-efficient of viscosity of a fluid is said to be one deca-poise if a tangential force of 1 N per meter square is required to maintain a relative velocity of 1 ms-1 between its layer 1 m apart.

C.G.S:- η = 1 poise = 1 dyn sec/cm2

Coefficient of viscosity of a fluid is said to be one poise if a tangential force of 1 dyn per square cm is required to maintain a relative velocity of 1 cms-1 between its layers 1 cm apart.

Relation between deca-poise and poise:-

1 deca-poise = 10 poise

Dimension formula for η:-

η = Fdr/Adv = [M1L-1T-1]

Fluidity:- Reciprocal of coefficient of viscosity of a fluid is called its fluidity.

Fluidity = 1/η

Unit of fluidity: poise-1

Dimension of fluidity: [M-1L1T1]

Kinematic viscosity:- Kinematic viscosity of a fluid is defined as the ration between its coefficient of viscosity to the density of fluid.

Kinematic viscosity = η/ρ

Units of kinematic viscosity:- C.G.S – 1 stoke = cm2 s-1

Kinetic viscosity of a fluid having its dynamic viscosity one poise and density one g cm-3 is said to be 1 stoke.

Dimensional formula of kinematic viscosity = η/ρ = [M0L2T-1]

Critical velocity (Reynold’s Number):- Critical velocity (vc) is the maximum velocity of the flow of liquid flowing in a streamlined flow.

vc = NR η/ρD

Here η is the coefficient of viscosity of liquid, ρ is the density of liquid and D is the diameter of the tube.

Reynold’s Number, NR = ρvcD/ η

Stokes law:- In accordance to Stoke’s law, force of viscosity F depend upon,

(a) Co-efficient of viscosity of fluid η

(b) Radius of the moving body r

(c) Velocity of body v

So, force of viscosity, F = 6π η r v

Terminal velocity:- v = 2/9 [r2 (ρ-σ)/η]

η = 2/9 [r2 (ρ-σ)g/v]

Variation of viscosity with a change in temperature and pressure:-

(a) Effect of temperature:-

η= A /(1+Bt)c

Here A, B and C are constants.

Again, ηv1/2 = Aec/vt

Here, A and C are constants and v is the relative velocity.

(b) Effect of pressure:- Co-efficient of viscosity of liquids increases due to an increase in pressure but there is no relation, so far, to explain the effect.

Change in viscosity of gases:-

(a) Effect of temperature:- Co-efficient of viscosity of a gas at a given temperature is given by,

η= η0AT1/2

Here T is the absolute temperature of gas.
YouTube Channel

Telegram Group

Telegram Channels

Comments

Popular posts from this blog

11 Class Master Key and Books

Knowledge Factory New Channel: Get all subjects master key from this Google Drive link 👇🏻👇🏻 https://drive.google.com/drive/u/0/mobile/folders/1BuvOCBI_y56nyOwAcVeiG5LUbtBGjeXK Get all subjects textbooks from this Google Drive link 👇🏻👇🏻 https://drive.google.com/folderview?id=11cIU550K5YlwdGqjY5uhGeEVfVHlH9iE

all organic chemistry lectures by DN sir. (Allen, kota)

KNOWLEDGE FACTORY.......... 🙃🙃 Aab kota bhi hamare mutthi main.  D N sir from allen institute, kota. DN SIR (ORGANIC CHEMISTRY) Lecture 1 https://d3pqbp55enojba.cloudfront.net/5347540.mp4 Lecture 2 https://d3pqbp55enojba.cloudfront.net/5354521.mp4 Lecture 3 https://d3pqbp55enojba.cloudfront.net/5360505.mp4 Lecture 4 https://d3pqbp55enojba.cloudfront.net/5375009.mp4 Lecture 5 https://d3pqbp55enojba.cloudfront.net/5382818.mp4 Lecture 6 https://d3pqbp55enojba.cloudfront.net/5387062.mp4 Lecture 7 https://d3pqbp55enojba.cloudfront.net/5393283.mp4 Lecture 8 https://d3pqbp55enojba.cloudfront.net/5405035.mp4 Lecture 9 https://d3pqbp55enojba.cloudfront.net/5410071.mp4 Lecture 10 https://d3pqbp55enojba.cloudfront.net/5413820.mp4 Lecture 11 https://d3pqbp55enojba.cloudfront.net/5418531.mp4 Lecture 12 https://d3pqbp55enojba.cloudfront.net/5424967.mp4 Lecture 13  https://d3pqbp55enojba.cloudfront.net/5428657.mp4 Lecture 14 https://d3pqbp55enojba.cloudfront.net/5431822.mp4 Lecture 15 http...

11th Class All Book PDF Download

For more Study Material  Join 🔜  https://t.me/knowledgefactory_55 11th Class All Book PDF Download Biology  https://drive.google.com/file/d/1HabfYNKdLijL7UBy7IfowXeJgFSfrMZG/view?usp=drivesdk Physics  https://drive.google.com/file/d/1xIPg_P-d34HfKopxvIZpakPmY27t3oDl/view Chemistry https://drive.google.com/file/d/1e3lZafbWlX2ExhknApxe-rcia2b1GM7w/view Information Technology https://drive.google.com/file/d/10nM37xNgpyHOgO2knvm6yYB-zUHNrDDc/view English https://drive.google.com/file/d/1OxGjnWsbnOnYJj8JVoKJ8Tcd0CxJ2gLc/view Mathematics and Statics -1 (For Commerce Students) https://drive.google.com/file/d/19Yx1lmmsXee-IfZWf7bVjCgXhqNLEGh6/view Mathematics and Statistics-II (For Commerce Students) https://drive.google.com/file/d/1TVG6z8v0LC_zCjifMTHSXJFW6tRXBJRe/view Mathematics and Statistics-I (For Arts and Science Students) https://drive.google.com/file/d/1q_KVYffIlB0lHtWLr_C3FXfQKYFxrVQu/view Mathematics and Statistics-II (For Arts and Science Students) https://drive...

Navneet Question Bank For CET

https://drive.google.com/file/d/1I-22kXAJ4ct_t5Ze_fcjY7E9f09plu1h/view?usp=drivesdk

Biological classification notes, class 11,NEET

Hello! Friends, ✨Welcome to knowledge factory. ✨ 👉I know you are starting preparation for NEET as well as JEE.  👉Today, I provide you, very intresting and useful study material  👉Biological classification notes  👉This notes are well prepared by biology experts. 👉This notes are paid. So, use carefully and share your friends. Click on the below link.👇  https://drive.google.com/file/d/1-RoG7PDqnADhX7PnHc_WVf6UsbV18_ID/view?usp=drivesdk Have a great day.  I hope,this is important to you.  👉Please, follow me and subscribe to our channel.  Join for more update..  Join :  https://t.me/knowledgefactory123 Good bye...🙃  Take care... 🙃 Happy learning... 🙃  

Class🎯 11th mh board 🎯 pdfPhysics all chapter Notes📲Biology all chapter notes📲📲

Class🎯 11th mh board 🎯 pdf Physics all chapter Notes📲                 ❇️❇️👇❇️❇️ https://drive.google.com/folderview?id=19_OIGO5LB1UvSE4pHP7NirAa1gkt_cYM Biology all chapter notes📲📲             ❇️❇️👇❇️❇️ https://drive.google.com/folderview?id=1E0r7ay4uKpyTtsaRAO361MSryXuD8q6d  

Resources and Development class 10 Geography Notes

Resources Everything in our environment which can be used to satisfy our needs and is technologically accessible, economically feasible and culturally acceptable is termed as ‘Resource’. Human beings themselves are essential components of resources. They transform material available in the environment into resources and use them. Classification of Resources Resources can be classified in the following ways: (a) On the basis of origin – biotic and abiotic (b) On the basis of exhaustibility – renewable and non-renewable (c) On the basis of ownership – individual, community, national and international (d) On the basis of the status of development – potential, developed stock and reserves a) On the Basis of Origin – Biotic and Abiotic Biotic Resources are obtained from the biosphere and have life. Eg: Human beings, flora and fauna, fisheries, livestock etc. Abiotic Resources: All those things which are composed of non-living things are called abiotic resources. Eg: rocks and me...

CET Form

https://docs.google.com/forms/d/e/1FAIpQLSdLoLxWgcAdHmAtg4sFNT2-gD71_ak58cuJU87kwnmP9YwIfg/viewform?usp=pp_url Only for SSC 2021 Students  Compulsory fill Share to Everyone

Lenses..

  Lenses..     Question 1: Match the columns in the following table and explain them. Column 1 Column 2 Column 3 Farsightedness  Nearby object can be seen clearly Bifocal lens Presbyopia Far away object can be seen clearly Concave lens Nearsightedness Problem of old age Concave lens Answer: Column 1 Column 2 Column 3 Farsightedness Far away object can be seen clearly Convex lens Presbyopia Problem of old age Bifocal le ns Nearsightedness  Nearby object can be seen clearly Concave lens Farsightedness : This defect is also known as Hypermetropia. It is an eye defect in which a person is unable to see nearby objects clearly but can see the far away objects ...

What is Engineering? | Types of Engineering

  What is Engineering? | Types of Engineering           Engineers use science and math to come up with practical solutions to problems.   (Image credit: Ollyy | Shutterstock ) Engineering is the application of science and math to solve proble null ms. Engineers figure out how things work and find practical uses for scientific discoveries. Scientists and inventors often get the credit for innovations that advance the human condition, but it is engineers who are instrumental in making those innovations available to the world. In his book, " Disturbing the Universe " (Sloan Foundation, 1981), physicist Freeman Dyson wrote, "A good scientist is a person with original ideas. A good engineer is a person who makes a design that works with as few original ideas as possible. There are no prima donnas in engineering." The history of engineering is part and parcel of the history of human civilization. The   Pyramids   of Giza,   Stonehenge , the ...