# Fluid Mechanics & Fluid Machines

date post

15-Oct-2015Category

## Documents

view

667download

36

Embed Size (px)

description

### Transcript of Fluid Mechanics & Fluid Machines

Properties of Fluids S K Mondals Chapter 1

1. Properties of Fluids

Contents of this chapter 1. Definition of Fluid 2. Characteristics of Fluid 3. Ideal and Real Fluids 4. Viscosity 5. Units of Viscosity 6. Kinematic Viscosity 7. Units of Kinematic Viscosity 8. Classification of Fluids 9. Effect of Temperature on Viscosity 10. Effect of Pressure on Viscosity 11. Surface Tension 12. Pressure Inside a Curved Surface 13. Capillarity 14. Derive the Expression for Capillary Rise

Theory at a Glance (for IES, GATE, PSU)

Definition of Fluid A fluid is a substance which deforms continuously when subjected to external shearing forces.

Characteristics of Fluid 1. It has no definite shape of its own, but conforms to the shape of the containing vessel. 2. Even a small amount of shear force exerted on a fluid will cause it to undergo a

deformation which continues as long as the force continues to be applied. 3. It is interesting to note that a solid suffers strain when subjected to shear forces

whereas a fluid suffers Rate of Strain i.e. it flows under similar circumstances.

Concept of Continuum

Page 1 of 372

SThwhvaassp De(prMafluFo

He If anchdeTh

Onmofrebesomthecomsh A freconUsBe

Hois OtThactIn tem

Id1.

S K Mohe concept ohere the prriables. Althsumes a coace, instead

escribing a ressure, velocathematical

uid medium or example d

ere is th

is very nother extreange their fined at the

his is called

ne of the facolecular denee path ( )tween two me charactee gas can mparison toould be ana

dimensionleee path andntinuum. sually wheneyond this cr

slip flotransitfree-m

owever, for usual to say

ther factor whe time shoutivity holds continuummperature,

deal and Ideal Fluid

An ideal

ondalsof continuumroperties ofhough any m

ontinuous dd of the actu

fluid flow qcity etc.) anl descriptions as a contindensity at a

he volume of

large is aeme if inumber at

e smallest m continuum

ctors considnsity. It is th). It is calcusuccessive eristic lengtbe treated

o some charalysed by th

ess paramed L is the

n Kn> 0.01, tritical range

ow (0.01 < Ktion flow (0.olecule flowthe flow regy that the flwhich checkuld be sma good.

m approach, etc. can be

d Real d l fluid is one

Ps m is a kind f the mattmatter is co

distribution ual conglome

quantitativend fluid pros of flow on uum has fir point is nor

f the fluid el

affected by is very smadifferent ti

magnitude o limit and is

dered importhe distance ulated by fincollisions. I

th in the flow as a contracteristic le molecular

eter known characteris

the concept e of Knudse

Kn < 0.1), 1 < Kn < 10)

w (Kn > 10). gimes considluid is a conks the validill enough s

fluid propeexpressed a

Fluids

e which has

Properti

of idealizatter are conomposed of sof mass wieration of se

ely makes ioperties var

this basis hrmly becomermally defin

lement and

the inhomoall, randommes. In the

of , befores denoted by

tant in dete between thnding statisIf the meanw domain (itinuous meength, the g

r theory.

as Knudsentic length.

of continuuen number,

) and

dered in thintinuum. ity of continso that the

erties such as continuou

ies of Flu

tion of the cnsidered as several molithin the meparate mol

it necessaryry continuoave proved e establishened as

m is the ma

ogeneities inm movemente continuume statisticaly c.

ermining thhe moleculesstical averan free path i.e., the mol

edium. If thgas cannot

n number, KIt describe

m does not the flows ar

is course, K

nuum is the random sta

as density, us functions

uids

continuous continuouslecules, the

matter or sylecules.

y to assumeusly from oto be reliab

ed.

ass

n the fluid mt of atoms

m approximal fluctuation

he validity os which is chge distanceis very sma

lecular denshe mean frbe consider

Kn = / L, es the degre

hold good. re known as

n is always

elapsed timatistical des

viscosity, ts of space an

Chadescription s functionsconcept of c

ystem with

e that flowone point toble and tre

medium. Co(or moleculation point ns become s

of continuumharacterised

e the molecuall as compsity is very hree path isred continuo

where is ee of depar

s

less than 0

me between scription of

thermal connd time.

apter 1 of matter

s of space continuum no empty

variables o another.

eatment of

onsidering les) would density is ignificant.

m model is d by mean ules travel pared with high) then s large in ous and it

the mean rture from

0.01 and it

collisions. molecular

nductivity,

Page 2 of 372

Properties of Fluids S K Mondals Chapter 1

no viscosity no surface tension and incompressible 2. Real Fluid An Real fluid is one which has viscosity surface tension and compressible Naturally available all fluids are real fluid.

Viscosity Definition: Viscosity is the property of a fluid which determines its resistance to shearing stresses. Cause of Viscosity: It is due to cohesion and molecular momentum exchange between fluid layers. Newtons Law of Viscosity: It states that the shear stress () on a fluid element layer is directly proportional to the rate of shear strain.

The constant of proportionality is called the co-efficient of viscosity.

When two layers of fluid, at a distance dy apart, move one over the other at different velocities, say u and u+du.

Velocity gradient = dudy

According to Newtons law dudy

or = dudy

Velocity Variation near a solid

boundary

Where = constant of proportionality and is known as co-efficient of Dynamic viscosity or only Viscosity

As dudy

= Thus viscosity may also be defined as the shear stress required producing unit

rate of shear strain.

Units of Viscosity S.I. Units: Pa.s or N.s/m2 C.G.S Unit of viscosity is Poise= dyne-sec/cm2 One Poise= 0.1 Pa.s 1/100 Poise is called centipoises. Dynamic viscosity of water at 20oC is approx= 1 cP

Page 3 of 372

Properties of Fluids S K Mondals Chapter 1

Kinematic Viscosity It is the ratio between the dynamic viscosity and density of fluid and denoted by

Mathematically dynamic viscositydensity

= =

Units of Kinematic Viscosity S.I units: m2/s C.G.S units: stoke = cm2/sec One stoke = 10-4 m2/s Thermal diffusivity and molecular diffusivity have same dimension, therefore, by analogy, the kinematic viscosity is also referred to as the momentum diffusivity of the fluid, i.e. the ability of the fluid to transport momentum.

Classification of Fluids 1. Newtonian Fluids These fluids follow Newtons viscosity equation.

For such fluids viscosity does not change with rate of deformation. 2. Non- Newtonian Fluids These fluids does not follow Newtons viscosity equation.

Such fluids are relatively uncommon e.g. Printer ink, blood, mud, slurries, polymer solutions.

Non-Newtonian Fluid (dydu )

Purely Viscous Fluids Visco-elastic Fluids

Time - Independent Time - Dependent Visco-elastic Fluids

Edydu +=

Example: Liquid-solid combinations in pipe flow.

1. Pseudo plastic Fluids

1;

= ndydu

n

Example: Butter

3. Bingham or Ideal

1.Thixotropic Fluids

)(tfdydu

n

+

=

f(t)is decreasing Example: Printer ink; crude oil

2. Rheopectic Fluids

Page 4 of 372

Properties of Fluids S K Mondals Chapter 1

Plastic Fluid n

o dydu

+=

Example: Water suspensions of clay and flash

)(tfdydu

n

+

=

f(t)is increasing Example: Rare liquid solid suspension

Fig. Shear stress and deformation rate relationship of different fluids

Effect of Temperature on Viscosity With increase in temperature Viscosity of liquids decrease Viscosity of gasses increase Note: 1. Temperature responses are neglected in case of Mercury. 2. The lowest viscosity is reached at the critical temperature.

Effect of Pressure on Viscosity Pressure has very little effect on viscosity.

But if pressure increases intermolecular gap decreases then cohesion increases so viscosity would be increase.

Page 5 of 372

Properties of Fluids S K Mondals Chapter 1

Surface tension Surface tension is due to cohesion between particles at the surface. Capillarity action is due to both cohesion and adhesion.

Surface tension The tensile force acting on the surface of a liquid in contact with a gas or on the surface between two immiscible liquids such that the contact surface behaves like a membrane under tension.

Pressure Inside a Curved Surface For a general curved surface with radii of curvature r1 and r2 at a point of interest

1 2

1 1pr r

= + a. Pressure inside a water droplet, 4p

d =

b. Pressure inside a soap bubble, 8pd =

c. Liquid jet. 2pd =

Capillarity A general term for phenomena observed in liquids due to inter-molecular attraction at the liquid boundary, e.g. the rise or depression of liquids in narrow tubes. We use this term for capillary action.

Capillary rise and depression phenomenon depends upo