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CE6451 Fluid Mechanics and Machinery
What is Fluid Mechanics? First, what is a fluid?
Three common states of matter are solid, liquid, and gas.
A fluid is either a liquid or a gas.
Fluid:A fluid is a substance which is capable of flowing. A fluid
may be classified in to Liquid, gas and Vapour.
Next, what is mechanics? Mechanics is essentially the application of the laws of
force and motion. Conventionally, it is divided into two
branches, statics and dynamics.
Fluid Mechanics:
It deals with the behavior of fluid under the condition of
rest and motion. It may be divided in to three parts: Statics,
Kinematics and dynamics.
UNIT I FLUID PROPERTIES AND FLOW CHARACTERISTICS
Units and dimensions‐ Properties of fluids‐ mass density, specific weight, specific
volume, specific gravity, viscosity, compressibility, vapor pressure, surface tension
and capillarity. Flow characteristics – concept of control volume ‐ application of
continuity equation, energy equation and momentum equation.
Fluid Properties: 1. Density
2. Specific Gravity
3. Viscosity
4. Surface Tension
5. Capillarity
6. Compressibility
7. Bulk modulus
8. Vapour pressure
Density:
Mass density or specific mass: ρ
The density of a fluid is defined as its mass per unit volume at
standard temperature and pressure.
fluidtheofVolumefluidtheofMass
=ρ
ρ=m/v
unit , kg/m3
For water, ρ = 1000 kg/m3
Specific Weight or weight density: wIt is defined as Weight per unit volume at
standard temperature and pressure
gfluidofVolume
fluidofMassfluidofVolumefluidofWeightw ×==
w = ρg ;Unit: N/m3 ; w for water=9.81 kN/m3
Specific Volume: vIt is defined as Volume per unit mass of the fluid.
v=V/m = 1/ρ
Unit, m3/kg1 m3 = 1000 litres
Specific Gravity : S
It is the ratio of the specific weight of the liquid to thespecific weight of the standard fluid.
waterpure theof weight Specificliquid theof weight specific
=avitySpecificGr
Weight Density of Liquid= S X Weight density of water= S X 1000 X 9.81 N/m3
Density of Liquid= S X density of water= S X 1000 kg/m3
Kinematic viscosity:It is defined as the ratio between the dynamic viscosity and mass density of fluid.
Units: m2/s ; 1 Stroke = 10-4 m2/s
Viscosity:Dynamic viscosity:
Viscosity is defined as the property of fluid which offers resistance to flow.
Unit : Ns/m2 ; 1 Poise = (1/10) Ns/m2 ; 1 Centipoise= (1/100) Poise
,,dydu
dydu μττα =
ρμν =
Dynamic Viscosity
ForceArea
Shear stress ( τ)
Shear rate (du/dy)
Slope of lineμ =
dyduτμ =
Types of Fluids:
Shear stress
Shear rate du/dy
Ideal Solid
Ideal Fluid
Ideal Fluid:
A fluid, which is incompressible and is having no viscosity, is known as Idealfluid. It is only imaginary Fluid
Real Fluid:
A fluid, which is having viscosity, is known as Real fluid. All fluids are Realfluids.
Newtonian fluids:
These fluids follow Newton’s viscosity equation. For such fluids μ does notchange with rate of deformation. Exp. Water, Kerosene etc.,
Non Newtonian fluids:
There fluids which do not follow the linear relationship between the shearstress and the rate of deformation. Exp. Polymer solutions, Blood et.,
Compressibility:When a fluid is subjected to a pressure increase the
volume of the fluid decreases. It is known as compressibility. Itis reciprocal of bulk modulus.
Compressibility = 1/k
Bulk modulus:It is define as the ratio of compressive stress to volumetric
strain.
The negative sign indicates the volume decreases as pressureincreases.
Unit :‐
vdvdpk −=
2mN
Surface Tension of Liquids
The phenomenon of surface tension arises due to the two
kinds of intermolecular forces. Surface Tension is caused by
the force of cohesion at the free surface.
(i) Cohesion : The force of attraction between the molecules of
the same liquid. Surface tension is due to cohesion between
particles at the free surface.
(ii) Adhesion : The force of attraction between unlike molecules
of a solid boundary surface in contact with the liquid
Case I ‐Water droplet:Let, P= Pressure inside the droplet above outside pressureD= Diameter of the dropletσ = Surface tension of the liquid
i. Pressure force = and
ii. Surface tension force acting around the circumference =σx π d
Under equilibrium conditions these two forces will be equal and opposite,
2
4dP π
×
dp
ddP
σ
πσπ
44
2
=
×=×
Case II ‐ Soap bubble:
i. Pressure force = , andii. Surface tension force acting around the circumference =2(σXπd)
2
4dP π
×
( )
dp
ddP
σ
πσπ
8
24
2
=
×=×
( )
dp
ldlPσσ2
2
=
×=××
Case III‐ A liquid Jet:i. Pressure force = p x l x d , andii. Surface tension force acting around the circumference =σX 2l
Capillarity:
Capillarity is a phenomenon by which a liquid rises into a thin
glass tube above or below its general level. surface relative to the
adjacent level of the fluid is called capillarity.
This phenomenon is due to the combined effect of cohesion and
adhesion of liquid particles.
For water θ= 0
For mercury θ= 1400
Expression for Capillary Rise:
σ=Surface tension of the liquidθ= Angle of contact between the liquid and glass tube
ρ = Density of the liquid
The weight of the liquid of height h in the tube = (Area of the tube x h) x ρ x g
ghd ×××= ρπ 2
4Vertical component of the surface tensile force
θπσθσ
coscos)(
××=××=
dnceCircumfere
Equating these two eq. θπσρπ cos4
2 ××=××× dghd
dggd
dh××
=××
××=
ρθσ
ρπθπσ cos4
4
cos2
dgh
××=ρ
σ4If θ is equal to zero
Expression for Capillary Fall:
σ=Surface tension of the liquidθ= Angle of contact between the liquid and glass tube
ρ = Density of the liquid
Intensity of the pressure at the depth = (Area of the tube x h) x ρ x g
ghd ×××= ρπ 2
4Vertical component of the surface tensile force
θπσθσ
coscos)(
××=××=
dnceCircumfere
Equating these two eq. θπσρπ cos4
2 ××=××× dghd
gd
dh××
××=
ρπθπσ
2
4
cos
dgh
××=ρ
θσ cos4θ For mercury and glass tube is 138o
Vapour pressure:• All liquids have a tendency to evaporate when exposed to a
gaseous atmosphere. The vapour molecules exert a partial
pressure in the space above the liquid, known as vapour pressure.
Gas Laws:Boyle’s LawAt a given temperature for a given quantity of gas, the product
of the pressure and the volume is a constant.P1V1= P2V2
Ideal Gas Law:Ideal Gas Law relates pressure to Temp for a gas
P = ρRTT = Absolute temperature in oK unitsR= Gas constant = 287 Joule / Kg‐oK
Universal Gas constant:
PV=mRT
Where,M=Mass of gas in kg; V= Specific Volume.P=Absolute pressure ; T=Absolute temperature
Pressure in a Fluid
hgp ρ=
Pressure:Force per unit area: 1 N/m2 = Pascal = Pa
Standard Atmosphere P = 101.33 kPa = 101.3 kN/m2
=10.3 m of mg