1
KTU ONLINE STUDY APP
MECHANICS OF FLUIDS
2019 SCHEME – MECHANICAL
MODULE -1
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KTU ONLINE STUDY APP
FLUID MECHANICS
Fluid mechanics is that branch of engineering science which deals with the behaviour of fluid (liquids
and gases) under the conditions of rest and in motion
Fluid mechanics branches in to:
Fluid statics: study of incompressible fluids at rest
Fluid kinematics: it deals with velocities and accelerations and the patterns of flow without considering
the forces or energy causing the motion
Fluid Dynamics: it deals with the relations between velocities, accelerations of fluid with the forces or
energy causing motion
What is a Fluid?
A fluid is a substance which deforms continuously when subjected to external shear stress however
small the shear stress may be.
Both liquids and gases come under the category of fluids. Liquid are difficult to compress whereas gases
can be compressed easily.
KNUDSEN NUMBER
It is the ratio of mean free path to the characteristic length of flow
Kn = X / L, it is used to describe the degree of departure from continuum
Kn>0.01, the concept of continuum does not hold good
Any fluid can be treated as a continuous medium when kn<.01
PROPERTIES OF FLUIDS
1. Density or Mass Density (ρ)
Density or mass density of a fluid is defined as the ratio of mass of fluid to its volume
𝑚
ρ= 𝑣
SI unit: kg/m3 Dimension: M1 L-3
Measured using hydro meter or pycnometer
air 1.2 - water 1000 -mercury 13600- steel 7850- wood 600- gold 19600 kg/m3
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KTU ONLINE STUDY APP
2. Specific Weight or Weight Density (γ or w or ρg)
Specific weight or weight density of a fluid is the ratio between weight of fluid to its volume
𝑊 𝑚𝑔
w=γ= 𝑣 = 𝑣
=ρg
SI unit = N/m3
Specific weight of water = 1000 X 9.81 = 9810 N/m3
Air 11.77 N/m3 water -9.81, mercury 133.3,-steel 77, - wood 5.9, - gold 192.3 KN/m3
3. Specific Volume (Vs.)
Volume occupied by unit mass of fluid
1
Volume occupied by unit mass of fluid, Vs = 𝜌
It is the reciprocal of mass density, and its Unit is kg/m3
4. Specific gravity (S) or Relative density (RD) :
It is the ratio of mass density of any matter to the mass density of a standard fluid
𝜌 𝛾
S= =
𝜌𝑤𝑎𝑡𝑒𝑟 𝛾𝑤𝑎𝑡𝑒𝑟
No units
4. Viscosity -Newton’s laws of viscosity
Viscosity is defined as the property of a fluid which offers resistance to the movement of one layer of
fluid over another adjacent layer of fluid
The top surface causes a shear stress on
the adjacent lower layer while the lower
layer causes a shear stress on the adjacent
top layer.This shear stress is directly
proportional to the rate of change of
velocity
𝑑𝑢 𝑑𝑢
τα or τ=µ where µ is constant of proportionality called coefficient of
𝑑𝑦 𝑑𝑦
dynamic viscosity or viscosity. This relation is also called the newton’s laws of viscosity.
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KTU ONLINE STUDY APP
Units and Dimensions for Dynamic Viscosity (µ)
SI unit: pa.sec or N. sec / m2
CGS: Poise = Dyne.sec /cm2
Conversion 1 poise = 0.1 pa.sec
Dimension: ML-1T-1
Note :-
If viscosity is given in poise, it must be divideD by 10 to gets it equivalent numerical value in SI
units
Sometimes a unit of centipoise is used where
1
1 centipoise = 100poise
The viscosity of water at 200 C is 0.01 poise or 1 centipoise
KINEMATIC VISCOSITY
It is defined as the ratio between the dynamic viscosity and density of fluid
It is denoted by Greek symbol ʋ (nu)
dynamic viscosity µ
ʋ= =
mass density 𝜌
Units
SI system: m2/sec
CGS : cm2/sec
One stoke =1 cm2/sec=10-4 m2/sec
Dimension: L2T-1
KTU ONLINE STUDY APP
MECHANICS OF FLUIDS
2019 SCHEME – MECHANICAL
MODULE -1
, 2
KTU ONLINE STUDY APP
FLUID MECHANICS
Fluid mechanics is that branch of engineering science which deals with the behaviour of fluid (liquids
and gases) under the conditions of rest and in motion
Fluid mechanics branches in to:
Fluid statics: study of incompressible fluids at rest
Fluid kinematics: it deals with velocities and accelerations and the patterns of flow without considering
the forces or energy causing the motion
Fluid Dynamics: it deals with the relations between velocities, accelerations of fluid with the forces or
energy causing motion
What is a Fluid?
A fluid is a substance which deforms continuously when subjected to external shear stress however
small the shear stress may be.
Both liquids and gases come under the category of fluids. Liquid are difficult to compress whereas gases
can be compressed easily.
KNUDSEN NUMBER
It is the ratio of mean free path to the characteristic length of flow
Kn = X / L, it is used to describe the degree of departure from continuum
Kn>0.01, the concept of continuum does not hold good
Any fluid can be treated as a continuous medium when kn<.01
PROPERTIES OF FLUIDS
1. Density or Mass Density (ρ)
Density or mass density of a fluid is defined as the ratio of mass of fluid to its volume
𝑚
ρ= 𝑣
SI unit: kg/m3 Dimension: M1 L-3
Measured using hydro meter or pycnometer
air 1.2 - water 1000 -mercury 13600- steel 7850- wood 600- gold 19600 kg/m3
, 3
KTU ONLINE STUDY APP
2. Specific Weight or Weight Density (γ or w or ρg)
Specific weight or weight density of a fluid is the ratio between weight of fluid to its volume
𝑊 𝑚𝑔
w=γ= 𝑣 = 𝑣
=ρg
SI unit = N/m3
Specific weight of water = 1000 X 9.81 = 9810 N/m3
Air 11.77 N/m3 water -9.81, mercury 133.3,-steel 77, - wood 5.9, - gold 192.3 KN/m3
3. Specific Volume (Vs.)
Volume occupied by unit mass of fluid
1
Volume occupied by unit mass of fluid, Vs = 𝜌
It is the reciprocal of mass density, and its Unit is kg/m3
4. Specific gravity (S) or Relative density (RD) :
It is the ratio of mass density of any matter to the mass density of a standard fluid
𝜌 𝛾
S= =
𝜌𝑤𝑎𝑡𝑒𝑟 𝛾𝑤𝑎𝑡𝑒𝑟
No units
4. Viscosity -Newton’s laws of viscosity
Viscosity is defined as the property of a fluid which offers resistance to the movement of one layer of
fluid over another adjacent layer of fluid
The top surface causes a shear stress on
the adjacent lower layer while the lower
layer causes a shear stress on the adjacent
top layer.This shear stress is directly
proportional to the rate of change of
velocity
𝑑𝑢 𝑑𝑢
τα or τ=µ where µ is constant of proportionality called coefficient of
𝑑𝑦 𝑑𝑦
dynamic viscosity or viscosity. This relation is also called the newton’s laws of viscosity.
, 4
KTU ONLINE STUDY APP
Units and Dimensions for Dynamic Viscosity (µ)
SI unit: pa.sec or N. sec / m2
CGS: Poise = Dyne.sec /cm2
Conversion 1 poise = 0.1 pa.sec
Dimension: ML-1T-1
Note :-
If viscosity is given in poise, it must be divideD by 10 to gets it equivalent numerical value in SI
units
Sometimes a unit of centipoise is used where
1
1 centipoise = 100poise
The viscosity of water at 200 C is 0.01 poise or 1 centipoise
KINEMATIC VISCOSITY
It is defined as the ratio between the dynamic viscosity and density of fluid
It is denoted by Greek symbol ʋ (nu)
dynamic viscosity µ
ʋ= =
mass density 𝜌
Units
SI system: m2/sec
CGS : cm2/sec
One stoke =1 cm2/sec=10-4 m2/sec
Dimension: L2T-1
