Fluid Properties Modular Unit

Ministry of Higher Education & Scientific Research
Foundation of Technical Education
Technical College of Basrah
CH1: Fluid Properties
Training Package
in
Fluid Mechanics
Modular unit 1
Fluid Properties
By
Risala A. Mohammed
M.Sc. Civil Engineering
Asst. Lect.
Environmental & Pollution Engineering Department
2011

1- Over view
1-1 Target population
For the students of second class in
Environmental engineering Department in
Technical College

1-2 Rationale
The study of fluids properties represent a very
important input for the study of fluid mechanics. Where it
is very important that the student learns the characteristics
and properties of the fluid like density ,viscosity, and
specific gravity. Where these terms will be used in the
equations and derivations in subsequent chapters , such as
pressure and energy equations.

1-3 Central Idea
The main goals of this chapter are:-
1- Define the fluid.
2- Know the properties of fluid.

1-4 Instructions
1- Study over view thoroughly
2- Identify the goal of this modular unit
3- Do the Pretest and if you :-
*Get 9 or more you do not need to proceed
*Get less than 9 you have to study this modular
4- After studying the text of this modular unit , do the post test
and if you :-
*Get 9 or more , so go on studying modular unit two
*Get less than 9 , go back and study the modular unit one

1-5 Performance Objectives
At the end of this modular unit the student will be able
to :-
1- Define the fluid
2- Define the fluid density, specific gravity, surface tension,
Vapour pressure, elasticity and viscosity of fluid
3- calculate :
• Fluid density
• Specific gravity
• Bulk modulus of elasticity
• Shear stress
• Coefficient of viscosity

2- Pre test
-
Choose the Correct Answer( 10 mark):
1- The branch of Engineering-science, which deals with water at rest or in motion is called
(a) hydraulics (b) fluid mechanics (c) applied mechanics (d) kinematics.
2- A solid can resist which of the following stresses?
(a) Tensile (b) Compressive (c) Shear (d) All of the above.
3- ……….possesses no definite volume and is compressible.
(a) Solid (b) Liquid (c) Gas (d) Vapour.
4- Compressibility is the reciprocal of
(a) bulk modulus of elasticity (b) shear modulus-of elasticity
(c) Young's modulus of elasticity (d) any of the above.
5- ratio of the specific weight of the liquid to the specific weight of a standard fluid is known as
(a) specific volume (b) weight density (c) specific gravity (d) viscosity.

Pre test
-
 6- The property of a fluid which determines its resistance to shearing stress is called
 (a) viscosity (b) surface tension (c) compressibility (d) none of the above
 7- Fluids which do not follow the linear relationship between shear stress and rate of deformation are
 termed as .... fluids.
 (a) Newtonian (b) Non-Newtonian (c) dilatent (d) ideal
 8- The viscosity of liquids ..... with increase in temperature.
 (a) Decreases (b) increases
 (c) first decreases and then increases (d) first increases and then decreases.
 9- Surface tension is caused by the force of ..... at the free surface.
 (a) cohesion (b) adhesion (c) both (a) and (b) (d) none of the above.
 10- Which of the following is an example of phenomenon of surface tension?
 (a) Rain drops (b) Rise of sap in a tree (c) Break up of liquid jets (d) All of the above.
Not
Check your answers in key answer page

3- The Text
3-1 Introduction
-
A fluid is defined as a substance that continually deforms (flows)
under an applied shear stress regardless of how small the applied
stress. All liquids and all gases are fluids. Fluids are a subset of the
phases of matter and include liquids, gases, plasmas and, to some
extent, plastic solids .
Liquids flow under gravity until they occupy the lowest possible
regions of their containers (they have defined volume but not a defined
shape). Gases expand to fill their container (they have no neither
defined shape and volume
Liquids form a free surface (that is, a surface not created by the
container) while gases do not.

3-2 Density
Density of a fluid, ,
Definition: mass per unit volume,
slightly affected by changes in
temperature and pressure.
 = mass/volume = m/
Units: M/L3

Fluid Density.
The density of
water at 4ºC is
1000 kg/m3 [1
kg/l] [1 g/cm3]
The density
of air at 0ºC
and 1 atm of
pressure is
1.293 kg/m3
dV
dm


Density of water
versus temperature
Build a table of
densities of Gold,
Mercury, Water,
Wood, Air, and
Helium. Include also
typical soil density,
Temp
(°C)
Density
(g/cm3)
30 0.9957
20 0.9982
10 0.9997
4 1.0000
0 0.9998
−10 0.9982
−20 0.9935
−30 0.9839

3-3 Specific Weight
-
Specific weight of a fluid, 
Definition: weight of the fluid per unit volume
Arising from the existence of a gravitational force
The relationship  and g can be found using the following:
Since  = m/
 = g
therefore
Units: F/L3
Typical values:
Water = 9814 N/m3;
Air = 12.07 N/m3

3-4 Specific gravity -
The specific gravity (or relative density) can be defined in two
ways:
Definition 1: A ratio of the density of a liquid to the density
of water at standard temperature and pressure
(STP) (20C, 1 atm), or
Definition 2: A ratio of the specific weight of a liquid to the
specific weight of water at standard
temperature and pressure (STP) (20C, 1 atm),
STP
water
liquid
STP
water
liquid
SG
@
@ 






Example(1)
A reservoir of oil has a mass of 825 kg. The reservoir has a
volume of 0.917 m3. Compute the density, specific weight, and
specific gravity of the oil.
Solution:
3
/
900
917
.
0
825
m
kg
m
volume
mass
oil 





3
oil m
/
N
8829
81
.
9
x
900
g
mg
volume
weight








9
.
0
998
900
@



STP
w
oil
oil
SG



3-5 Surface Tension
• Surface tension coefficient s can be defined as the intensity of
intermolecular traction per unit length along the free surface of
a fluid, and its SI unit is N/m.
• The surface tension effect is caused by unbalanced cohesion
forces at fluid surfaces which produce a downward resultant
force which can physically seen as a membrane.
• The coefficient is inversely proportional to temperature and is
also dependent on the type of the solid interface.
• For example, a drop of water on a glass surface will have a
different coefficient from the similar amount of water on a
wood surface.

Surface Tension
The effect may be becoming significant for small fluid system such as liquid
level in a capillary, as depicted in Fig. 1.6, where it will decide whether the
interaction form by the fluid and the solid surface is wetted or non-wetted.
If the adhesion of fluid molecules to the adjacent solid surface is stronger
than the intermolecular cohesion, the fluid is said to wet on the surface.
Otherwise, it is a non-wet interaction.

Surface Tension
 The pressure inside a drop of fluid can be calculated using a free-body diagram of a
spherical shape of radius R cut in half, and the force developed around the edge of
the cut sphere is 2R.
 This force must be balance with the difference between the internal pressure pi and
the external pressure pe acting on the circular area of the cut. Thus,
2R = pR2
p = pi –pe = 2
R

Example(2)
Calculate the capillary effect in millimetres in a glass tube of 4 mm diameter when immersed in
(i) water and (ii) mercury. The temperature of the liquid is 2 c and the value of surface tension
of water and mercury at 20C in contact with air are 0.073 5 Nlm and 0.51 Nm respectively.
The contact angle for water q= 0’ and for mercury q =130’Take specific weight of water at
20°C as equal to 9790 N/m3.
solution

3-6 Vapour pressure
• Vapour pressure is the partial pressure produced by fluid vapour in an
open or a closed container, which reaches its saturated condition or the
transfer of fluid molecules is at equilibrium along its free surface.
• In a closed container, the vapour pressure is solely dependent on
temperature. In a saturated condition, any further reduction in
temperature or atmospheric pressure below its dew point will lead to the
formation of water droplets.
• On the other hand, boiling occurs when the absolute fluid pressure is
reduced until it is lower than the vapour pressure of the fluid at that
temperature.
• For a network of pipes, the pressure at a point can be lower than the
vapour pressure, for example, at the suction section of a pump.
Otherwise, vapour bubbles will start to form and this phenomenon is
termed as capitation.

3-7 Elasticity (Compressibility)
• If pressure acting on mass of fluid increases: fluid contracts
• If pressure acting on mass of fluid decreases: fluid expands
• Elasticity relates to amount of deformation for a given change in
pressure
Vdp
dV 
Vdp
E
dV
v
1




d
dp
V
dV
dp
Ev 

 Ev = bulk modulus of elasticity

3-8 Viscosity
• Viscosity, , is a measure of resistance to fluid flow as a result of
intermolecular cohesion. In other words, viscosity can be seen as
internal friction to fluid motion which can then lead to energy
loss.
• Different fluids deform at different rates under the same shear
stress. The ease with which a fluid pours is an indication of its
viscosity. Fluid with a high viscosity such as syrup deforms more
slowly than fluid with a low viscosity such as water. The viscosity
is also known as dynamic viscosity.
 Units: N.s/m2 or kg/m/s
 Typical values:
Water = 1.14x10-3 kg/m/s; Air = 1.78x10-5 kg/m/s

Viscosity
• The viscosity of a gas increases with temperature, but the viscosity of
a liquid decreases with temperature – it can be explained by examining
the causes of viscosity.
• The resistance of a fluid to shear depends upon its cohesion and upon its
rate of transfer of molecular momentum.
• A liquid, with molecules much more closely spaced than a gas, has
cohesive forces much larger than a gas. Cohesion - predominant cause of
viscosity in a liquid; and since cohesion decreases with temperature, the
viscosity does likewise
• A gas, on the other hand, has very small cohesive forces. Most of its
resistance to shear stress is the result of the transfer of molecular
momentum.

Viscosity
Flow between a fixed and a moving plate
Fluid in contact with plate has same velocity as plate (no slip condition)
u = x-direction component of velocity
u=V
Moving plate
Fixed plate
y
x
V
u=0
B y
B
V
y
u 
)
( Fluid

Viscosity
Flow through a long, straight pipe
Fluid in contact with pipe wall has same velocity as wall
(no slip condition)
u = x-direction component of velocity
r
x
R
















2
1
)
(
R
r
V
r
u
V
Fluid

Viscosity
 Shear-stress relations for different fluids
 Newtonian fluids: linear relationship
 Slope of line = coefficient of proportionality) = “viscosity
 Newton’s Law of Viscosity
 Viscosity
 Units
dy
dV


dy
dV

 
dy
dV /

 
2
2
/
/
/
m
s
N
m
s
m
m
N 

V
V+dv

kinematic viscosity
 μ - absolute viscosity or the dynamic viscosity
 ν - kinematic viscosity (the ratio of viscosity to mass density):
- occurs in many applications (e.g., in the dimensionless Reynolds
number for motion of a body through a fluid, Vl/ν, in which V is
the body velocity and l is a representative linear measure or the body
size)
 The dimensions of ν are L2T-1.
 SI unit: 1 m2/s, has no name.
 Viscosity is practically independent of pressure and depends upon
temperature only.
– The kinematic viscosity of liquids, and of gases at a given pressure,
is substantially a function of temperature.

Example(3)

Example(4)

Example(5)

Example(6)
A 400 mm diameter shaft is rotating at 200 r.p.m. in a bearing of length 120 mm. If the thickness
of oil film is 1.5 mm and the dynamic viscosity of the oil is 0.7 N.s/m2• determine
(i) Torque required to overcome friction in bearing; ~
(ii) Power utilized in overcoming viscous resistance.

Example(6)

4- Post test
Q1))
Determine the viscosity of fluid between shaft
and sleeve in Fig. shown below
Q2))
Water in a hydraulic press, initially at 20 psia, is subjected to a pressure of 17000 psia
at 68 OF. Determine the percentage decrease in specific volume if the average bulk
modulus of elasticity is 365 000 psi.
Q3))
The surface tensions of mercury and water at 60 "C are 0.47 N/m and 0.0662 N/m,
respectively. What capillary-height changes will occur in these two fluids when they are
in contact with air in a glass tube of radius 0.30 mm? Use (q= 130° for mercury, and 00
for water;  = 132.3 kN/m3 for mercury, and 9.650 kN/m3 for water.
Q4))
. A metal plate 1.25 m x 1.25 m x 6 mm thick and weighing 90 N is placed midway in the
24 mm gap between the two vertical plane surfaces. The gap is filled with an oil of specific
gravity 0.85 and dynamic viscosity 3.0 N.s/m2• Determine the force required to lift the
plate with a constant velocity of 0.15 m/s.
2.5 mark for each equation

5- Key answer
pre test
1- ( a ) 2- ( d ) 3- ( c ) 4- ( a ) 5- ( c )
6- ( a ) 7- ( b ) 8- ( a ) 9- ( a ) 10- ( d )
post test
Q1))

Key answer
Q2))
Q3))

Key answer
Q4))

6- References
1. Evett, J., B. and Liu, C. 1989 “2500 solved problems in fluid mechanics and
hydraulics” Library of Congress Cataloging- in-Publication Data, (Schaum's
solved problems series) ISBN 0-07-019783-0
2. Rajput, R.,K. 2000 “ A Text Book of Fluid Mechanics and Hydraulic
Machines”. S.Chand & Company LTD.
3. White, F., M. 2000 “ Fluid Mechanics”. McGraw-Hill Series in Mechanical
Engineering.
4. Wily, S., 1983 “ Fluid Mechanics”. McGraw-Hill Series in Mechanical
Engineering.

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