3. DIMENSIONS AND UNITS:
is the measure by which a physical
variable is expressed quantitatively.
There are four Primary dimensions:
Mass (M),
Length (L),
Time (T) and
Temperature (t).
4. Types of quantities:
Geometry quantities:
The study of fluid under rest.
Kinematic quantities:
The study of fluid under motion (velocity,
acceleration)
Dynamic quantities:
The study of forces and their analysis causing
the fluid motion/deformation.
5. .
Quantity Common symbols Dimensions
Geometry Area A L2
Volume V L3
Second moment area I L4
Kinematics Velocity V LT-1
Acceleration a LT-2
Angular velocity ω T-1
Quantity of flow Q L3T-1
Dynamics Mass flow rate m MT-1
Force F MLT-2
Moment, Torque T ML2T2
Energy, Work, Heat E, W ML2T-2
Power P ML2T-3
Pressure, Stress P, ζ ML-1T-2
6. There are primary unit systems in use
1- International System of units (SI).
2- English Engineering System of units
(FPS).
3- French System of units (CGS).
4- American system of units (FSS).
Units:
is a particular way of attaching a
number to the quantitative dimension.
7. Dimension CGS unit FSS units FPS units SI units
Length (L) Centimeter
(cm)
Foot (ft) Foot (ft) Meter (m)
Mass (M) Gram (gm) Slug=32.2 IbM Pound
(IbM)
Kilogram
(kg)
Time (T) Second (sec) Second (sec) Second
(sec)
Second
(sec)
8. FLUID PROPERTIES
1- Density
2- Specific weight
3- Specific gravity (relative density)
4- Viscosity
5- Bulk modulus
6- capillary
7- Surface tension
9. 1- Density
The mass per unit volume of the fluid
V
m
Units: (Kg/m3)
The value of density of water is 1000 Kg/m3.
10. 2- Specific Weight
It is the ratio between the weights of the
fluid to its volume. The weight per unit
volume of the fluid is called weight
density
V
W
Units: (N/m3or Kg/m2/s2)
g
11. 3- Specific Gravity (S.G.)
The ratio of the specific weight (or
density) of a fluid to the specific weight
(or density) of a standard fluid.
For liquids the standard fluid taken is
water and for gases the standard liquid
taken is air.
Water
Liquid
Water
Liquid
G
S
.
.
12. Example:
The specific weight of a certain liquid is 85.3
Ib/ft3. Determine its density and specific
gravity.
3
2
3
slug/ft
65
.
2
ft /s
32.2
/ft
Ib
85.3
g
1.37
/ft
slug
1.94
/ft
slug
2.65
3
3
4
at
water 0
c
S.G. =
13. 4- Viscosity
It is defined as the property of a fluid which
offers resistance to the movement of one layer
of the fluid over another adjacent layer of the
fluid.
14.
15. The constant of proportionality is known as the
Dynamic viscosity
y
u
Newton’s law of viscosity
17. Example:
Crude oil having a viscosity of 9.52* 10-4 Ib s / ft2
contained between parallel plates. The bottom
plate is fixed and upper plate moves when a force
P is applied as shown. If the distance between two
plates is 0.1 in., what value of P is required to
translate the plate with a velocity of 3 ft/s?
the effective area of the upper plate is 200 in2.
18.
P plate area
y
u
dy
du
Ib
ft
in
ft
s
ft
ft
s
Ib
476
.
0
)
in
144
200
)(
)
12
/
1
.
0
(
/
3
)(
.
10
(9.52 2
2
2
2
4
-
P
19. 5- Bulk Modulus (K)
modulus is the modulus of elasticity for a
fluid. It is the ratio of the change in unit
pressure to the corresponding volume
change per unit volume
Volume
Original
Volume
in
Change
=
Modulus
Bulk
pressure
in
Change
K
dP
V
V
d
21. Surface tension can be defined as the force
act normal to a meter-long hypothetical line
drawn on the fluid surface.
Surface tension is the reason for capillary
rise and capillary depression, soap bubbles,
allowing small insects to sit on the liquid
surface, etc.
= F/L
22. CAPILLARITY
Capillarity is defined as a phenomenon of rise or
fall of a liquid surface in a small tube relative to
the adjacent general level of liquid when the
tube is held vertically in the liquid.
Cohesion: it is the force of attraction between
similar types of molecules.
adhesion: it is the force of attraction between
liquids and solid containing liquid.
