1. MET 306
Fluid Mechanics
Lecture # 1
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2. Objective
Determine Unit and Dimensions
Identify the key fluid properties used in the
analysis of fluid behavior
Calculate common fluid properties given
appropriate information
Explain effects of fluid compressibility
Use the concept of viscosity and surface
tension
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3. Unit and Dimensions
A dimensions is used to measured the physical
quantity with out numerical value.
A unit is the way to assign a number to
dimension
 L= length is dimension
 m= unit used for length
Two system of the fundamental dimension
1. FLT
2. MLT
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4. Unit and Dimensions
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5. Unit and Dimensions
Example:
m L 1
Velocity : LT
s T
Most of the fluid problem required the basic fundamental dimension
witch (MLT)
2
Force : F ma MLT
The equation of the velocity for uniformly acceleration body
V Vo at
Where:
Vo is the initial velocity
a is the acceleration
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t is the time

6. Unit and Dimensions
Dimensionally homogeneous
All theoretically derived equation are dimensionally homogeneous that is the
dimensions of the lift side of the equation must be the same as those on the right side.
V Vo at
1 1 2
LT LT LT T
1 1 1
LT LT LT
1 1
LT 2 LT
The equation of the velocity for uniformly acceleration body is dimensionally
homogeneous and the 2 is a constant number
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7. Unit and Dimensions
Dimensionally homogeneous
Check whether this equation is dimensionally homogeneous or NOT
1-Equation of a freely falling body
2
d 16 . 1t
Where
d= distance
t= time
2-Volume rate flow equation
Where Q 0 . 61 A 2 gh
Q= Flow rate
A= Area
g= gravity
h= height
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8. Systems of Units
International System (SI)
British gravitational system(BG)
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9. Measures of Fluid Mass and Weight
 Density
 The density of the fluid designated by Greek symbol (ρ)
 Defined as a mass per unit volume
 Used to characterize the mass of fluid
 BG= slugs/ ft3 and SI= kg/m3
 Specific Weight
 The specific weight of the fluid designated by Greek symbol (γ)
 Defined as weight per unit volume
 Used to characterize the weight of the system
 BG= lb/ ft3 and SI= N/m3
 Specific Gravity
 The specific gravity of the fluid designated by SG
 Defined as a ratio of the density of the fluid to the density of the water
 The density of the water @ 4oC is BG=1.94 slugs/ft3 and SI=1000 kg/m3
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10. Measures of Fluid Mass and Weight
Specific Gravity (Example)
Calculate the density of the mercury in two system
BG and SI by knowing the SGmercury @ 4oC is 13.55
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11. Ideal Gas Law
 Gas are highly compressible in comparison to
liquid, So from the Ideal gas law change in the
temperature or the pressure of the gases can
directly change the density.
p R T
Where p is the absolute pressure, ρ is the density, T
is the absolute temperature and R is gas constant
 R=R/m
 R is universal gas constant 8314.3J/kg mole K
 m is the molar mass
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12. Ideal Gas Law
Example
The absolute pressure and temperature of a gas in large
chamber are found to be 500 kPa and 60oC respectively. Find
the density if the air has m =28.97
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13. Viscosity
 Dynamic viscosity
BG and SI
du
Slug/ft s Kg/ms
dy
See Figure 1.1
SI
Kinematic Viscosity v m2/s
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14. Viscosity
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15. Viscosity
 Example
Determine the value of the Reynolds number using SI system
for fluid with viscosity of 0.38 N.s/m2 and specific gravity of
0.91 flow into pipe with diameter of 25 mm with velocity of
2.6 m/s.
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18. Surface Tension
 At interface between a liquid and the gas forces
develop in the liquid surface which case the surface to
behave as “skin” or “membrane”
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19. Surface Tension(σ)
The pressure inside the drop can be calculated using free body diagram .
The force developed around the edge due to the surface tension is 2πRσ
this force must be balance by the pressure difference
2
2 R p R
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20. Surface Tension(σ)
2 R 2
ϴ R h 2 R cos
2
R h h
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21. Surface Tension(σ)
Example
What diameter of clean glass tubing is required to
rise water at 20oC in tube to 1mm. Where σ of
water is 0.0728 N/m and the θ =0.
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