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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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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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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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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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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