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MET 306Fluid Mechanics

Lecture # 1

Objective

Determine Unit and DimensionsIdentify the key fluid properties used in the

analysis of fluid behaviorCalculate common fluid properties given

appropriate informationExplain effects of fluid compressibilityUse the concept of viscosity and surface

tension

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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 dimensionm= unit used for length

Two system of the fundamental dimension1. FLT2. MLT

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Unit and Dimensions

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Unit and Dimensions

Example:

Most of the fluid problem required the basic fundamental dimension witch (MLT)

1: LTT

L

s

mVelocity

2: MLTmaFForce

The equation of the velocity for uniformly acceleration body

atVV o

Where:Vo is the initial velocity a is the acceleration t is the time

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Unit and Dimensions

Dimensionally homogeneousAll 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.

11

111

211

2

LTLT

LTLTLT

TLTLTLT

atVV o

The equation of the velocity for uniformly acceleration body is dimensionally homogeneous and the 2 is a constant number

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Unit and Dimensions

Dimensionally homogeneousCheck whether this equation is dimensionally homogeneous or NOT

1-Equation of a freely falling body

21.16 td Where d= distancet= time

2-Volume rate flow equation

ghAQ 261.0Where Q= Flow rateA= Areag= gravity h= height

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Systems of Units

International System (SI)British gravitational system(BG)

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Measures of Fluid Mass and Weight

DensityThe density of the fluid designated by Greek symbol (ρ)Defined as a mass per unit volumeUsed to characterize the mass of fluid BG= slugs/ ft3 and SI= kg/m3

Specific WeightThe specific weight of the fluid designated by Greek symbol (γ)Defined as weight per unit volumeUsed to characterize the weight of the systemBG= lb/ ft3 and SI= N/m3

Specific GravityThe specific gravity of the fluid designated by SGDefined as a ratio of the density of the fluid to the density of the waterThe density of the water @ 4oC is BG=1.94 slugs/ft3 and SI=1000 kg/m3

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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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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.

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

TRp

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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Viscosity Dynamic viscosity

dy

du BG and SI

Slug/ft s Kg/ms

See Figure 1.1

Kinematic Viscosity

vSI

m2/s

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Viscosity

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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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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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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

22 RpR

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Surface Tension(σ)

ϴR2

hR2 h

cos22 RhR

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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.