Fluid Properties and Units

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Fluid Properties and Units

• CVEN 311

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Continuum

• All materials, solid or fluid, are composed of
  molecules discretely spread and in continuous
  motion.
• However, in dealing with fluid-flow relations on
  a mathematical basis, it is necessary to replace
  the actual molecular structure by a hypothetical
  continuous medium, called the continuum.

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Continuum

• In a continuum, the physical variable at a point
  in space is the averaged value of the variable in
  a small sphere.
• How good is the assumption?

3x1010 molecules of air
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Dimensions and Units

• The dimensions have to be the same for each term
  in an equation
• Dimensions of mechanics are
• length
• time
• mass
• force
• temperature

L
T
M
MLT-2
?
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Dimensions and Units

• Quantity Symbol Dimensions
• Velocity V LT-1
• Acceleration a LT-2
• Area A L2
• Volume ? L3
• Discharge Q L3T-1
• Pressure p ML-1T-2
• Gravity g LT-2
• Temperature T ?
• Mass concentration C ML-3

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Dimensions and Units

• Quantity Symbol Dimensions
• Density r ML-3
• Specific Weight g ML-2T-2
• Dynamic viscosity m ML-1T-1
• Kinematic viscosity ? L2T-1
• Surface tension ? MT-2
• Bulk mod of elasticity E ML-1T-2

fluid
These are _______ properties!
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How many independent properties? _____
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Definition of a Fluid

• a fluid, such as water or air, deforms
  continuously when acted on by shearing stresses
  of any magnitude. - Munson, Young, Okiishi

Water Oil Air Why isnt steel a fluid?
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Fluid Deformation between Parallel Plates
Side view
Force F causes the top plate to have velocity
U. What other parameters control how much force
is required to get a desired velocity?
Distance between plates (b)
Area of plates (A)
Viscosity!
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Shear Stress
dimension of
Tangential force per unit area
Rate of angular deformation
change in velocity with respect to distance
rate of shear
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Fluid classification by response to shear stress

• Newtonian
• Ideal Fluid
• Ideal plastic

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Rate of deformation
Shear stress ?
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Fluid Viscosity

• Examples of highly viscous fluids
• ______________________
• Fundamental mechanisms
• Gases - transfer of molecular momentum
• Viscosity __________ as temperature increases.
• Viscosity __________ as pressure increases.
• Liquids - cohesion and momentum transfer
• Viscosity decreases as temperature increases.
• Relatively independent of pressure
  (incompressible)

molasses, tar, 20w-50 oil
increases
increases
_______
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Example Measure the viscosity of water

• The inner cylinder is 10 cm in diameter and
  rotates at 10 rpm. The fluid layer is 2 mm thick
  and 10 cm high. The power required to turn the
  inner cylinder is 50x10-6 watts. What is the
  dynamic viscosity of the fluid?

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Solution Scheme

• Restate the goal
• Identify the given parameters and represent the
  parameters using symbols
• Outline your solution including the equations
  describing the physical constraints and any
  simplifying assumptions
• Solve for the unknown symbolically
• Substitute numerical values with units and do the
  arithmetic
• Check your units!
• Check the reasonableness of your answer

Solution
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Role of Viscosity

• Statics
• Fluids at rest have no relative motion between
  layers of fluid and thus du/dy 0
• Therefore the shear stress is _____ and is
  independent of the fluid viscosity
• Flows
• Fluid viscosity is very important when the fluid
  is moving

zero
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Dynamic and Kinematic Viscosity

• Kinematic viscosity (__) is a fluid property
  obtained by dividing the dynamic viscosity (__)
  by the fluid density

m2/s
Connection to Reynolds number!
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Density and Specific Weight

• Density (mass/unit volume) r ___________
• density of water
• density of air at atmospheric pressure and 15 ?C
• Specific Weight (weight per unit volume) g
• __________________

Specific mass
1000 kg/m3
1.22 kg/m3
g r g 9806 N/m3
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Perfect Gas Law
Note deviation from the text!

• PV nRT
• R is the universal gas constant
• T is in Kelvin

Use absolute pressure for P and absolute
temperature for T
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Bulk Modulus of Elasticity

• Relates the change in volume to a change in
  pressure
• changes in density at high pressure
• pressure waves
• _________
• ______ __________

-
Water
sound
water hammer
speed of sound
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Vapor Pressure
liquid
101 kPa
What is vapor pressure of water at 100C?
Connection forward to cavitation!
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Cavitation
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Cavitation Damage
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Surface Tension

• Pressure increase in a spherical droplet

DppR2
2pRs
Surface molecules
DppR2 2pRs
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Example Surface Tension

• Estimate the difference in pressure (in Pa)
  between the inside and outside of a bubble of air
  in 20ºC water. The air bubble is 0.3 mm in
  diameter.

R 0.15 x 10-3 m
s 0.073 N/m
Statics!
What is the difference between pressure in a
water droplet and in an air bubble?
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Outline the solution

• Restate the goal
• Identify the given parameters and represent the
  parameters using symbols
• Outline your solution including the equations
  describing the physical constraints and any
  simplifying assumptions

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Viscosity Measurement Solution
wr
2prh
r 5 cm t 2 mm h 10 cm P 50 x 10-6 W 10 rpm
Fwr