Fluids

1
Chapter 11

• Fluids

2
Defining a Fluid

• Ability to flow
• Gas or liquid
• Difference between gas and liquid
• Liquid has a definite volume

3
Mass Density

• Mass per unit volume
• Symbol gt r????
• Units gt kg/m3

• Specific Gravity
• Ratio of density of a substance to the density of
  water at 4 C
• Density of water is 1000 kg/m3 at 4C

4
Pressure

• Force per unit area

• Units gt
• N/m2 pascal(Pa)
• psi
• 1 bar 105 Pa

5
Atmospheric Pressure

• Caused by the weight of air above
• Extremely large pressure
• 1 atm 1.013105 Pa
• Exerted in all directions
• Barometers measure pressure

6
Pressure and Depth

• Fluid pressure increases with depth

7
Pressure and Depth

• Gauge pressure is only pressure relative to the
  atmospheric pressure
• Absolute or Total pressure must include the
  pressure of the atmosphere

8
Example Problem

• How much pressure would a submarine have to
  withstand at a depth of 5 km in the ocean? (? of
  sea water1.025 103kg/m3)

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Example Problem
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Example Problem
11
Pascals Principle

• Applied pressure to a fluid in a closed container
  is transmitted equally throughout the fluid
• Example Hydraulic lifts

12
Archimedes Principle

• A Buoyant Force that acts upward on an object
  submerged in or floating on a liquid

• Apparent weight of the object will be less

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Archimedes Principle
14
Archimedes Principle
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Archimedes' Principle

• A buoyant force is equal to the weight of the
  fluid displaced

FB
Fg
16
Floating Object
FB

• Net force is zero on floating object

Fg
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Archimedes' Principle

• Submerged object

FB
Fg
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Archimedes Principle

• Objects will float if the density of the object
  is less than or equal to the density of the liquid

19
Example Problem

• A piece of metal weighs 100.0 N in the air and 68
  N in water. What is the density of the metal?
  (Density of water1.00103kg/m3)

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Example Problem
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Example Problem
22
Fluids in Motion

• Steady vs Unsteady Flow
• Steady flow
• Velocity of particles at any point is constant
• Velocity at another point may be different, but
  still constant for that point
• RiverFaster in the center and slower on the
  edges
• Unsteady flow
• Velocity of particles at a point continually
  changes
• Turbulent flow-an extreme case of unsteady flow
• River Rapids

23
Fluid in Motion

• Compressible vs Incompressible
• Incompressible
• Density of fluid is constant
• Liquids
• Compressible
• Gases are highly compressible

24
Fluid in Motion

• Viscous vs Nonviscous
• Viscous
• Does not flow readily
• One layer hinders other layers from flowing
  freely
• Honey-High Viscosity
• Water-Low viscosity
• No real fluid is nonviscous

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Ideal Fluid

• Incompressible
• Non-viscous
• Non-turbulentwould form nice straight constant
  streamlines

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Equation of Continuity

• Mass flow rate
• mass of fluid per second that flows through a
  tube
• Kg/s

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Equation of Continuity

• Mass flow rate is constant for any given section
  of pipe
• What enters at one end of the pipe, must exit the
  other side of the pipe

• Thus, fluids will flow faster if size of tube
  gets smaller.

• Incompressible fluid
• Density is constant
• Called the volume flow rate

28
Example Problem

• Water flows through a 4.1 m diameter tunnel at a
  speed of 3.0 m/s. It then enters a 2.7m tunnel
  at the same level where the pressure is 82 kPa.
• Find the velocity of the water in the small
  tunnel.

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Example Problem
30
Bernoullis Equation

• Pressure in a fluid is inversely proportional to
  fluid velocity
• Explains unbalanced force in acceleration of
  fluids
• Lift in planes
• As a fluid raises its elevation, the pressure
  decreases because of less fluid above it

31
Principles of Fluid Flow

• Bernoullis Equation
• Conservation of energy in fluids
• Work-energy theorom
• Uses energy per unit volume

32
Example Problem

• A large storage tank, open at the top, develops a
  hole 5 m below the surface of the water. What is
  the velocity of the water when it leaves the
  hole?

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Example Problem
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Example Problem
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Example Problem

• Water flows through a 4.1 m diameter tunnel at a
  speed of 3.0 m/s. It then enters a 2.7m tunnel
  at the same level where the pressure is 82 kPa.
• Find the pressure in the wide portion of the
  tunnel.

36
Viscous Flow

• Fluid Flow is hindered by viscosity
• A fluid is visualized as thin layers
• Slowest at a boundary
• Fastest at the center
• Called Laminar flow
• A force is required to keep offset the forces
  from neighboring layers

37
Viscous Flow

• Force required to move any layer depends on
• Area of contact(A)
• Velocity of layer(v)
• Distance from immobile surface(y)
• Coefficient of viscocity (?)Units are Pa?s

38
Viscous Flow

• This force is caused by a difference in pressure
  between two points in a pipe for viscous flow
• Flow rate depends on
• Pressure difference
• Radius of pipe
• Length of pipe
• Viscosity of fluid