Transcript ME 101

ME 101:
Fluids Engineering
Chapter 6
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ME-101
Two Areas for Mechanical Engineers
Fluid Statics
– Deals with stationary objects
• Ships, Tanks, Dams
– Common calculations:
• Pressure
• Buoyancy
Fluid Dynamics
– Either fluid or object is in motion
– Calculations include:
• Flow Rate, Velocity, Drag Force, Lift Force, etc.
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Mechanical Engineers
• Typical fluids
– Water, Air, Oil, Nitrogen, Coolants, etc.
• Why is it important?
– 98% of electricity in US is generated by some form of fluid
process (hydroelectric, steam turbines, wind)
– Aeronautics
– Biomedical
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What is a Fluid?
Substance unable to resist a shear force without moving
– Deforms continuously when subjected to a shear stress
– Motion continues until force is removed
Flow – Response of a fluid to shear stress
that produces a continuous motion
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Two types of Fluids
• A liquid is an incompressible fluid
– Water, Oil, Coolants, Gasoline, etc.
• A gas can be easily compressed
– Air, Nitrogen, Propane, etc.
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Properties of Fluids
What is a fluid shear force?
Example: Consider a deck of cards
Top card moves the most, bottom card is stationary
– No-slip at solid-fluid boundary – stationary
– Each layer moves at different speed
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Newtonian Fluid
F

A
Applied force balanced
by shear stress exerted
by the fluid on the plate
v
 
h
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Viscosity
v
 
h
 - measure of friction or
resistance to shear force
Honey has higher
viscosity than water
Often see cP (centipoise)
Water = 1cP at Room Temperature
8
kg
1 P  0.1
m s
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What happens when fluids interact with solids?
The forces created are known as buoyancy, drag, and lift
– Buoyancy is the force developed when a solid object is immersed in
a fluid (no relative motion)
– Lift and Drag forces arise when fluids interact with a solid object
(relative motion)
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Why Does Pressure Increase with Depth?
Pressure grows in direct proportion to the
depth and density of the fluid
p1 A  po A   hAg
p1  po   gh
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Buoyancy
FB  W   fluid gVobject
W
FB
Buoyancy force is related to the weight of the fluid displaced
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Laminar and Turbulent Flows
Laminar Flow
Turbulent Flow
Irregular flow pattern –
fluid moving fast, flow
patterns break up,
become random
Fluid flows smoothly –
associated with slow
moving fluids (relatively)
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What determines laminar or turbulent flow?
• Must consider the following:
– Size of object moving through fluid (or size of pipe/duct fluid
is flowing through)
– Speed of object (or of fluid)
– Density and viscosity of fluid
• Exact relationship among these variables discovered
by British engineer Osborne Reynolds
• Reynolds number
– Dimensionless parameter describes that transition
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Reynolds Number
– l is a characteristic length – pipe diameter, diameter of sphere,
diameter of air duct, etc.
– ν is velocity
– ρ is density
– µ is viscosity
 vl
Re 

Ratio between the inertia (density related) and viscous forces
(viscosity related) acting within a fluid
– When fluid moves quickly or is not very viscous or dense, Re large,
inertia disrupts the flow – turbulent
– When fluid is slow, very viscous, or very dense, Re is small, viscous
effects stabilize the fluid – laminar
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Reynolds Number
Flow is turbulent when
Re > 4000
Flow is laminar when
Re<2000
Experiments and detailed computer
simulations necessary to understand
complexity of fluids flowing in real
hardware at real operating speeds
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Dimensionless Numbers
• Reynolds Number
 vl
Re 

L
• Poisson’s Ratio d   d
L
• Mach Number Ma 
speed of object (or fluid)
speed of sound (or information)
v
L /T
 
c
L /T
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Pipe Flow
• Fluids flow from high pressure to low pressure
• Flow develops shear stress at boundary
• Shear stresses balance pressure differential
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Laminar Pipe Flow
Laminar velocity distribution for any
point across the cross-section:
Re < 2000
  r 2 
v  vmax  1    
 R 


vmax
d 2 p

16 L
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Pipe Flow
Volumetric flow rate, q (volume/time)
– Often more interested in knowing the volume of fluid flowing
through a pipe during a certain time interval
For steady, incompressible, laminar flow, the volumetric
flow rate in a pipe is:
 d p
q
128 L
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Volumetric Flow Rate
Conservation of Mass – Incompressible Fluid
V1  V2
A1v1  A2 v2
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Aerodynamic Forces
For straight and level flight:
Lift = Weight
Thrust = Drag
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Drag Force
1
FD  Av 2C D
2
• Resists high-speed motion through fluid (air or water)
• CD quantifies how streamlined an object is
• Valid for any object or flow
• Drag force is parallel to direction of fluid flow
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Lift Force
1
FL  Av 2C L
2
• Lift due to pressure differences between upper and
lower surfaces
• Lift force increases with increasing angle of attack
• Lift force is perpendicular to direction of fluid flow
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Airplane Wing – Turbulent Flow
Stall Condition
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