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ME 101:Fluids Engineering
Chapter 6
ME-1011
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.
ME-1012
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
ME-1013
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
ME-1014
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.
ME-1015
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
ME-1016
Newtonian Fluid
ME-101
F
A
Applied force balanced by shear stress exerted by the fluid on the plate
v
h
7
Viscosity
ME-101
sm
kg1.0P1
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
What happens when fluids interact with solids?
ME-101
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)
9
Why Does Pressure Increase with Depth?
ME-101
1
1
o
o
p A p A hAg
p p gh
Pressure grows in direct proportion to the depth and density of the fluid
10
Buoyancy
ME-101
B fluid objectF W gV
W
FB
Buoyancy force is related to the weight of the fluid displaced
11
Laminar and Turbulent Flows
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Laminar Flow Turbulent Flow
Fluid flows smoothly – associated with slow
moving fluids (relatively)
Irregular flow pattern – fluid moving fast, flow
patterns break up, become random
12
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
ME-10113
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
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
ME-101
Revl
14
Reynolds Number
ME-101
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
15
Dimensionless Numbers
• Reynolds Number
• Poisson’s Ratio
• Mach Number
ME-101
speed of object (or fluid)
speed of sound (or information)
/
/
Ma
v L T
c L T
Revl
Ld d
L
16
Pipe Flow
• Fluids flow from high pressure to low pressure
• Flow develops shear stress at boundary
• Shear stresses balance pressure differential
ME-10117
Laminar Pipe Flow
Laminar velocity distribution for any
point across the cross-section:
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Re < 2000
2
max 1r
v vR
2
max 16
d pv
L
18
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:
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4
128
d pq
L
19
Volumetric Flow Rate
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2211
21
vAvA
VV
Conservation of Mass – Incompressible Fluid
20
Aerodynamic Forces
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For straight and level flight:Lift = WeightThrust = Drag
21
Drag Force
ME-101
DD CAvF 2
2
1
• 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
22
Lift Force
ME-101
LL CAvF 2
2
1
• 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
23
Airplane Wing – Turbulent Flow
ME-101
Stall Condition
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