ME 101:Fluids Engineering

Chapter 6

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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

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F

A

Applied force balanced by shear stress exerted by the fluid on the plate

v

h

7

Viscosity

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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

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What happens when fluids interact with solids?

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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?

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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

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Buoyancy

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B fluid objectF W gV

W

FB

Buoyancy force is related to the weight of the fluid displaced

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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

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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

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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Revl

14

Reynolds Number

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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

• Poisson’s Ratio

• Mach Number

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speed of object (or fluid)

speed of sound (or information)

/

/

Ma

v L T

c L T

Revl

Ld d

L

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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:

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Re < 2000

2

max 1r

v vR

2

max 16

d pv

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:

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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

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Aerodynamic Forces

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For straight and level flight:Lift = WeightThrust = Drag

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Drag Force

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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

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Lift Force

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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

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Airplane Wing – Turbulent Flow

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Stall Condition

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