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### Aero Engineering 315

Lesson 10GR#1 Review

GR#1 Review

- Bring calculator, pencils & your brain
- Calculator policy: “This examination is CLOSED BOOK/CLOSED NOTES. You are allowed a calculator, a straight edge, and an exam supplement as resource materials for this exam. However, you may not use your calculator's memory functions to store course notes, memory equations or homework solutions.”
- Point breakdown

Multiple choice conceptual – 65

Multiple choice short work – 50

Long workout – 35

Total points – 150

- Understanding the concepts and definitions, and being familiar with the equations we’ve used so far, are keys to success

Sir George Cayley

Otto Lilienthal

Samuel Langley

Wright Brothers

Secretary of the Smithsonian; $50,000 US grant to develop a powered airplane; developed efficient internal combustion engine; aircraft design neglected need for control

First to propose separate lift & thrust mechanisms; developed basic requirements for stability and control; researched alternatives to steam power

Tested airfoils in wind tunnel; built and flew gliders; used wing warping and full elevator to control aircraft; first successful crewed, heavier-than-air sustained flight on Dec 17, 1903

The Glider Man with over 2500 flights; first successful man-carrying glider in 1891

History of Aeronautical DesignIntroduction to Aircraft Design

- Why design a brand new airplane? _________________________________
- Who defines the need? _________________________________
- List the three steps in the design cycle: _________________________________
- List the three design phases: _________________________________

to satisfy a need

the user

synthesis, analysis, decision making

conceptual, preliminary, detail

Flow Properties

- List the four fundamental flow properties: _____________________________________
- These four flow properties are ______ properties
- P, r, T are _______ quantities, while V is a _______ quantity
- Units
- P:
- r:
- T:
- V:

pressure, temperature, density, velocity

point

scalar

vector

lb/ft2 or N/m2

slugs/ft3 or kg/m3

°R or K

ft/s or m/s

Equation of State

- The equation of state we use for gases is the ____________________________________
- This relation applies at a _______ for gases:
- The gas constant (R) for air is ___________________________
- A gas that obeys the perfect gas law is called a _______________

perfect gas law: P = rRT

point

at moderate temperatures and pressures

no chemical reactions or molecular breakups

very low molecular attraction

1716 ft•lb/sl•°R or 287 N•m/kg•K

perfect gas

Hydrostatic Equation

dP = -rgdh

- The hydrostatic equation (______________) says that as height increases, ___________ ____________
- To derive the hydrostatic equation, we must assume a ________ fluid (sum of vertical forces is zero)
- If we assume r = _________ (as for _________), we can integrate the hydrostatic equation to obtain the manometry equation: __________________

pressure

decreases

static

constant

liquids

P2 – P1 = -rl g(h2-h1)

Standard Atmosphere

- The standard atmosphere tabulates values of _________, ____________, and ________ at various altitudes
- In deriving the standard atmosphere (three unknowns), we had only two equations: ________________________________________
- To develop the third equation, we used balloon flights to measure ______________ in the atmosphere
- You are flying at 32,000 ft on a standard day. What is the atmospheric pressure? _______________ Temperature? _______________
- You are flying at a pressure altitude of 7.0 km. What is the atmospheric pressure? _______________ Temperature? _______________

pressure

temperature

density

perfect gas law and hydrostatic equation

temperatures

574.6 lb/ft2

404.8°R

41,105 N/m2

don’t know!

Standard Atmosphere

- You are flying at a geometric altitude of 14,000 ft, a pressure altitude of 15,000 ft, and a temperature altitude of 16,000 ft. What is the outside air density? __________________________________________
- A thermometer mounted to your aircraft measures an air temperature of 242.71 K. What is your temperature altitude? _______________
- The tropopause divides the _____________ from the ______________; for several tens of thousands of feet above the tropopause, standard air temperature __________________
- An altimeter is just a __________ gauge calibrated in units of __________ instead of __________

r = 1195 lb/ft2 / (1716 ft•lb/sl•R • 461.7°R) = 0.001508 sl/ft3

7.0 km

troposphere

stratosphere

remains constant

pressure

altitude

pressure

More Aero Definitions

aero properties

region of interest

- Flow field: specification of _________________ in a _________________________________
- Steady flow: flow in which properties at a ________ are invariant with respect to _______
- Streamline: imaginary line (curve) where the flow is _________ to the line at every point
- Flow ________ cross a streamline
- Streamtube: collection of _____________ passing through a plane ____________________ to the flow direction
- One-dimensional (1-D) flow: properties are __________ across the cross section of the flow and vary only in the ________ direction
- A point where flow velocity slows to zero is a ____________ point; the associated streamline is a _____________ streamline

point

time

tangent

cannot

streamlines

perpendicular

constant

flow

stagnation

stagnation

Mass Flow Rate and theContinuity Equation

1-D

.

- If we assume ____ flow, we can calculate mass flow rate: m = _______
- If we assume ________ flow through a streamtube, then no mass is being stored (and mass is neither created nor destroyed), and m = ____________
- The continuity equation is the expression of the principle of ________________________ for fluid flows
- Continuity equation: _________________
- For incompressible (r = const) flows, such as _________, and air slower than __________ ____________________, the continuity equation reduces to _____________

rAV

steady

.

constant

conservation of mass

r1A1V1 = r2A2V2

liquids

100 m/s or

330 ft/s or 225 mph

A1V1 = A2V2

Sources of Aerodynamic Forces

Pressure

normal

- __________ forces: act ________ to the surface
- __________ (_________) forces: act ____________ to the surface

Shear

viscous

tangential

Euler’s Equation, Bernoulli’s Equation

dP = -rVdV

- Euler’s Equation (____________) assumptions:
- Bernoulli’s Equation (_________________________) additional assumption:
- Bernoulli’s Equation says that ________________ is constant along a ____________
- P represents ________ pressure and ½rv2 represents _________ pressure (__)
- P + q = P0 (_______ pressure)
- A pitot tube measures _______ pressure

Flow along a streamline

Steady flow

Body forces (gravity/magnetic) negligible

Inviscid (frictionless) flow

P∞ + ½rV∞2 = P1 + ½rV12

Incompressible flow (r = constant)

total pressure

streamline

static

dynamic

q

total

total

Airspeed Measurement and ICeT

ndicated

what you see

- I___________ airspeed: ______________ __________________________________
- C___________ airspeed: corrected for _______________________; VC = __________
- e___________ airspeed: corrected for _______________________; Ve = __________
- T___________ airspeed: corrected for _______________________; VT = ___________
- Ground speed: aircraft velocity relative to the ________; VG = __________
- Dynamic pressure: q = ½rV2 = ½rSLVe2
- Be prepared to work backwards!

on your airspeed indicator

alibrated

position error

VI + DVP

quivalent

non-standard pressures

f•VC

rue

non-standard densities

ground

VT + Vwind

Viscous Flow

skin friction

pressure

- Profile (viscous) drag is composed of _______________ drag and __________ drag
- V = __ at the surface of a solid object (_________ condition)
- Viscosity is the tendency for a fluid to resist __________________________
- Viscosity can be described as ______________________
- For liquids, viscosity ___________ at higher temperatures; for gases, viscosity ___________ at higher temps
- The edge of a boundary layer is considered the location where V = ___% of the local freestream velocity
- _______ pressure remains constant through the boundary layer; ________ pressure decreases toward the surface
- _______ effects are only important in the boundary layer; outside the boundary layer, we can assume __________ flow

no-slip

0

velocity discontinuities

resistance to flow

decreases

increases

99

Static

dynamic

Viscous

inviscid

Viscous Flow

dimensionless

inertial

viscous

- Reynolds number, a ______________ parameter, is the ratio of __________ forces to _________ forces (Re = ___________)
- Viscous forces dominate in a _________ boundary layer; inertial forces dominate in a ___________ boundary layer
- Transition: boundary layer changes from _________ to ___________; Reynolds number at the transition point is __________
- As a rule of thumb, ReXcrit ≈ _________; locations where Re > ReXcrit have ___________ boundary layers
- Turbulent boundary layers have ________ dV/dy at the wall, so they produce ______ skin friction drag
- Boundary layer transition can be affected by: ______________________________________________________________________________________________
- Pressure drag is also known as drag due to ____________; flow separation occurs when flow momentum cannot overcome an ___________ (or unfavorable) pressure gradient (dP/dx ___ 0), i.e. when dV/dy = ____

rVx/m

laminar

turbulent

laminar

turbulent

ReXcrit

500,000

turbulent

high

more

surface roughness; freestream turbulence; aircraft

vibration; heat transfer; adverse pressure gradient

separation

adverse

0

>

Viscous Flow

reduction

- Flow separation causes a ___________ in lift and an __________ in pressure drag
- Pressure drag is the result of the loss of _______ pressure in the boundary layer and thus a _______ pressure imbalance
- ___________ boundary layers have higher V close to the surface, and _________ separation and ___________ pressure drag
- Dimples on a golf ball help transition the boundary layer to ___________, delaying __________ and reducing ________ drag
- For blunt objects, skin friction drag is _____ important, pressure drag is _____ important, and ____________ BL is preferred
- For streamlined objects, skin friction is _____ important, pressure drag is _____ important, and ___________ BL is preferred

increase

total

total

Turbulent

delay

reduce

turbulent

separation

pressure

less

more

turbulent

more

less

laminar

Example Problem

You are flying at a pressure altitude of 15,000 ft. Outside air temperature is -5°F. Your indicated airspeed is 130 kts; your flight manual indicates a position error of -5 kts. At a point on the upper surface of the wing, the velocity is determined to be 300 ft/s.

a) Determine the outside air density

b) Determine your true airspeed

c) Determine the static pressure acting on the upper surface of the wing

(Use perfect gas law: r = 0.001531 sl/ft3)

(Use ICeT: VT = V∞ = 155.3 kts = 262.46 ft/s)

(Incompressible, so use Bernoulli:

P∞ + ½rV∞2 = Pwing + ½rVwing2 Pwing = 1178.8 lb/ft2)

Final Hints

- Review homework problems 1–15
- Review lesson 2–7 readings – handouts are useful!
- Be very familiar with your green supplemental data package (clean copy available for GR)
- Know “memory” equations (handout package)
- If desired, review lesson slides on k: drive (k:\campus\df\dfan\ae315\instructor folders\ McCann)
- I’ll be home Sunday for last-minute questions

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