Aero Engineering 315

Lesson 3

Flow Properties, Hydrostatic Equation, Standard Atmosphere, and Altimetry

Define the four fundamental aero properties Pressure, Density, Temperature, Velocity

Be able to make unit conversions (SI English)

Solve problems using the perfect gas law Explain the physical meaning of the hydrostatic

equation Use standard atmosphere tables Define and use the various types of altitude

HP, HT, H Understand how an altimeter works Understand how manometers work

Overview/Outcomes

Fundamental Aero Properties

Pressure – P (lb/ft2 -or- N/m2) Measure of momentum exchange between

molecules Density – slugs/ft3 -or- kg/m3)

Measure of how many molecules per volume Temp – T (oR = oF + 460 -or- K = oC + 273)

Measure of KE or random molecular motion Velocity – V (ft/s -or- m/s)

Directed flow (i.e. not random motion) These are point properties The three fundamental properties are related via

an equation of state For perfect gases, this is the Perfect Gas Law

Scalar quantities

Vector quantity

Primary dimensions Secondary (derived) dimensions

SYSTEM Force Length Time Temp Mass Pressure P

Density

Velocity V

English engineering

units

lb ft s R slug (lbs2/ft)

(lb/ft2)

(sl/ft3)

(ft/s)

Units

Primary dimensions Secondary (derived) dimensions

SYSTEM Mass Length Time Temp Force Pressure P

Density

Velocity V

SI units

kg m s K N ( kgm/s2)

Pa (N/m2)

(kg/m3)

(m/s)

Arbitrary magnitude assigned to dimensions

English – Metric Unit Conversions

MARS CLIMATE ORBITER LOST—BOARD RELEASES REPORT…,

“Wide-ranging managerial and technical actions are underway at NASA's Jet Propulsion Laboratory, Pasadena, CA, in response to the loss of the Mars Climate Orbiter…”

“The 'root cause' of the loss of the spacecraft was the failed translation of English units into metric units in a segment of ground-based, navigation-related mission software”, said Arthur Stephenson, chairman of the Mars Climate Orbiter Mission Failure Investigation Board”

NASA Press Release: 99-134 (Nov. 10, 1999)

Equation of State Pressure, temperature, and density are related

to each other by the Equation of State: the Perfect Gas Law

P = R T Only applies to gases at moderate temperatures and

pressures No chemical reactions or molecular breakups Molecules not forced so close that they stick (i.e. very

low molecular attraction) R is the Gas Constant

1716 ftlb/slugoR 287 Nm/kgK

A gas that obeys the Perfect Gas Law is called a perfect gas

(for air)

Perfect Gas Law Example

With a thermometer, you measure the air temperature to be 60F. Your barometer indicates an air pressure of 14 psi. What is the air density?

Hydrostatic Equation

hdgdP

What’s the physical meaning of this?How does it work with air?How about a liquid?

Why a Standard Atmosphere?

Thrust

Lift

Drag

Weight• Aerodynamic forces such as lift and drag depend on the

variation of the four fundamental properties (Pressure, Temperature, Density, and Velocity) within the flow field about the aircraft. Also, engine performance (i.e. thrust) is a function of these properties.

• THESE PROPERTIES VARY WITH ALTITUDE!• Must be able to model and predict these values AND must have

a common reference to compare aircraft

Standard Atmosphere—How Do We Get There?

Three unknowns Pressure Temperature Density

Two equations Perfect Gas Law Hydrostatic Equation

Determine temperature empirically

Standard Atmosphere Temperature Model(English Engineering Units)

350370390410430450470490510530550

0 6 12 18 24 30 36 42 48 54 60 66 72 78 84

Altitude (k ft)

Te

mp

era

ture

(oR

)

Stan Atmos eeu

H = 36,152 ft

T = 389.99 oR

T = To +Th*(H - Ho)

Th = - 0.00356

To = 518.69 oR

Ho = 0 ft

Troposphere StratosphereTropopause

Stan Atmosphere SI

Standard Atmosphere Temperature Model(Standard International Units)

200210220230240250260270280290300

0 2 4 6 8 10 12 14 16 18 20 22 24

Altitude (Km)

Te

mp

era

ture

(K

)

H = 11.02 km

T = 216.66 K

T = To +Th*(H - Ho)

Th = -6.489

To = 288.16 K

Ho = 0 Km

The Standard Atmosphere

0

20

40

60

80

100

120

160 180 200 220 240 260 280 300

Temperature, T, Kelvin

Alt

itu

de,

h, k

m

Troposphere

Stratosphere

Nearly all manned aircraftfly below this altitude

The Standard Atmosphere

Note: Refer to your green supplemental data book

The Standard Atmosphere

Standard day - atmospheric conditions correspond to the standard atmosphere table

Pressure altitude (Hp) - the standard day altitude which corresponds to a measured pressure

Temperature altitude (HT ) - the standard day altitude which corresponds to a measured temperature

Density altitude (H)- the standard day altitude which corresponds to a measured density

Example

We are in Colorado at 6,000 ft mean-sea-level. The temperature is 55oF and hP (pressure altitude) is 7,000 ft. What are hT and h (to the nearest 1,000 ft)?

Using P = RT

= 0.00204 slugs/ft3 h 5,000’

Using T = 55oF hT = 1,000’

Next Lesson (4)… Prior to Class

Work homework problems 1 thru 5 Read 3.1.1 – 3.2.2

In Class Altimetry Manometers Continuity Equation Incompressible and compressible flow

(What you did, and the AF impact—9 bullets)

- Supervises 11 doctors, nurses, and technicians in the USAFA pediatric clinic- Plans, schedules, and directs training activities for 22-member squadron- Program manager’s chief advisor on all technical activities, including design, fabrication, test and deployment

(What you do—6 bullets)

- Developed and implemented new wing-level safety program--unit mishap rate reduced by 47%- Engineered block upgrade to weapon system--extends lethal range by 10%, improves combat patrol time 50%- Championed new Advanced Technology Demonstration for system improvements; saved the program $7M

(Standardized for your unit)

(Save your best stuff for the back side; include discriminators—9 bullets)- Best lieutenant I’ve ever supervised in over 20 years--superior engineer, effective manager, decisive leader- One of my best lieutenants--can always be depended upon to successfully complete the most challenging tasks - Manages with authority--her program recommendations saved $300K in limited Air Force test funds- Unbounded aviation and leadership potential--ready for flight lead--definitely send to SOS at first opportunity!

- My #3 of 22 lieutenants--Hanscom AFB CGO of the Quarter (#1 of 422)--a commander in the making!- Outstanding young officer--easily handles all challenges--he shines when faced with adversity- Cut-above leadership; Three Star agency director sought Lt Brown’s advice for his congressional testimony- The best of the best--obvious command material; I recommend her for team leadership, SOS in residence a must!

(5 bullets)