Aero Engineering 315 Lesson 3 Flow Properties, Hydrostatic Equation, Standard Atmosphere, and Altimetry

Overview/Outcomes 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, Hr Understand how an altimeter works Understand how manometers work

Fundamental Aero Properties Pressure – P (lb/ft2 -or- N/m2) Measure of momentum exchange between molecules Density – r (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

Units 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 P = r R T Pressure, temperature, and density are related to each other by the Equation of State: the Perfect Gas Law P = r 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 ftlb/slugoR 287 Nm/kgK 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 60F. Your barometer indicates an air pressure of 14 psi. What is the air density?

Hydrostatic Equation 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

Troposphere Stratosphere Tropopause T = To +Th*(H - Ho) Th = - 0.00356 To = 518.69 oR Ho = 0 ft H = 36,152 ft T = 389.99 oR Troposphere Stratosphere Tropopause Stan Atmos eeu

T = To +Th*(H - Ho) Th = -6.489 To = 288.16 K Ho = 0 Km H = 11.02 km T = 216.66 K Stan Atmosphere SI

The Standard Atmosphere

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 (Hr) - 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 hr (to the nearest 1,000 ft)? Using P = rRT r = 0.00204 slugs/ft3 hr = 5,000’ Using T = 55oF hT = 1,000’

Next Lesson (4)… Prior to Class In Class Work homework problems 1 thru 5 Read 3.1.1 – 3.2.2 In Class Altimetry Manometers Continuity Equation Incompressible and compressible flow

(Standardized for your unit) (What you do—6 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 did, and the AF impact—9 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

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