Aero Engineering 315

Lesson 4

Flow Definitions, Continuity Equation, Compressible and Incompressible Flow

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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

Standard Atmosphere example

An aircraft flying at a geometric altitude of 20,000 ft has instrument readings of P = 900 lb/ft2 and T = 460 deg R.

a. Find hP, hT, and h to the nearest 1000 ft

b. If the aircraft were flying in a standard atmosphere, what would be the relationship among hP, hT, and h?

Altimetry An altimeter is just a pressure gauge calibrated in

units of altitude instead of pressure Standard atmosphere is used to calibrate gauge dial

Establishes relationship between pressure and altitude Adjustable reference pressure allows correcting for

non-standard day pressure

Atmospheric PressureReference Pressure

Pressure Port

Manometers

Devices for measuring pressure differences Assume height difference is small - implies g

is constant Assume the fluid is liquid - is constant

dP gdh

dP g dh

P P g h h

1

2

1

2

2 1 2 1( )

hP2

P1

liquid constant

+

Manometry Equation

Hydrostatic equation

Define some more basic aero terms Flow field, steady flow, streamline, stream

tube, one-dimensional flow Explain the continuity equation

Physical meaning Assumptions needed to use it Solve problems using the continuity

equations Define compressible and incompressible flow Describe two ways a flow can transmit a

force

Overview/Outcomes

More Aero Definitions…• Flow field

• Specification of the aero properties (P, T, & V) in a region of interest

• Steady flow• Properties at a point are invariant with respect to time

• Streamline• Imaginary line where flow is tangent to the line at

every point• Stream tube

• A collection of streamlines passing through a plane perpendicular to the flow direction

• One-dimensional flow• Properties are constant across the cross section of

flow (i.e. they vary only in one direction)

Mass Flow Rate Example

A garden hose with a cross sectional area of 1 in2 has water flowing through it at a velocity of 1 ft/s. What is the mass flow rate? Assume 1-D flowWater density is 1.94 slugs/ft3

(see your handout)

Next Lesson (5)… Prior to Class

Work homework problems through #7 Read 3.2.3-3.2.4 and 3.3.5-3.3.7 Read Bernoulli’s Equation handout

In Class Euler’s Equation Bernoulli’s Equation Pressure and shear forces