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Aerodynamics > Fundemental Principles of Aerodynamics > Flashcards

Fundemental Principles of Aerodynamics Flashcards

1
Q

What are the fundamental principles used in aerodynamics?

A

CONSERVATION of MASS;
NEWTON’S SECOND LAW of MOTION;
FIRST LAW of THERMODYNAMICS;
IDEAL GAS LAW

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2
Q

What is a streamline?

A

The LINE in a FLUID FIELD, on which the VELOCITY VECTOR of ANY POINT, is the TANGENT of the POINT at ANY TIME;
They DO NOT INTERCEPT

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3
Q

What does the continuity equation tell us?

What is the equation?

A

The MASS FLOWING IN is EQUAL to the MASS FLOWING OUT ie: the MASS FLOW RATE of a FLUID between STREAMLINES is CONSTANT;
ρ1.v1.A1 = ρ2.v2.A2 - COMPRESSIBLE fluids;
v1.A1 = v2.A2 - INCOMPRESSIBLE fluids, VOLUMETRIC FLOW RATE is CONSTANT

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4
Q

What is the physics principle behind the continuity equation?

A

The CONSERVATION of MASS where the MASS in a CONTROLLED SYSTEM CANNOT be CREATED and DESTROYED if there is NOT a SOURCE or a SINK

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5
Q

What does Bernoulli’s theorem tell us?
What are the conditions?
What is the equation?

A

For a FLOW of an INCOMPRESSIBLE IDEAL FLUID along its STREAMLINE, the SUM of the POTENTIAL ENERGY (gρh), KINETIC ENERGY (ρv^2/2) and the CAPABILITY to produce WORK due to PRESSURE at ANY POINT on the streamline remains CONSTANT;

STREAMLINE FLOW, STEADY STATE FLOW, INCOMPRESSIBLE FLUID, NO FRICTION;

C = ghρ + p + ρv^2/2

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6
Q

How is Bernoulli’s theorem derived?

A

.

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7
Q

When P represents a constant in Bernoulli’s equation, what is the equation and what do each of the components represent?

A

P = ghρ + p + ρv^2/2

P: TOTAL pressure
ghρ: POTENTIAL pressure
p: STATIC pressure
ρv^2/2: DYNAMIC pressure

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8
Q

What is Bernoulli’s equation when the unit is in terms of a length/height?
What does each component represent?
What is the condition?

A

H = p/ρg + h + v^2/2g

H: TOTAL head;
p/ρg: STATIC head;
h: NATURAL head;
v^2/2g: DYNAMIC head

The FLIUD is INCOMPRESSIBLE

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9
Q

When h is assumed to be constant, what is Bernoulli’s equation?
What does the equation show?

A

P = p + ρv^2/2;

The SUM of STATIC and DYNAMIC PRESSURE is EQUAL to TOTAL PRESSURE

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10
Q

What is the stagnation point?
What can stagnation pressure be equal to given a certain condition?
What are static pressure, density and temperature called at this point?

A

The point where AIRSPEED DECREASES to 0m/s, and STATIC pressure reaches MAXIMUM;
EQUAL to TOTAL PRESSURE for an INCOMPRESSIBLE air flow;
STAGNATION pressure;
STAGNATION density;
STAGNATION temperature

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11
Q

What are the main applications of Bernoulli’s equation?
What does it analyse to achieve these?
What are the conditions assumed?

A

AIR FLOW RATE to aircraft ENGINE;
AIRSPEED;
LIFT PRODUCED by an AEROFOIL;

DYNAMIC FORCES and AIR PROPERTIES;

SUBSONIC flight, where AIRSPEED does NOT normally EXCEED 250kts, AIR treated as INCOMPRESSIBLE

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12
Q

What is the Venturi effect?

What is Venturi tube used for?

A

The REDUCTION of STATIC PRESSURE in a fluid is CAUSED by DECREASING the CROSS-SECTIONAL AREA of the flow path;
Used as a FLOW RATE meter

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13
Q

Using equations, explain how a Venturi calculates specific parameters in a horizontal tube with two different cross sectional areas?

A

An INCOMPRESSIBLE fluid flows through a NARROWER section, causing the VELOCITY to INCREASE due to CONTINUITY equation;

The two sections can be described through BERNOULLI’S equation: gh1ρ + p1 + ρv1^2/2 = gh2ρ + p2 + ρv2^2/2, since h1 = h2 the DIFFERENCE in v CAUSES a DIFFERENCE in p;

Therefore the equation becomes Δp = (p1 - p2) = ρ/2(v2^2 - v1 ^2);

Since Δp is MEASURED by the HEIGHTS/STATIC HEADS in vertical pipes Δp = ρgΔL where ΔL is the DIFFERENCE between STATIC HEADS;

From CONTINUITY v2 = (A1/A2)v1 therefore SUBSTITUTING back into BERNOULLI’S ρgΔL = ρ/2((A1^2/A2^2)v1^2 - v1^2) = ρv1^2/2((A1^2/A2^2) - 1);

Then REARRANGE for v1 = √2gΔL x (A2^2/(A1^2 - A2^2))

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14
Q

What is a pilot tube used for?
How does it work?
What is the equation used?

A

A PITOT TUBE is used to MEASURE AIRSPEED;
There are TWO CHANNELS one measures STAGNATION (TOTAL) PRESSURE and one measures STATIC PRESSURE;
The OUT PUT is the DIFFERENCE between the two PRESSURES which equals DYNAMIC PRESSURE;
V = √(2(pt - ps)/ρ)

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15
Q

How is lift produced by a subsonic aerofoil?

A

Air flows over an aerofoil with a SMALL AOA;
ABOVE the aerofoil the flow path AREA DECREASES, AIRSPEED INCREASES due to CONTINUITY EQUATION, and STATIC PRESSURE DECREASES due to BERNOULLI’S EQUATION;
BELOW the aerofoil the flow path AREA INCREASES, AIRSPEED DECREASES and STATIC PRESSURE INCREASES;
Due to the DIFFERENCE in STATIC PRESSURE, there is an VERTICAL UPWARD TOTAL FORCE (LIFT)

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16
Q

What is the ideal gas law?
What is the equation?
What is the alternate equation?

A

A mathematical expression that describes the RELATIONSHIPS of PRESSURE, DENSITY, and TEMPERATURE of an IDEAL GAS also called STATE EQUATION of GAS;
pV = nRT;
p/ρ =RmT

17
Q

What is the first law of thermodynamics?
What is the equation?
What does each component represent?

A

The HEAT energy RECEIVED/LOST by a system is EQUAL to the SUM of the CHANGE in INTERNAL ENERGY and WORK DONE/RECEIVED by the system;
Q = ΔE(int) + W;
Q: heat received (+) and lost (-);
ΔE(int): energy increase (+) and decrease (-);
W: work done by system (+) and received by system (-)

18
Q

What is the differential form of the first law of thermodynamics?
What theory can be applied to give a different equation? Why?

A

dQ = dE(int) + dW;
KINETIC THEORY of GAS, since the INTERNAL ENERGY is a FUNCTION of TEMPERATURE ONLY dE(int) = CvdT;
At the MICROSCOPIC level of THERMOPHYSICS WORK DONE by a gas can be expressed as the PRODUCT of PRESSURE and VOLUME CHANGE dW = pdV;
dQ = CvdT + pdV

19
Q

What is work equal to?

What does this equate to on the p-v graph?

A

W = Integral of pdV;

The AREA UNDER the GRAPH between the V LIMITS

20
Q

What is an isothermal process?
What is an example of this?
What are the equations associated with it?
What is the energy equal to? Why?

A

The TEMPERATURE of a GAS is kept CONSTANT in a THERMAL PROCESS;
BALLOON COMPRESSED slowly at atmospheric conditions, so that PRESSURE and VOLUME CHANGE but TEMPERATURE is CONSTANT;
p1V1 = p2V2 or p1/ρ1 = p2/ρ2;
Q = W since the TEMPERATURE is CONSTANT there is NO CHANGE in INTERNAL ENERGY

21
Q

What is an isobaric process?
What is an example of this?
What are the equations associated with it?
What is the energy equal to? Why?

A

The PRESSURE of a GAS system is kept CONSTANT in a THERMAL PROCESS;
Gas EXPANDING in a CYLINDER piston system to PUSH a PISTON carrying CONSTANT LOAD and CONSTANT SPEED where VOLUME and TEMPERATURE CHANGE;
V1/T1 = V2/T2 or ρ1T1 = ρ2T2;
Q = ΔE(int) + W since ΔE(int) is DEPENDENT on a DIFFERENCE in TEMPERATURE and W is DEPENDENT on a CHANGE of VOLUME

22
Q

What is an isochoric/isovolumetric process?
What is an example of this?
What are the equations associated with it?
What is the energy equal to? Why?

A

The VOLUME/DENSITY of a GAS system is kept CONSTANT in a THERMAL PROCESS;
MECHANICAL BULBS used in THERMOMETERS use a BOURBON TUBE with a FIXED VOLUME then a CHANGE in PRESSURE causes a CHANGE in TEMPERATURE and OUTPUT;
p1/T1 = p2/T2 or p1/p2 = T1/T2;
Q = ΔE(int) since there is NO CHANGE in VOLUME, W = 0 and ALL HEAT energy is CONVERTED into INTERNAL ENERGY CHANGE

23
Q

What is an adiabatic process?
What is an example of this?
What are the equations associated with it?
What is the energy equal to? Why?

A

Where there is NO HEAT TRANSFER during a THERMAL PROCESS;
AIR flowing OVER an AEROFOIL;
p1V1^γ = p2V2^γ or p1/ρ1^γ = p2/ρ2^γ or p1^1-γ/T1^γ = p2^1-γ/T2^γ;
dQ = 0 and -dE(int) = dW since the system CONVERTS its INTERNAL ENERGY to WORK OUTPUT

24
Q

What is the difference between Cp and Cv?

A

Cp is SPECIFIC HEAT of the FLUID when PRESSURE is CONSTANT;

Cv is SPECIFIC HEAT of the FLUID when VOLUME/DENSITY is CONSTANT

25
Q

What is the energy equation?

A

The SUM of the THERMODYNAMIC POTENTIAL ENERGY and KINETIC ENERGY of GAS of unit mass along a STREAMLINE is CONSTANT, if the system is ISOLATED and there is NO EXTERNAL HEAT EXCHANGE;
CpT + v^2/2 = ht + v^2/2 = E

26
Q

What is the stagnation temperature?
How is it calculated?
Where is it experienced?

A

Where the TEMPERATURE is MAXIMUM due to a VELOCITY of 0m/s. This also means THERMODYNAMIC POTENTIAL is at a MAXIMUM;
Using the ENERGY EQUATION;
The NOSE of an aircraft or LEADING EDGE of AEROFOIL

Aerodynamics (11 decks)

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