Fundemental Principles of Aerodynamics Flashcards
What are the fundamental principles used in aerodynamics?
CONSERVATION of MASS;
NEWTON’S SECOND LAW of MOTION;
FIRST LAW of THERMODYNAMICS;
IDEAL GAS LAW
What is a streamline?
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
What does the continuity equation tell us?
What is the equation?
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
What is the physics principle behind the continuity equation?
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
What does Bernoulli’s theorem tell us?
What are the conditions?
What is the equation?
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
How is Bernoulli’s theorem derived?
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When P represents a constant in Bernoulli’s equation, what is the equation and what do each of the components represent?
P = ghρ + p + ρv^2/2
P: TOTAL pressure
ghρ: POTENTIAL pressure
p: STATIC pressure
ρv^2/2: DYNAMIC pressure
What is Bernoulli’s equation when the unit is in terms of a length/height?
What does each component represent?
What is the condition?
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
When h is assumed to be constant, what is Bernoulli’s equation?
What does the equation show?
P = p + ρv^2/2;
The SUM of STATIC and DYNAMIC PRESSURE is EQUAL to TOTAL PRESSURE
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?
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
What are the main applications of Bernoulli’s equation?
What does it analyse to achieve these?
What are the conditions assumed?
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
What is the Venturi effect?
What is Venturi tube used for?
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
Using equations, explain how a Venturi calculates specific parameters in a horizontal tube with two different cross sectional areas?
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))
What is a pilot tube used for?
How does it work?
What is the equation used?
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)
How is lift produced by a subsonic aerofoil?
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)
What is the ideal gas law?
What is the equation?
What is the alternate equation?
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
What is the first law of thermodynamics?
What is the equation?
What does each component represent?
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 (-)
What is the differential form of the first law of thermodynamics?
What theory can be applied to give a different equation? Why?
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
What is work equal to?
What does this equate to on the p-v graph?
W = Integral of pdV;
The AREA UNDER the GRAPH between the V LIMITS
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?
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
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?
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
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?
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
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?
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
What is the difference between Cp and Cv?
Cp is SPECIFIC HEAT of the FLUID when PRESSURE is CONSTANT;
Cv is SPECIFIC HEAT of the FLUID when VOLUME/DENSITY is CONSTANT
What is the energy equation?
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
What is the stagnation temperature?
How is it calculated?
Where is it experienced?
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
