Aerodynamics - PRC Aeronautical Engineer Comprehensive Review PDF

PRC AERONAUTICAL ENGINEER COMPREHENSIVE REVIEW AERODYNAMICS Fundamentals of Low-High Speed Aerodynamics, Application of Aerodynamics to Fixed/ Rotary Wing Aircraft Configur ations, Performances, Stability and Control, Wind Tunnels, and Applications FOR 1AERO REVIEW PURPOSES ONLY FOR 1AERO REVIEW P...

PRC AERONAUTICAL ENGINEER COMPREHENSIVE REVIEW AERODYNAMICS Fundamentals of Low-High Speed Aerodynamics, Application of Aerodynamics to Fixed/ Rotary Wing Aircraft Configur ations, Performances, Stability and Control, Wind Tunnels, and Applications FOR 1AERO REVIEW PURPOSES ONLY FOR 1AERO REVIEW PURPOSES ONLY FOR 1AERO REVIEW PURPOSES ONLY SESSION: FUNDAMENTALS OF AERODYNAMICS The Force of Weight and Lift REVIEW LECTURER: ENGR. JHARIE MAE Before an airplane can leave the ground and fly the force SORIANO of weight must be balanced by a force which acts upwards. This force is called LIFT. The lift force must be increased What is Aerodynamics? until it is the same as the airplane's weight. It is the study of the motion of air and of the forces on solids in motion relative to the air. The Force of Weight, Lift and Thrust The science relating to the effects produced by air or other To generate a lift, force the airplane must be propelled gases in motion. The study of the properties of moving air, forward through the air by a force called THRUST, and especially of the interaction between the air and solid provided by the engine(s). bodies moving through it. The Force of Weight, Lift, Thrust and Drag The primary requirements of an aircraft are as follows: ✓ A wing to generate a lift force. From the very moment the airplane begins to move, air ✓ A fuselage to house the payload. resists its forward motion with a force called DRAG. ✓ Tail surfaces to add stability. ✓ Control surfaces to change the direction of flight Relationship of four main forces and, The greater the weight - the greater the lift ✓ Engines to make it go forward. requirement. The greater the lift - the greater the drag. The Force of Weight The greater the drag - the greater the thrust An airplane, like all bodies, has mass. With the aircraft required, and so on... stationary on the ground, it has only the force due to the acceleration of gravity acting upon it. This force, its General Definitions WEIGHT, acts vertically downward at all times. Mass Unit - Kilogram (kg) - 'The quantity of matter in a body.' The CONFIDENTIALITY NOTICE: The contents of this review guide are intended solely for 1Aero participants and may contain confidential and privileged information. If you are not the intended end-user, you are hereby notified that any use, dissemination, copying, or storage of this review guide is strictly prohibited. We got your back, fam. Page 1 +63 915 363 5759/ +63 949 588 3874 [email protected] Attitude ∙ Skills ∙ Knowledge web.facebook.com/everythingaviation.1Aero/ PRC AERONAUTICAL ENGINEER COMPREHENSIVE REVIEW AERODYNAMICS Fundamentals of Low-High Speed Aerodynamics, Application of Aerodynamics to Fixed/ Rotary Wing Aircraft Configur ations, Performances, Stability and Control, Wind Tunnels, and Applications FOR 1AERO REVIEW PURPOSES ONLY FOR 1AERO REVIEW PURPOSES ONLY FOR 1AERO REVIEW PURPOSES ONLY mass of a body is a measure of how difficult it is to start or Power stop. Unit - Watt (W) - Power is simply the rate of doing work. (The time taken to do work) Force Energy Unit - Newton (N) - 'A push or a pull'. That which causes or Unit - Joule (J) - Mass has energy if it has the ability to do tends to cause a change in motion of a body. work. The amount of energy a body possesses is measured by the amount of work it can do. Weight Unit - Newton (N) - 'The force due to gravity'. (F = m x g) Kinetic Energy Where (m) is the mass of the object and (g) is the Unit - Joule (J) - 'The energy possessed by mass acceleration due to the gravity constant, which has the because of its motion'. 'A mass that is moving can do value of 9·81 m/s2 (A 1 kg mass "weighs" 9·81 newtons) work in coming to rest’. Centre of Gravity (CG) Newton's first law of motion The point through which the weight of an aircraft acts. 'A body will remain at rest or in uniform motion in a An aircraft in flight is said to rotate around its CG. straight line unless acted on by an external force'. The CG of an aircraft must remain within certain forward and aft limits, for reasons of both stability Inertia and control. 'The opposition which a body offers to a change in Work motion'. A property of all bodies. Inertia is a quality, but Unit - Joule (J) - A force is said to do work on a body when measured in terms of mass, which is a quantity. it moves the body in the direction in which the force is acting. The amount of work done on a body is the product Newton's second law of motion of the force applied to the body and the distance moved by 'The acceleration of a body from a state of rest, or that force in the direction in which it is acting. uniform motion in a straight line, is proportional to the applied force and inversely proportional to the mass’. CONFIDENTIALITY NOTICE: The contents of this review guide are intended solely for 1Aero participants and may contain confidential and privileged information. If you are not the intended end-user, you are hereby notified that any use, dissemination, copying, or storage of this review guide is strictly prohibited. We got your back, fam. Page 2 +63 915 363 5759/ +63 949 588 3874 [email protected] Attitude ∙ Skills ∙ Knowledge web.facebook.com/everythingaviation.1Aero/ PRC AERONAUTICAL ENGINEER COMPREHENSIVE REVIEW AERODYNAMICS Fundamentals of Low-High Speed Aerodynamics, Application of Aerodynamics to Fixed/ Rotary Wing Aircraft Configur ations, Performances, Stability and Control, Wind Tunnels, and Applications FOR 1AERO REVIEW PURPOSES ONLY FOR 1AERO REVIEW PURPOSES ONLY FOR 1AERO REVIEW PURPOSES ONLY Velocity weight of the air above that surface. Atmospheric Unit - Meter per second (m/s). - 'Rate of change of pressure is measured with an instrument called a displacement' barometer. An aircraft always has Static pressure Acceleration acting upon it. Unit - Meters per second per second (m/s2) - 'Rate of Common units of pressure N/m2, lb/ft2, and atm change of velocity’. A force of 1 newton acting on a mass of 1 kg will produce an acceleration of 1 m/s2 Density 𝐹𝑜𝑟𝑐𝑒 Density is 'Mass per unit volume' (The "number" of 𝐴𝑐𝑐𝑒𝑙𝑒𝑟𝑎𝑡𝑖𝑜𝑛 = 𝑀𝑎𝑠𝑠 air particles in a given space). Since air is a (a) For the same mass; the bigger the force, the greater mixture of gases, it can be compressed. the acceleration. Common units of density kg/m3, slugs/ft3, and (b) For the same force; the larger the mass, the slower lbm/ft3 the acceleration. Density varies with static pressure, temperature, and humidity. Momentum a) Density decreases if static pressure decreases. Unit - Mass x Velocity (kg-m/s) - 'The quantity of motion b) Density decreases if temperature increases. possessed by a body'. The tendency of a body to c) Density decreases if humidity increases. continue in motion after being placed in motion. Temperature Newton's third law The measure of the average kinetic energy of the 'Every action has an equal and opposite reaction' particles in a gas The measure of the hotness or coldness of the The physical properties of the air body Pressure Common units of temperature are Kelvin (K), Atmospheric pressure is usually defined as the degree Celsius (C), degree Rankine (R), and force exerted against the earth’s surface by the degree Fahrenheit (F). CONFIDENTIALITY NOTICE: The contents of this review guide are intended solely for 1Aero participants and may contain confidential and privileged information. If you are not the intended end-user, you are hereby notified that any use, dissemination, copying, or storage of this review guide is strictly prohibited. We got your back, fam. Page 3 +63 915 363 5759/ +63 949 588 3874 [email protected] Attitude ∙ Skills ∙ Knowledge web.facebook.com/everythingaviation.1Aero/ PRC AERONAUTICAL ENGINEER COMPREHENSIVE REVIEW AERODYNAMICS Fundamentals of Low-High Speed Aerodynamics, Application of Aerodynamics to Fixed/ Rotary Wing Aircraft Configur ations, Performances, Stability and Control, Wind Tunnels, and Applications FOR 1AERO REVIEW PURPOSES ONLY FOR 1AERO REVIEW PURPOSES ONLY FOR 1AERO REVIEW PURPOSES ONLY Viscosity Summary The ability of the fluid to resist shearing stresses It is the sticky or adhesive characteristics of a fluid The values of standard air viscosities at sea level are: 𝜇0 = 3.7372 x 10−7 slug/ft.sec 𝜇0 = 1.7894 x 10−5 kg/m-sec Kinematic Viscosity The kinematic viscosity is the dynamic viscosity μ divided by the density of the fluid ρ. It is usually denoted by the Greek letter nu (ν). 𝜇 ν= 𝜌 Humidity Amount of water vapor in the air. The maximum amount of Source of all Aerodynamic Forces water vapor that air can hold varies with the temperature. 1. Pressure distribution on the surface The higher the temperature of the air, the more water vapor 2. Shear stress (friction) on the surface it can absorb. Air as a Perfect Gas 𝑃 = 𝜌𝑅𝑇 Where: P = Pressure in Pa or Psf ρ = density in kg/m3 or slugs/ft3 T = temperature in Kelvin or Rankine CONFIDENTIALITY NOTICE: The contents of this review guide are intended solely for 1Aero participants and may contain confidential and privileged information. If you are not the intended end-user, you are hereby notified that any use, dissemination, copying, or storage of this review guide is strictly prohibited. We got your back, fam. Page 4 +63 915 363 5759/ +63 949 588 3874 [email protected] Attitude ∙ Skills ∙ Knowledge web.facebook.com/everythingaviation.1Aero/ PRC AERONAUTICAL ENGINEER COMPREHENSIVE REVIEW AERODYNAMICS Fundamentals of Low-High Speed Aerodynamics, Application of Aerodynamics to Fixed/ Rotary Wing Aircraft Configur ations, Performances, Stability and Control, Wind Tunnels, and Applications FOR 1AERO REVIEW PURPOSES ONLY FOR 1AERO REVIEW PURPOSES ONLY FOR 1AERO REVIEW PURPOSES ONLY R = specific gas constant R for normal air: 287.08 J/kg. K or 1716 ft.lb/slug. R or 53.342 ft.lbf/lbm.R The Atmosphere ✓ The atmosphere is the medium in which an aircraft operates. ✓ The atmosphere is defined as the whole mass of Layers of the Earth’s Atmosphere air extending at a specified height Troposphere ✓ The atmosphere is the mechanical mixture of Stratosphere gases surrounding the earth) Ionosphere Exosphere Composition of the Atmosphere Nitrogen ------------------- 78.03% The TROPOSPHERE is the layer from the surface to an Oxygen --------------------- 20.99% average altitude of about 11 km. It is characterized by an Argon ------------------------ 0.94% overall decrease of temperature with increasing altitude. Carbon Oxide -------------- 0.03% Hydrogen -------------------- 0.01% At the top of the troposphere is the TROPOPAUSE, a very Helium ---------------------- 0.004% thin layer marking the boundary between the troposphere Neon ----------------------- 0.0012% and other gases and the layer above. Above the tropopause is the STRATOSPHERE. This layer is characterized by relatively small changes in temperature with height except for a warming trend near the top. CONFIDENTIALITY NOTICE: The contents of this review guide are intended solely for 1Aero participants and may contain confidential and privileged information. If you are not the intended end-user, you are hereby notified that any use, dissemination, copying, or storage of this review guide is strictly prohibited. We got your back, fam. Page 5 +63 915 363 5759/ +63 949 588 3874 [email protected] Attitude ∙ Skills ∙ Knowledge web.facebook.com/everythingaviation.1Aero/ PRC AERONAUTICAL ENGINEER COMPREHENSIVE REVIEW AERODYNAMICS Fundamentals of Low-High Speed Aerodynamics, Application of Aerodynamics to Fixed/ Rotary Wing Aircraft Configur ations, Performances, Stability and Control, Wind Tunnels, and Applications FOR 1AERO REVIEW PURPOSES ONLY FOR 1AERO REVIEW PURPOSES ONLY FOR 1AERO REVIEW PURPOSES ONLY The International Standard Atmosphere Coefficient of Dynamic Viscosity The values of temperature, pressure and density are never 𝜇𝑂 = 3.7372 x 10−7slug/ft-sec = 1.7894 x 10−5 kg/m-sec constant in any given layer of the atmosphere. To enable accurate comparison of aircraft performance and the Temperature Variation with Altitude calibration of pressure instruments, a 'standard' For 0-11km or 0-36000 ft atmosphere has been adopted. The standard atmosphere 𝑇 𝑇 = 𝑇0 + 𝑎ℎ ; 𝜃 = 𝑇0 represents the mean or average properties of the Where: atmosphere. 𝑇 𝜃 = 𝑇 , temperature ratio 0 T = temperature at any altitude above sea level up to tropopause in °R or K 𝑇0 = 519 °R or 288 K a = temperature gradient or lapse rate (= -0.003566°R/ft or - 0.00651 K/m or -6.51 K/km) h = any altitude above sea level up to tropopause in ft or m or km Pressure Variation with Altitude For 0-11km or 0-36000 ft Standard Value for Air at Sea level Pressure 𝑃 𝑇 5.26 =[ ] 𝑃𝑂 = 14.7 lb./ 𝑖𝑛2 = 2116.8 lb./ 𝑓𝑡 2 = 29.92” Hg 𝑃0 𝑇0 = 76 cm Hg = 760 mm Hg = 101325 Pa = 1 atm = 1.01325 bar Density 𝑃 𝑎ℎ 5.26 𝛿= = (1 + ) 𝜌𝑂 = 0.002377 slug/ 𝑓𝑡 3 = 1.225 kg/ 𝑚3 𝑃0 𝑇0 Temperature: 𝑇𝑂 = 519 °R = 288 K CONFIDENTIALITY NOTICE: The contents of this review guide are intended solely for 1Aero participants and may contain confidential and privileged information. If you are not the intended end-user, you are hereby notified that any use, dissemination, copying, or storage of this review guide is strictly prohibited. We got your back, fam. Page 6 +63 915 363 5759/ +63 949 588 3874 [email protected] Attitude ∙ Skills ∙ Knowledge web.facebook.com/everythingaviation.1Aero/ PRC AERONAUTICAL ENGINEER COMPREHENSIVE REVIEW AERODYNAMICS Fundamentals of Low-High Speed Aerodynamics, Application of Aerodynamics to Fixed/ Rotary Wing Aircraft Configur ations, Performances, Stability and Control, Wind Tunnels, and Applications FOR 1AERO REVIEW PURPOSES ONLY FOR 1AERO REVIEW PURPOSES ONLY FOR 1AERO REVIEW PURPOSES ONLY Where: Problems 𝑃 𝛿 = 𝑃 , pressure ratio 1. Determine the ambient density (kg/cu meter) of a 0 B737 flying at 35,000 ft to Singapore. P = pressure at any altitude above sea level up to Answer: 0.38 tropopause in lb. / ft2 or Pa 2. Calculate the temperature, pressure, and density Po = 2116.8 lb./ft2 or 101325 Pa at 24,000 ft in the standard atmosphere a = -0.003566 °R/ft or -0.00651 K/m or -6.51 K/km Answer: T = 433.416 K, P = 820.39 lb/ft2, 𝜌 = h = any altitude above sea level up to tropopause in ft or 1.103x10-3 slugs/ft3 m or km Density Variation with Altitude Temperature Variation with Altitude (11km For 0-11km or 0-36000 ft -25km) 𝜌 𝑇 4.26 =[ ] T = 390.15 °R or 216.5 K (constant from 11km up to 25 𝜌0 𝑇0 km) 𝜌 𝑎ℎ 4.26 𝜎= = (1 + ) 𝜌0 𝑇0 Where: Pressure Variation with Altitude (11km - 𝜌 𝜎 = 𝜌 , density ratio 25km) 0 English System ρ = density at any altitude above sea level up to 𝑃 1.26 tropopause in slug/ft3 or kg/m3 𝛿= = 4.805𝑋10−5 ℎ 𝑃0 𝑒 𝜌0 = 0.002377 slug/ft3 or 1.225kg/m3 Where: a = -0.003566 °R/ft or – 0.00651 K/m or -0.51 K/km P = pressure at any altitude above 36000ft up to 80000ft h = any altitude above sea level up to tropopause in ft or in lb./ft2 m or km 𝑃0 = 2116.8 lb./ft2 h = any altitude above tropopause up to stratopause in feet CONFIDENTIALITY NOTICE: The contents of this review guide are intended solely for 1Aero participants and may contain confidential and privileged information. If you are not the intended end-user, you are hereby notified that any use, dissemination, copying, or storage of this review guide is strictly prohibited. We got your back, fam. Page 7 +63 915 363 5759/ +63 949 588 3874 [email protected] Attitude ∙ Skills ∙ Knowledge web.facebook.com/everythingaviation.1Aero/ PRC AERONAUTICAL ENGINEER COMPREHENSIVE REVIEW AERODYNAMICS Fundamentals of Low-High Speed Aerodynamics, Application of Aerodynamics to Fixed/ Rotary Wing Aircraft Configur ations, Performances, Stability and Control, Wind Tunnels, and Applications FOR 1AERO REVIEW PURPOSES ONLY FOR 1AERO REVIEW PURPOSES ONLY FOR 1AERO REVIEW PURPOSES ONLY Metric System: ALTIMETERS 𝑃 1.26 An altimeter is a pressure gauge which indicates an 𝛿= = 1.578𝑋10−4 ℎ 𝑃0 𝑒 altitude in the standard atmosphere corresponding to the Where: measured pressure. P = pressure at any altitude above 11km up to 25km in Pressure altitude, hp – is the altitude given by an Pa altimeter set to 29.92 “Hg. 𝑃0 = 101325 Pa Density altitude, hd – is the altitude corresponding to a h = any altitude above tropopause up to stratopause in given density in the standard atmosphere. meters Temperature altitude, ht – is the altitude corresponding Density Variation with Altitude (11km -25km) to a given temperature in the standard atmosphere. English System 𝜌 1.68 𝜎= = 4.805𝑋10−5ℎ Problems 𝜌0 𝑒 Where: 1. Find the Pressure and Density at 15 km height? ρ = density at any altitude above 36000ft up to 80000ft in Answer: P15km =11970.5 Pa; 𝜌15km = 0.193 kg/m3 slug/ft3 2. Find the pressure and Temperature at an altitude where 𝜌0 = 0.002377 slug/ft3 the density is 0.168kg/m3 in Standard atmosphere. h = any altitude above 36000ft up to 80000ft Answer: T=216.5K; P=10,441.67 Pa 3. A standard altimeter reads 4,500 meters when the ambient temperature is 275K. What are the density altitude Metric System and the temperature altitude? 𝜌 1.68 𝜎= = 1.578𝑋10−4ℎ Answer: ht = 1996.93 m; hd = 5061.93m 𝜌0 𝑒 Where: 4. At a certain altitude, a standard altimeter reads 3,000 meters. If the density altitude is 2,500 meters, find the true ρ = density at any altitude above 11km up to 25km in temperature. kg/m3 Answer: T = 255.14K 𝜌0 = 1.225 kg/m3 h = any altitude above 11,000m up to 25,000m in meters CONFIDENTIALITY NOTICE: The contents of this review guide are intended solely for 1Aero participants and may contain confidential and privileged information. If you are not the intended end-user, you are hereby notified that any use, dissemination, copying, or storage of this review guide is strictly prohibited. We got your back, fam. Page 8 +63 915 363 5759/ +63 949 588 3874 [email protected] Attitude ∙ Skills ∙ Knowledge web.facebook.com/everythingaviation.1Aero/ PRC AERONAUTICAL ENGINEER COMPREHENSIVE REVIEW AERODYNAMICS Fundamentals of Low-High Speed Aerodynamics, Application of Aerodynamics to Fixed/ Rotary Wing Aircraft Configur ations, Performances, Stability and Control, Wind Tunnels, and Applications FOR 1AERO REVIEW PURPOSES ONLY FOR 1AERO REVIEW PURPOSES ONLY FOR 1AERO REVIEW PURPOSES ONLY Types of Altitude 1. Indicated Altitude Indicated altitude is simply the altitude you read directly off your altimeter 4. Temperature Altitude It is the altitude corresponding to a given temperature in the standard atmosphere 5. True Altitude True altitude is the vertical distance of your airplane 2. Pressure Altitude above sea level. It is the altitude given by an altimeter set to 29.92 “Hg. 6. Absolute Altitude 3. Density Altitude Constantly changing, absolute altitude is the distance It is pressure altitude corrected for non-standard measurement of your airplane above the ground. temperature. When it's hot outside, your airplane doesn't perform as well. Your takeoff distance is longer, and you don't climb as fast. That's because with hot temperatures, density altitude increases, and your airplane "feels" like it's flying at a higher altitude. CONFIDENTIALITY NOTICE: The contents of this review guide are intended solely for 1Aero participants and may contain confidential and privileged information. If you are not the intended end-user, you are hereby notified that any use, dissemination, copying, or storage of this review guide is strictly prohibited. We got your back, fam. Page 9 +63 915 363 5759/ +63 949 588 3874 [email protected] Attitude ∙ Skills ∙ Knowledge web.facebook.com/everythingaviation.1Aero/ PRC AERONAUTICAL ENGINEER COMPREHENSIVE REVIEW AERODYNAMICS Fundamentals of Low-High Speed Aerodynamics, Application of Aerodynamics to Fixed/ Rotary Wing Aircraft Configur ations, Performances, Stability and Control, Wind Tunnels, and Applications FOR 1AERO REVIEW PURPOSES ONLY FOR 1AERO REVIEW PURPOSES ONLY FOR 1AERO REVIEW PURPOSES ONLY BASIC AERODYNAMIC PRINCIPLES AND For compressible fluid, ρ ≠ constant (M ≥ 0.3 APPLICATIONS approximately) ρ1 𝐴1 𝑉1 = ρ2 𝐴2 𝑉2 Continuity Equation One of the fundamental laws of the universe is "ENERGY ρAV = constant and MASS can neither be created nor destroyed", only Differential form: 𝑑𝑉 𝑑𝐴 𝑑𝜌 changed from one form to another. + + =0 𝑉 𝐴 𝜌 To demonstrate the effect this basic 'Principle of Problems Continuity' has on aerodynamic theory, it is instructive to 1. A convergent duct has an inlet area of 5 sq. ft. Air enters consider a streamline flow of air through a tube which has the duct at 26 meters/ sec and exits at 32 meters/sec. What a reduced cross-sectional area in the middle. is the exit area in sq. ft? Answer: 4.1 sq. ft 2. A pipe is tapering in size, diminishing by 0.1 square ft per foot run. What is the change in velocity per foot run where the pipe is 4 square ft in cross section? If the velocity there is 90 ft per second, is the velocity increasing or decreasing? For incompressible fluid, ρ = constant (M < 0.3 Answer: 𝑑𝑉/𝑑𝑆 = 2.25 𝑓𝑝𝑠 𝑝𝑒𝑟 𝑓𝑡, 𝑖𝑛𝑐𝑟𝑒𝑎𝑠𝑖𝑛𝑔 approximately) 3. A circular pipe, 100 ft long tapers from 3 ft in diameter 𝐴1 𝑉1 = 𝐴2 𝑉2 at one end to 2 ft in diameter at the other. Fluid is flowing from the bigger toward the smaller. What is the rate of AV = constant increase in velocity per foot run at the entrance if the Differential Form: 𝑑𝑉 𝑑𝐴 velocity there is 80 ft per second? =− 𝑉 𝐴 Answer: 𝑑𝑉/𝑑𝑆 = 0.444 𝑓𝑝𝑠 𝑝𝑒𝑟 𝑓𝑡 4. Air having the standard sea level density has a velocity of 100 fps at a section of a wind tunnel, at another section CONFIDENTIALITY NOTICE: The contents of this review guide are intended solely for 1Aero participants and may contain confidential and privileged information. If you are not the intended end-user, you are hereby notified that any use, dissemination, copying, or storage of this review guide is strictly prohibited. We got your back, fam. Page 10 +63 915 363 5759/ +63 949 588 3874 [email protected] Attitude ∙ Skills ∙ Knowledge web.facebook.com/everythingaviation.1Aero/ PRC AERONAUTICAL ENGINEER COMPREHENSIVE REVIEW AERODYNAMICS Fundamentals of Low-High Speed Aerodynamics, Application of Aerodynamics to Fixed/ Rotary Wing Aircraft Configur ations, Performances, Stability and Control, Wind Tunnels, and Applications FOR 1AERO REVIEW PURPOSES ONLY FOR 1AERO REVIEW PURPOSES ONLY FOR 1AERO REVIEW PURPOSES ONLY having an area half as great at that at the first section the The significant point is that: Static Pressure + Dynamic flow velocity is 400mph. What is the density at the second Pressure is a constant. This constant can be referred to section? as Total Pressure, Stagnation pressure or Pitot Pressure. Answer: ρ2 = 0.000810 slugs per cu ft. “In a continuous flow of liquid, as velocity increases, Bernoulli’s Principles pressure decreases; and as velocity decreases, pressure "In the steady flow of an ideal fluid the sum of the increases.” pressure and kinetic energy per unit volume remains constant". Incompressible Bernoulli Equation Note: An ideal fluid is both incompressible and has no The term incompressible is traditionally used in the study viscosity of fluid dynamics to describe a flow in which appreciable changes in fluid density do not occur. Air, like all gases, is This statement can be expressed as: Pressure + Kinetic easily compressed. energy = Constant However, at low Mach numbers, air behaves in a way that mimics an incompressible fluid. What this means is 1 that the density changes that occur in airflows at low 𝑃 + 𝜌𝑉 2 = 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 2 speed have a negligible influence on the behavior of the airflow. Incompressible flows, ρ = constant (M < 0.3 approximately) ρ 𝑃 + 𝑉 2 = 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 2 ρ ρ 𝑃1 + 𝑉1 2 = 𝑃2 + 𝑉2 2 2 2 ρ 𝑃1 − 𝑃2 = (𝑉2 2 − 𝑉1 2 ) 2 CONFIDENTIALITY NOTICE: The contents of this review guide are intended solely for 1Aero participants and may contain confidential and privileged information. If you are not the intended end-user, you are hereby notified that any use, dissemination, copying, or storage of this review guide is strictly prohibited. We got your back, fam. Page 11 +63 915 363 5759/ +63 949 588 3874 [email protected] Attitude ∙ Skills ∙ Knowledge web.facebook.com/everythingaviation.1Aero/ PRC AERONAUTICAL ENGINEER COMPREHENSIVE REVIEW AERODYNAMICS Fundamentals of Low-High Speed Aerodynamics, Application of Aerodynamics to Fixed/ Rotary Wing Aircraft Configur ations, Performances, Stability and Control, Wind Tunnels, and Applications FOR 1AERO REVIEW PURPOSES ONLY FOR 1AERO REVIEW PURPOSES ONLY FOR 1AERO REVIEW PURPOSES ONLY What is a Venturi Tube? By Incompressible Bernoulli Equation: It is a convergent- divergent tube with a short cylindrical ρ ρ 𝑃1 + 𝑉1 2 = 𝑃2 + 𝑉2 2 2 2 throat or constricted section. 1 𝑃1 − 𝑃2 = ρ(𝑉22 -𝑉12 ) 2 By Incompressible Continuity Equation: 𝑄 = 𝐴1 𝑉1 = 𝐴2 𝑉2 𝑄 𝑄 𝑉1 = 𝑉2 = 𝐴2 𝐴2 1 𝑄 2 𝑄 2 Flow through a Venturi Tube 𝑃1 − 𝑃2 = ρ [( ) − ( ) ] 2 𝐴2 𝐴1 This device determines the rate of flow of fluid through ρ 2 1 2 1 2 the tube by measuring the difference in pressure between 𝑃1 − 𝑃2 = 𝑄 [( ) − ( ) ] 2 𝐴2 𝐴1 the throat section and the entrance section. Where: Q = rate of flow in ft3 /s or m3/s A = cross-sectional area in ft2 or m2 P = pressure in psf or Pa ρ = density in slug/ft3 or kg/m3 Flow Comparison in Venturi Tube Problems 1.A horizontal pipe, 1 ft in diameter, tapers gradually to 8 inches in diameter. If the flow is 500 cu ft of water per minute, what is the difference between the pressures in psf at the two sections? (Density of water 62.4 lb. per cu ft.) Answer: 443 lb./ft2 2. A water pipe 8 inches in diameter gradually tapers down to 4 inches in diameter. The rate of flow is 135 cu ft per minute. If the pressure is 20 psi where the diameter is 8 CONFIDENTIALITY NOTICE: The contents of this review guide are intended solely for 1Aero participants and may contain confidential and privileged information. If you are not the intended end-user, you are hereby notified that any use, dissemination, copying, or storage of this review guide is strictly prohibited. We got your back, fam. Page 12 +63 915 363 5759/ +63 949 588 3874 [email protected] Attitude ∙ Skills ∙ Knowledge web.facebook.com/everythingaviation.1Aero/ PRC AERONAUTICAL ENGINEER COMPREHENSIVE REVIEW AERODYNAMICS Fundamentals of Low-High Speed Aerodynamics, Application of Aerodynamics to Fixed/ Rotary Wing Aircraft Configur ations, Performances, Stability and Control, Wind Tunnels, and Applications FOR 1AERO REVIEW PURPOSES ONLY FOR 1AERO REVIEW PURPOSES ONLY FOR 1AERO REVIEW PURPOSES ONLY inches, what is the pressure (in psi) where the diameter is changes, which affect the local air temperature, viscosity, 4 inches? (Density of water 62.4 lb. per cu ft.) and thermal conductivity. Answer: 15.6 psi 3. Water flows through a horizontal pipe at velocity of 50 ft. Isentropic Flow per sec. Owing to the pipe gradually expanding to larger ✓ An adiabatic process is one in which no heat is size, the velocity decreases to 35 ft. per sec. What is the added or taken away; 𝛿𝑞 = 0 difference between pressures? ✓ A reversible process is one in which no frictional Answer: 1236.40 lb./ft2 or other dissipative effects occur. 4. A venturi tube narrows down from 4 in. in diameter to 2 ✓ An Isentropic process is one in which is both in. in diameter. What is the rate of water if the pressure at adiabatic and reversible. the throat i.e., 2 lb./in2 less than at the larger section? Answer: Q = 0.388 ft3/s Isentropic Flow Equation 5. A venturi tube in 6 in. in diameter at the entrance, where 𝛾 2𝛾 𝑃2 𝜌2 𝛾 𝑇2 𝛾−1 𝑊2 𝛾 𝑉𝑎2 𝛾−1 the pressure is 10 lb./in2 (gage). The throat is 4 in. in =( ) =( ) =( ) =( ) 𝑃1 𝜌1 𝑇1 𝑊1 𝑉𝑎1 diameter, there the pressure is 6 lb./in2 (gage). What is the 𝑃2 𝜌2 1.4 𝑇2 3.5 𝑊2 1.4 𝑉𝑎2 7 =( ) =( ) =( ) =( ) flow of water? 𝑃1 𝜌1 𝑇1 𝑊1 𝑉𝑎1 Answer: Q = 2.37 ft3/s 6. A 12 in. by 6 in venturi meter is located in a horizontal The Isentropic Flow equations are relevant to water line. If the pressure gages read 30lb/in2 and compressible flows only 16lb/in2, what is the flow rate? Answer: Q = 9.25ft3/s Problems 1. Air at standard pressure and temperature, has density Compressibility Effects of 1.225 𝑘𝑔/𝑚3. If the air is compressed adiabatically to 3 The term compressible flow is used to describe flow atm, what are the specific weight, density, and the regimes in which density changes are considered. temperature? Associated with these density changes are thermodynamic CONFIDENTIALITY NOTICE: The contents of this review guide are intended solely for 1Aero participants and may contain confidential and privileged information. If you are not the intended end-user, you are hereby notified that any use, dissemination, copying, or storage of this review guide is strictly prohibited. We got your back, fam. Page 13 +63 915 363 5759/ +63 949 588 3874 [email protected] Attitude ∙ Skills ∙ Knowledge web.facebook.com/everythingaviation.1Aero/ PRC AERONAUTICAL ENGINEER COMPREHENSIVE REVIEW AERODYNAMICS Fundamentals of Low-High Speed Aerodynamics, Application of Aerodynamics to Fixed/ Rotary Wing Aircraft Configur ations, Performances, Stability and Control, Wind Tunnels, and Applications FOR 1AERO REVIEW PURPOSES ONLY FOR 1AERO REVIEW PURPOSES ONLY FOR 1AERO REVIEW PURPOSES ONLY Answer: 𝑤2 = 26.33 𝑁/𝑚3, 𝜌 = 2.685 𝑘𝑔/𝑚3, T2 = 𝑉𝑎 = √𝛾𝑅𝑇 394.20 K Where: 2. Air at standard pressure and temperature is permitted to expand adiabatically to one-half atmospheric pressure. 𝛾 = 1.4 What is a) the density and b) the temperature? 𝑓𝑡 − 𝑙𝑏𝑓 𝑘𝑔 𝑅 = 1715.7 Answer: 𝜌2 = 0.747 𝑚3, T2 = 236.26 K 𝑠𝑙𝑢𝑔𝑠 − °𝑅 𝑉𝑎 = 49.02√𝑇 Speed of sound Metric System Sound waves travel through the air at a definite speed, the speed of sound. The speed of sound in a perfect gas 𝑉𝑎 = √𝛾𝑅𝑇 depends only on the temperature of the gas. Where: 𝛾𝑃 𝑉𝑎 = √ 𝛾 = 1.4 𝜌 𝐽 𝑅 = 287.08 𝑉𝑎 = √𝛾𝑅𝑇 𝑘𝑔 − °𝐾 Where: 𝑉𝑎 = 20.05√𝑇 𝑉𝑎 = Speed of sound 𝛾= Ratio of specific heats Problems R = Gas constant 1. Find the speed of sound in air at standard sea level conditions. T = Temperature Answer: 𝑉𝑎 = 340.26m/s or 𝑉𝑎 = 1116.75 ft/s Alternate Forms: 2. What is the speed of sound in air at 3,500m altitude. English System Answer: 𝑉𝑎 = 326.49 m/s CONFIDENTIALITY NOTICE: The contents of this review guide are intended solely for 1Aero participants and may contain confidential and privileged information. If you are not the intended end-user, you are hereby notified that any use, dissemination, copying, or storage of this review guide is strictly prohibited. We got your back, fam. Page 14 +63 915 363 5759/ +63 949 588 3874 [email protected] Attitude ∙ Skills ∙ Knowledge web.facebook.com/everythingaviation.1Aero/ PRC AERONAUTICAL ENGINEER COMPREHENSIVE REVIEW AERODYNAMICS Fundamentals of Low-High Speed Aerodynamics, Application of Aerodynamics to Fixed/ Rotary Wing Aircraft Configur ations, Performances, Stability and Control, Wind Tunnels, and Applications FOR 1AERO REVIEW PURPOSES ONLY FOR 1AERO REVIEW PURPOSES ONLY FOR 1AERO REVIEW PURPOSES ONLY Compressible Bernoulli’s Equation 550 ft per sec. What is the velocity where the pressure is 13.9 lb. per sq.in.? For compressible flows, ρ ≠ constant (M ≥ 0.3 approximately) 𝑉2 = 633.83 𝑓𝑡/𝑠𝑒𝑐 The flow in which the density changes from point to point 4. Consider an airplane flying at a standard altitude of 5 km in the flow. with a velocity of 270 m/s. At a point on the wing of the airplane, the velocity is 330 m/s. Calculate the pressure at 𝑉2 𝛾 𝑃 + = 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 this point. 2 𝛾−1ρ 5. A supersonic transport is flying at a velocity of 1500 mi/h 𝑉1 2 𝛾 𝑃1 𝑉2 2 𝛾 𝑃2 + = + at a standard altitude of 50,000 ft. The temperature at a 2 𝛾 − 1 𝜌1 2 𝛾 − 1 𝜌2 point in the flow over the wing is 793.32°R. Calculate the Problems flow velocity at that point. 1. In an undisturbed airstream, the pressure is 101325 Pa, Measurement of Airspeed the density is 1.225 kg/m3 and the speed is 160m/s. Find the velocity if the pressure is 90000 Pa 1. Low speed airspeed Indicators (Incompressible Flow) V2 = 212 m/s 2. In an undisturbed airstream, where the pressure is 14.7 Consider a pitot static tube as shown below: lb per sq in and the temperature is 59°F, the velocity is 520 Your pitot tube measures "ram pressure," which is a ft per sec. Where the velocity is 600 ft per sec., what is the combination of dynamic and static pressure. If you're local pressure? parked on the ramp, your ram pressure only includes the 𝑃2 = 2,012.21 𝑙𝑏 𝑝𝑒𝑟 𝑠𝑞 𝑓𝑡 static component. As you start to move forward, ram pressure includes both static and dynamic pressure. 3. In an undisturbed airstream, where the pressure is 14.7 lb. per sq in and the temperature is 59°F, the velocity is CONFIDENTIALITY NOTICE: The contents of this review guide are intended solely for 1Aero participants and may contain confidential and privileged information. If you are not the intended end-user, you are hereby notified that any use, dissemination, copying, or storage of this review guide is strictly prohibited. We got your back, fam. Page 15 +63 915 363 5759/ +63 949 588 3874 [email protected] Attitude ∙ Skills ∙ Knowledge web.facebook.com/everythingaviation.1Aero/ PRC AERONAUTICAL ENGINEER COMPREHENSIVE REVIEW AERODYNAMICS Fundamentals of Low-High Speed Aerodynamics, Application of Aerodynamics to Fixed/ Rotary Wing Aircraft Configur ations, Performances, Stability and Control, Wind Tunnels, and Applications FOR 1AERO REVIEW PURPOSES ONLY FOR 1AERO REVIEW PURPOSES ONLY FOR 1AERO REVIEW PURPOSES ONLY Where: 𝑃𝑡 = Pressure at the stagnation point (zero-speed). Also known as stagnation pressure or total pressure. 𝑞̅ = dynamic pressure Static pressure at a given point is the pressure we would feel if we were moving along with the flow at that point. Your airspeed indicator is really a scale, which compares Total pressure at a given point in a flow is the pressure the static pressure from your static ports to ram pressure that would exist if the flow were slowed down isentropically (static + dynamic) from your pitot tube. The two static to zero velocity. pressures cancel each other out, and you're left with dynamic pressure. Dynamic pressure translates into your Dynamic pressure is the pressure of a fluid that results airspeed. from its motion. It is the difference between the total pressure and static pressure. 2. High Speed airspeed Indicators (Compressible Flow) The Mach Number (M) The flow velocity divided by the speed of sound 𝑉 1 𝑀= 𝑉𝑎 𝑃 + 𝜌𝑉 2 = 𝑃𝑡 2 Where: 1 𝑃𝑡 − 𝑃 = 𝜌𝑉 2 = 𝑞̅ 2 M = Mach Number CONFIDENTIALITY NOTICE: The contents of this review guide are intended solely for 1Aero participants and may contain confidential and privileged information. If you are not the intended end-user, you are hereby notified that any use, dissemination, copying, or storage of this review guide is strictly prohibited. We got your back, fam. Page 16 +63 915 363 5759/ +63 949 588 3874 [email protected] Attitude ∙ Skills ∙ Knowledge web.facebook.com/everythingaviation.1Aero/ PRC AERONAUTICAL ENGINEER COMPREHENSIVE REVIEW AERODYNAMICS Fundamentals of Low-High Speed Aerodynamics, Application of Aerodynamics to Fixed/ Rotary Wing Aircraft Configur ations, Performances, Stability and Control, Wind Tunnels, and Applications FOR 1AERO REVIEW PURPOSES ONLY FOR 1AERO REVIEW PURPOSES ONLY FOR 1AERO REVIEW PURPOSES ONLY V = Speed of object Answer: 0.70 𝑉𝑎 = Speed of sound 3. A jet transport is flying at a standard altitude of 30,000 ft with a velocity of 550mi/hr. What is the Mach number? Answer: 0.811 Three different regimes of aerodynamic flows 3. Airspeed Correction 1. If M 1, the flow is supersonic. Two other specialized aerodynamic regimes 1. If 0.8 < M < 1.2, the flow is transonic. 2. If M > 5, the flow is hypersonic. Calibrated Air Speed: (CAS). It is indicated airspeed Problems corrected for instrument and positional errors. At certain airspeeds and with certain flap settings, the installation and 1. What true velocity (in kts) is a high-speed instrument errors may total several knots. This error is reconnaissance plane maintaining at Mach = 3.0 cruise at generally greatest at low airspeeds, with nose high pitch 65,000 ft on a standard day? attitudes. Answer: 1720 knots Equivalent Air Speed: (EAS). An accurate measure of 2. Compute the Mach number of an aircraft flying at a flight dynamic pressure when the aircraft is flying fast. Air level of 27000 ft on its flight to Cebu. With its cruising entering the pitot tube(s) is compressed, which gives a speed of 420 knots. false dynamic pressure (lAS) reading, but only becomes CONFIDENTIALITY NOTICE: The contents of this review guide are intended solely for 1Aero participants and may contain confidential and privileged information. If you are not the intended end-user, you are hereby notified that any use, dissemination, copying, or storage of this review guide is strictly prohibited. We got your back, fam. Page 17 +63 915 363 5759/ +63 949 588 3874 [email protected] Attitude ∙ Skills ∙ Knowledge web.facebook.com/everythingaviation.1Aero/ PRC AERONAUTICAL ENGINEER COMPREHENSIVE REVIEW AERODYNAMICS Fundamentals of Low-High Speed Aerodynamics, Application of Aerodynamics to Fixed/ Rotary Wing Aircraft Configur ations, Performances, Stability and Control, Wind Tunnels, and Applications FOR 1AERO REVIEW PURPOSES ONLY FOR 1AERO REVIEW PURPOSES ONLY FOR 1AERO REVIEW PURPOSES ONLY significant at higher speeds. It is IAS corrected for Problems 'position' AND 'compressibility' error. 1. A high-speed jet fighter is flying at an altitude of 8 km. A pitot tube on the wing tip measures a pressure of 50 kPa. 2(𝑃𝑡 − 𝑃) 𝑉𝑒 = √ Calculate the true airspeed of the jet fighter (in 𝜌0 meters/sec). Where: Answer: 235.43 m/s 𝑃𝑡 = total pressure or stagnation pressure 2. An airplane is flying at standard sea level conditions at P = static pressure 45 meters per second. What is the difference between total 𝜌0 = density at sea level and static pressure? Answer: 𝑃𝑡− 𝑃 = 1,240.31 𝑃𝑎 True Air Speed: (TAS) or (V). The speed of the aircraft 3. An airplane is flying at standard sea level conditions at through the air. THE ONLY SPEED THERE IS - All the airspeed of 75 meters per second. What is the total other, so called, speeds are pressures. pressure? Answer: 𝑃 = 104,770.31 𝑃𝑎 2(𝑃𝑡 − 𝑃) 𝑉𝑇𝑅𝑈𝐸 = √ 𝜌∞ 4. An airplane is flying at standard sea level, the difference between total and static pressure is 1,750 Pa. What is the 𝑉𝑒 𝑉𝑇𝑅𝑈𝐸 = airspeed in meters per second? √𝜎 Answer: 𝑉 = 53.45 𝑚/𝑠 Where: 𝜌 5. The altimeter on a low-speed Cessna 150 private 𝜎 = 𝜌 , density ratio 0 aircraft reads 5000 ft. By an independent measurement, 𝜌∞ = freestream density the outside air temperature is 505°R. If a Pitot tube mounted on the wing tip measures a pressure of 1818 CONFIDENTIALITY NOTICE: The contents of this review guide are intended solely for 1Aero participants and may contain confidential and privileged information. If you are not the intended end-user, you are hereby notified that any use, dissemination, copying, or storage of this review guide is strictly prohibited. We got your back, fam. Page 18 +63 915 363 5759/ +63 949 588 3874 [email protected] Attitude ∙ Skills ∙ Knowledge web.facebook.com/everythingaviation.1Aero/ PRC AERONAUTICAL ENGINEER COMPREHENSIVE REVIEW AERODYNAMICS Fundamentals of Low-High Speed Aerodynamics, Application of Aerodynamics to Fixed/ Rotary Wing Aircraft Configur ations, Performances, Stability and Control, Wind Tunnels, and Applications FOR 1AERO REVIEW PURPOSES ONLY FOR 1AERO REVIEW PURPOSES ONLY FOR 1AERO REVIEW PURPOSES ONLY lb./ft2. What is the true velocity of the airplane? What is the Where: equivalent airspeed? V = tangential velocity in ft/s or m/s Answer: Ve = 218.470 ft/s; Vtrue = 236.339 ft/s 𝑉∞ = freestream velocity in ft/s or m/s Kutta-Joukowski Theorem Ө = angle through the point on the surface of the cylinder It is a pivotal relation in the circulation theory of lift. This with the main direction of the airflow in deg. theorem lets us perform a contour line integral around the shape of interest and immediately obtain the lift due to the By Incompressible Bernoulli Equation pressure distribution on that shape. 𝑃 𝑉 2 𝑃∞ 𝑉∞ 2 Alternate explanation of generation of lift that are in reality + = + 𝜌 2 𝜌∞ 2 not the fundamental explanation but rather are more of an effect of lift being produced, not the cause. – one of this is 1 𝑃 = 𝑃∞ + 𝜌∞ (𝑉∞ 2 − 𝑉 2 ) 2 called the circulation theory of lift 1 Physical Explanation of Circulation Theory of lift 𝑃 = 𝑃∞ + 𝜌∞ [𝑉∞ 2 − (2𝑉∞ 𝑆𝐼𝑁𝜃)2 ] 2 𝝆∞ 𝑽∞ 𝟐 𝑷 = 𝑷∞ + (𝟏 − 𝟒𝒔𝒊𝒏𝟐 𝜽) 𝟐 Where: 𝑙𝑏 𝑃 = 𝑃𝑟𝑒𝑠𝑠𝑢𝑟𝑒 𝑎𝑡 𝑎𝑛𝑦 𝑝𝑜𝑖𝑛𝑡 𝑜𝑛 𝑡ℎ𝑒 𝑠𝑢𝑟𝑓𝑎𝑐𝑒 𝑜𝑓 𝑐𝑦𝑙𝑖𝑛𝑑𝑒𝑟 𝑖𝑛 𝑜𝑟 𝑃𝑎 𝑓𝑡 2 Flow about a circular cylinder 𝑙𝑏 𝑃∞ = 𝑓𝑟𝑒𝑒𝑠𝑡𝑟𝑒𝑎𝑚 𝑝𝑟𝑒𝑠𝑠𝑢𝑟𝑒 𝑖𝑛 𝑜𝑟𝑃𝑎. 𝑓𝑡 2 𝑠𝑙𝑢𝑔 𝑘𝑔 𝜌∞ = 𝑓𝑟𝑒𝑒𝑠𝑡𝑟𝑒𝑎𝑚 𝑑𝑒𝑛𝑠𝑖𝑡𝑦 𝑖𝑛 𝑜𝑟 3. 𝑓𝑡 3 𝑚 CONFIDENTIALITY NOTICE: The contents of this review guide are intended solely for 1Aero participants and may contain confidential and privileged information. If you are not the intended end-user, you are hereby notified that any use, dissemination, copying, or storage of this review guide is strictly prohibited. We got your back, fam. Page 19 +63 915 363 5759/ +63 949 588 3874 [email protected] Attitude ∙ Skills ∙ Knowledge web.facebook.com/everythingaviation.1Aero/ PRC AERONAUTICAL ENGINEER COMPREHENSIVE REVIEW AERODYNAMICS Fundamentals of Low-High Speed Aerodynamics, Application of Aerodynamics to Fixed/ Rotary Wing Aircraft Configur ations, Performances, Stability and Control, Wind Tunnels, and Applications FOR 1AERO REVIEW PURPOSES ONLY FOR 1AERO REVIEW PURPOSES ONLY FOR 1AERO REVIEW PURPOSES ONLY Problems For total Lift 𝐿𝑇 = 𝐿 𝑥 𝑙 1. A uniform current of air with a speed of 100ft per sec. flows around a circular cylinder. At a distance from the Where: cylinder the pressure is atmospheric. What is the 𝐿𝑇 =Total lift in N or lb pressure at a point on the surface of the cylinder so L = Lift in 𝑙𝑏 or 𝑘𝑔 𝑓𝑡 𝑚 located that a radial line through the point makes an 𝑠𝑙𝑢𝑔𝑠 𝑘𝑔 𝜌∞ = freestream densit