1. 5% short answers for what specific application did Henri Pitot develop the Pitot tube? what was the name of NACA s (now NASA) first research laboratory? in what country (per Anderson) was the first wind tunnel designed/built? Name 1 of 2 people who first mathematically provided an equation to solve D Alembert s paradox (hint: both names are used in the single name of the most important (xxx-xxx) aero eqns) Per Anderson, who has been called the father of aerodynamics 2. 5% Consider our discussion of units and the consistent use of Newton s Second Law (F = ma), derive the conversion factor between the derived unit of force Newton and the inconsistent unit of kg as a force (where a subscript f might be used to infer force because of the context). If kg is used as a unit of force, why is it referred to as an inconsistent unit? 3. 10% During a pressurization test at standard sea level conditions for an aircraft fuselage, it is pressurized filled with air until the gage pressure is 5000 kg/m 2 and the internal temperature is 25 o C. Find the specific volume of the air in the fuselage. note 1: check that units work here the unit of pressure is kg/m 2 and must be converted to N/m 2 note 2: gage pressure is the difference between the internal and external pressure The fuselage has a volume = 3500 m 3. All air is removed. Determine the buoyant force of the fuselage. note: the (gross) buoyant force results by displacing the weight of fluid (here, the atmosphere) with a volume of a body (here, the fuselage)
4. 5% Given the pressure and shear distribution on the wing as shown, z c = chord = 10 m τ = τ(x) = 2x N/m 2 V p = constant = 10 N/m 2 Find the drag force D due to the shear stress. span (along y) = b = 50 m x 5. 5% Atmosphere and Altitude: (a) list the 6 types of altitude. 1. geometric 2. 3. 4. 5. 6. b. Why is the version of the hydrostatic equation that uses altitude "h" instead of "h G " used in the development of the standard atmosphere? 6. 10% The temperature profile for planet Q is shown. The gas constant, R gas, Q, and surface conditions g o,q, T S,Q and p S,Q are known. 20k ft 15k ft h planet Q a. Label the isothermal and gradient regions. b. Compute the lapse rate for the gradient region. 10k ft c. Determine the pressure at 15k ft (properly identify all terms and equations, and outline all steps.) note 1: p 10k,Q must be found at the top of the isothermal region before p 15k,Q may be found note 2: temperature must be converted to R 0 T -100 o F 100 o F
7. 5% Assume we are ascending in the space shuttle. At 30 km, a 15 percent decrease in pressure per second is measured. Using the hydrostatic equation, find the equation to determine the rate of climb of the shuttle. Assume ρ and g are constant: ρ = ρ 30 km and g = g o. note: the statement At 30 km, a 15 percent decrease in pressure per second is measured. means dp/dt = -.15p 30 km /sec 8. 5% Given Euler s equation, dp = -ρv dv, derive Bernoulli s equation. Bernoulli s equation states the total pressure ( p + q ) is constant along a streamline, under what conditions are we allowed to use this same constant total pressure for ALL streamlines in a flow? 9. 10% An altimeter on a low-speed (M < 0.3) airplane provides pressure altitude from which p is known. The air temperature is known as T. As designed, a precisely mounted Pitot-static probe measures the pressure, P. a) Identify (name) the two pressures that are components of P. b) Derive the equation to determine the true airspeed, V TAS, appropriate for low (incompressible) speed. c) Derive the equation to determine the equivalent airspeed, V EAS. d) Considering the concept of dynamic pressure, what is meant by equivalent airspeed, V EAS? e) Why are the sea level values of p s and a s used in the ASI that measures high subsonic speeds?
10. 10% Low speed incompressible flow passes through a wind tunnel. The cross sectional area is given below. Station 1 has standard sea level conditions. 1 p s, ρ s, T s 2 3 1 2 h A 1 = 10 m 2 A 2 = 2 m 2 A 3 = 12 m 2 inset A manometer is filled with mercury (see inset, and ρ hg is known) and is used to measure the pressure difference between the total pressure at station 1 and the static pressure at station 2. This pressure difference is measured and given as h. In terms of the known information, find the velocity, static pressure, and total pressure at station 2. note 1: here, the manometer is set to read p = -ρ hg g o h where p = p 2 p o. With consistent units -ρ hg g o h has units of force per area (pressure). note 2: the total pressure (aka the stagnation pressure ), p o is a constant in the entire flow. What is the pressure measured by a Pitot tube placed in the flow at Station 3? 11. 5% short answers What is meant by isentropic flow? What viscous-related flow feature does x cr represent? Name the 2 forms (sources, types) of drag present on an airfoil. What gas (or fluid) property directly relates the velocity gradient of the boundary layer to shear stress? What is d Alembert s paradox?
12. 15% An aircraft is flying at standard sea level conditions. p a S = p V T o S = T ρ S = ρ m m a) given low subsonic conditions: M 0.1; V = 30 ; Va 50 s = s, determine the static pressure at point a. note: this case is incompressible flow use Bernoulli s eqn. b determine the dynamic pressure at point b if p b = 0.9 atm. m m b) given high subsonic conditions V = 200 ; M = 0.70; Va = 270, s s determine the stagnation pressure at point o. note 1: this case is compressible flow (but no shock) use the isentropic and energy equations; the temperature (and Mach No.) change from point to point determine the static pressure at point a.
13. 10% Consider isentropic flow of air through a supersonic nozzle, reservoir p R T R exit T e A e Given measurements of pressure and temperature in the reservoir and given temperature and area at the exit, a) At the exit, find the Mach number, velocity, and mass flow. note: Reservoir conditions are stagnation conditions. b) Where is static pressure the maximum? And, what is the value? note: the static pressure is the total pressure if the flow is brought to rest isentropically.