aerodynamics notes 01
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Welcome to Aerodynamics (AEEM 2042C) (pass and project syllabus) My name is David Munday, 310 Rhodes, 556‐1284, [email protected] Aerodynamics is a subset of fluid mechanics and we will begin with general principals of fluid mechanics and later specialize to the case where the fluid in question is air and further to those air problems related to aerospace. So what is a fluid? Will not support shear without continuous deformation
A liquid or a gas, not a solid So what’s the difference? Micro‐scale: Molecules of a solid don’t flow over one another. A crystal or so close together they stick. Molecules of a liquid farther apart, but close enough to have attractive and repulsive forces Molecules of a gas far enough apart to not interact except through occasional collisions Macro scale Liquid or a gas. Solid in a container: does not change shape Liquid in a container: shear from gravity and deforms to fill container up to free surface Gas in container: expands or contracts to fill container, no free surface present Difference between liquid and gas is compressibility density can change significantly in a gas A gas doesn’t have to change density. Lots of cases it doesn’t. Generally M < 0.3 no significant density change. What is density? ρ Mass divided by volume, kg/m3 or lbm/ft3 or slugs/in3. Can be defined globally for a container of stuff, but We can consider any small portion of a fluid, mm3 or µm3 or even smaller and define a density ρ anywhere in the fluid. In some cases (M > 0.3) or deep in the ocean we mass see different ρ at different points in the flow.
It is a point property. lim → note V is volume, v is velocity
Can we choose smaller and smaller volume elements without limit? In theory we act as if we can – this is the continuum hypothesis We really can’t. At some point there are too few molecules in our volume for this to work. Limits on the continuum hypothesis: Mean free path, λ Knudson number, Kn == λ/l, continuum hypothesis holds for Kn << 1 else must use statistical mechanics instead of fluid mechanics Compressible vs incompressible Syllabus TAs
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Books Website Grading Policies Plagiarism
How do we do fluid mechanics? Analytical Experimental Numerical All of these require understanding of the analytical,
Experiments measure some things and derive others CFD solves the analytical equations
All the analysis we do in fluid mechanics is based on five principals. The rest is definitions and math.
1) Mass is conserved 0
2) Energy is conserved 0
3) Momentum relation (Newton’s second)
4) Equation of state (eg. Ideal gas law )
5) Relation between temperature and internal energy (eg. )
Pressure
lim → , units N/m2, Pa, lb/ft2 lb/in2, psi, bar, atm, in Hg, in H2O
Absolute, gage and differential pressure Shear stress
lim → , same units
Temperature Related to energy content, units, °F, °R, °C, K, 0°F = 458.67°R 0°C = 274.15K Problems: Determine a density discuss limits of significant figures and units Given a container 1.00 in on a side is filled with mercury (Hg). The container is measured on a balance and the mass is 221.2 g. Neglect the mass of the empty container. What is the density of the mercury in the container in g/cm3?
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Assumed: The density is uniform throughout the container The mass of the container is negligible V = (1.00 in)3 = (2.54 cm)3 = 16.4 cm3 m = 221.2 g ρ = m/V = 221.2g/16.4cm3 = 13.48780488 g/cm3 = 13.5 g/cm3 Note: The textbook value for Hg is 13.534 g/cm3 Given ideal gas equation, R, P and ρ, find T discuss units The most common form of the equation of state is the ideal gas equation This equation contains the gas constant, R which is different for different gasses. For Helium (He) is 12,420 ft lb/slug‐oR or 2,077 J/kg‐K or 2.077 kJ/kg‐K. A 1000 ft3 container contains 3.00 slugs of Helium at 140 psia. Find the temperature of the gas in °F. ρ = 300 slugs / 1000 ft3 = 0.00300 slugs/ft3
140 / 12 /
0.00300 / 12,420 / °541° 81
Given ideal gas equation, R, P and ρ, find T mismatched units Carbon dioxide (CO2) is delivered in a 265 liter dewar containing 593 lbm of gas. The pressure in the dewar is 350 psig. What is the temperature of the gas in K? The gas constant for CO2 is 1,130 ft lb/slug‐oR or 188.9 J/kg‐K or 0.1889 kJ/kg‐K. Assumptions: The pressure outside the dewar is the sea level standard pressure of 14.7 psia. First get things in consistent units: V = 265 l (m3/1000 l) = 0.265 m3 m = 593 lbm (1kg/2.20462lbm) = 269 kg P = 350 psig = 364.7 psia P = 365 psia (6,894.75729 Pa/psia) = 2,520,000 Pa = 2.52 x 106 N/m2 ρ = m/V = 269 kg/0.265 m3 = 1.02 x 103 kg/m3
2.52 10 /
1.02 10 / 188.9 /13.1
Given uniform pressure on top and bottom of wing and area, calculate normal force Given wing area and drag calculate shear stress assuming it is uniform over both surfaces