Lecture+2-Standard+Atmosphere

Lecture+2-Standard+Atmosphere - AOE 2104Intro to Aerospace...

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Click to edit Master subtitle style Virginia Tech Lecture 2 AOE 2104 Introduction to Aerospace Engineering Lecture 2 Standard Atmosphere AOE 2104—Intro to Aerospace Engineering Fall 2010 26 August 2010
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Click to edit Master subtitle style Virginia Tech Lecture 2 Review of the Syllabus- Questions? AOE 2104—Intro to Aerospace Engineering Fall 2010 26 August 2010
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Click to edit Master subtitle style Virginia Tech Lecture 2 Standard Atmosphere – Why and How? Designing an aircraft requires knowledge of the four basic aerodynamic quantities. What are they? P, ρ , T, and V What else do we need to know? Aircraft operating conditions vary with altitude. We can relate p and v. p, ρ , and T are related through the Equation of State. Need to obtain a relation for p, ρ , or T as a function of altitude in order to compare experimental (wind tunnel) and actual flying conditions. Standard Atmosphere Model provides? the variations of these 3 properties with altitude. AOE 2104—Intro to Aerospace Engineering Fall 2010 26 August 2010
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Click to edit Master subtitle style Virginia Tech Lecture 2 AOE 2104—Intro to Aerospace Engineering Fall 2010 26 August 2010
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Click to edit Master subtitle style Virginia Tech Lecture 2 Before describing the variations of p, ρ , and T with altitude, one needs to define what altitude is to be used. 3 Types of Altitudes: Geometric (aircraft) hG = altitude measured from sea level. Absolute (usually used for space applications) ha = altitude measured from the center of the Earth. └►ha = hG + r where r is the radius of the Earth. e.g. Newton’s Law of Gravitation: Geopotential (“fictitious” altitude) h = fictitious altitude used to compute the Standard Atmosphere Model. Altitudes - Definitions AOE 2104—Intro to Aerospace Engineering Fall 2010 26 August 2010
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Click to edit Master subtitle style Virginia Tech Lecture 2 Hydrostatic Equation First step to calculate the variations of p, ρ , and T with altitude consists in finding the relation between pressure, density and altitude. Consider an element of fluid at rest with dimensions (1,1,hG): p Increasing altitude 0 ( ) 0 (1 1) (1 1 ) ( ) (1 1) 0 G Vertical F pS mg p dp S p dh g p dp ρ = ⇒ - + + + = ⇒ - × × + × × × + + × × = G dp = -ρgdh Hydrostatic Equation Note : p, ρ , and g are functions of hG Top and bottom surface area Volume of the fluid element AOE 2104—Intro to Aerospace Engineering Fall 2010 26 August 2010
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Click to edit Master subtitle style Virginia Tech Lecture 2 First, let assume that gravity does not vary with altitude, so that g = g0 the value of gravity at the surface of the Earth. Replacing in the H.E we get Note that hG has been replaced by h so the equation numerically matches the H.E.
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Lecture+2-Standard+Atmosphere - AOE 2104Intro to Aerospace...

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