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What is the primary purpose of using a standard atmosphere in engineering?
What is the primary purpose of using a standard atmosphere in engineering?
The standard atmosphere starts at an altitude that is different from sea level.
The standard atmosphere starts at an altitude that is different from sea level.
False (B)
What is the standard sea level temperature in Celsius?
What is the standard sea level temperature in Celsius?
15
The geometrical altitude, denoted as ______, measures the height above sea level.
The geometrical altitude, denoted as ______, measures the height above sea level.
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Match the following terms with their definitions:
Match the following terms with their definitions:
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What does the term 'pressure altitude' refer to?
What does the term 'pressure altitude' refer to?
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The pressure altitude and the true altitude are always the same.
The pressure altitude and the true altitude are always the same.
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If a standard atmosphere table indicates that a temperature of 265.4 K corresponds to 3500 m, what is the 'temperature altitude'?
If a standard atmosphere table indicates that a temperature of 265.4 K corresponds to 3500 m, what is the 'temperature altitude'?
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The density altitude is the altitude indicated in the standard atmosphere for a given ______ value.
The density altitude is the altitude indicated in the standard atmosphere for a given ______ value.
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Match the following altitude types with their definitions:
Match the following altitude types with their definitions:
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What is the value of the acceleration due to gravity at Earth's surface (go)?
What is the value of the acceleration due to gravity at Earth's surface (go)?
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The density and pressure of air vary linearly with height, similar to water.
The density and pressure of air vary linearly with height, similar to water.
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The hydrostatic equation applies to both compressible and _____ static fluids.
The hydrostatic equation applies to both compressible and _____ static fluids.
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What is the result of using go, a constant, rather than g = f(height) in the hydrostatic equation?
What is the result of using go, a constant, rather than g = f(height) in the hydrostatic equation?
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What does 'dhG' represent in the context of the air cube analysis?
What does 'dhG' represent in the context of the air cube analysis?
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The forces on the vertical surfaces of the air cube are not considered in the hydrostatic equation since they are not balanced.
The forces on the vertical surfaces of the air cube are not considered in the hydrostatic equation since they are not balanced.
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The hydrostatic equation is a differential equation that relates pressure to _____.
The hydrostatic equation is a differential equation that relates pressure to _____.
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What is the primary reason for the difference between geometric height (hG) and geopotential height (h)?
What is the primary reason for the difference between geometric height (hG) and geopotential height (h)?
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The difference between geopotential and geometric height is significant, particularly at lower altitudes.
The difference between geopotential and geometric height is significant, particularly at lower altitudes.
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What is the approximate altitude of the tropopause in kilometers?
What is the approximate altitude of the tropopause in kilometers?
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In regions where temperature varies linearly with height, the rate of change is known as the ______.
In regions where temperature varies linearly with height, the rate of change is known as the ______.
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Match the atmospheric layers with their approximate height ranges:
Match the atmospheric layers with their approximate height ranges:
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Which atmospheric layer is characterized by a constant temperature region between 11km and 25km?
Which atmospheric layer is characterized by a constant temperature region between 11km and 25km?
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The temperature in the thermosphere consistently decreases with increasing altitude.
The temperature in the thermosphere consistently decreases with increasing altitude.
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What is the temperature in Kelvin at the base of the troposphere?
What is the temperature in Kelvin at the base of the troposphere?
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For isothermal regions with constant temperature, calculations start with the fixed values at the ______, T1, p1, and 1.
For isothermal regions with constant temperature, calculations start with the fixed values at the ______, T1, p1, and 1.
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Which of these is not a region in the standard atmosphere?
Which of these is not a region in the standard atmosphere?
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Study Notes
AER 416: Part 3 Standard Atmosphere
- Engineers use a standard atmosphere for design and performance assessment.
- The standard atmosphere represents the average atmospheric conditions at different heights above Earth's surface.
- The standard atmosphere starts at sea level (height zero).
- The standard atmosphere data is typically presented in tabular format.
- Appendices A (SI units) and B (Imperial units) in the course text contain tables of the standard atmosphere.
- The course material explores the derivation of the standard atmosphere table and how to apply it.
Standard Sea Level Conditions
- Pressure: 101,325 Pa or 2116.7 lbf/ft²
- Density: 1.225 kg/m³ or 0.002378 slug/ft³
- Temperature: 15°C or 288.16 K or 59°F or 518.69 °R
Height Definitions
- r: Radius of the Earth (6356 km) from its center to sea level
- hG: Geometrical altitude (height above sea level)
- ha: Absolute altitude (height from the center of the Earth)
- ha = hG + r
Acceleration Due to Gravity
- The acceleration due to gravity, 'g', varies with height.
- Acceleration due to gravity at Earth's surface (go) = 9.81 m/s².
- G = universal gravitational constant (6.67x10⁻¹¹).
- me = mass of the Earth (5.972x10²⁴ kg).
- g(ha) = (Gme) / (ha)²
Relating g's
- The relationship between g at height ha and go (acceleration due to gravity at Earth's surface) is: g = go (r² / (r + hG)²).
Hydrostatic Equation
- The density and pressure of air do not vary linearly with height, unlike water.
- This is due to the compressibility of air.
- The analysis of a column of air begins with the hydrostatic equation, similar to analysis using water.
Deriving the Hydrostatic Equation
- Forces on a cube of air (1m x 1m) in the atmosphere are balanced.
- The force on the lower surface is p where p= pressure
- The force on the upper surface is p + dp where dp = small incremental change in pressure.
- The weight of the air within the cube acts downwards: density(volume of cube)(gravity force(g)).
- Sum of forces = 0; dp = (density x gravity x height)
Hydrostatic Equation (continued)
- This leads to a differential equation: dp = -ρ g dh
- This equation is based on the assumption of a constant value for g, rather than a value function g(h), for simplicity.
- The use of a constant value for go simplifies the calculations and analysis of the atmospheric effects and pressure.
Isothermal Regions
-
In isothermal regions, the temperature (T) is constant during any pressure variations.
-
The pressure and density change exponentially with height (in an isothermal region).
Gradient Regions
- In gradient regions, temperature (T) varies linearly with height.
- The relationship for temperature at any height is T = T1 + a(h - h1) where a is the lapse rate and h1 and T1 are the reference height and temperature.
Pressure, Temperature, and Density Altitudes
- The standard atmosphere defines pressure, temperature, and density altitudes.
- For example, a pressure of 61.6 kPa corresponds to a pressure altitude of 4000 m.
- The pressure/density/temperature altitude is the standard atmosphere altitude that is given for a particular pressure/density/temperature and is not necessarily a reflection of the actual altitude.
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Description
Explore the principles behind the standard atmosphere used in engineering for design and performance assessment. This quiz covers atmospheric conditions, height definitions, and standard sea level conditions, as well as the derivation of related tables. Ideal for students in aerospace engineering courses.
