Notes, summaries, assignments, exams, and exercises for Physics for Other courses

Introduction to Computational Fluid Dynamics (CFD)

Definition of CFD: CFD is the process of mathematically predicting physical fluid flow by solving the governing equations using computational power. Every CFD analysis uses a mathematical model and numerical method based on the Navier-Stokes (N-S) equations. Physical properties are calculated based on defined operating conditions.

Main objectives:

• Minimize the cost of the system
• Understanding and comprehension of the problem
• Improve behavior
• Reduce the time and cost of the design stage

3 Fundamental Principles:

1. Mass is conserved
2. F=m*a (Newton's 2nd Law)
3. Energy is conserved

Mass Conservation Principle: The rate of increase of mass in a fluid element equals the net rate of flow of mass into the fluid element....

The Sun's Structure and Activity

The Solar Atmosphere: Layers and Characteristics

The Sun's atmosphere consists of three primary layers: the Photosphere, the Chromosphere, and the Corona.

Photosphere

• Part of the Sun we see: Covers the distance over which the Sun changes from transparent to opaque.
• Thin layer of gas, 300–400 km deep.
• Below this layer, the gas is denser and hotter, but light does not escape.
• Produces an absorption line spectrum.

Chromosphere

• Lies immediately above the photosphere.
• Discovered during eclipses in the 17th century.
• Approximately 2,000–3,000 km thick.
• Density is about 1/10,000 that of the photosphere.
• Produces an emission line spectrum.
• Its red color results from hydrogen (H) emission (n=3 to n=2 transition line).

Corona

• Observed

Mechanisms of the Vestibular System

Vestibular System Sensitivity to Acceleration: Mechanism

The vestibular system is sensitive to acceleration (linear or rotational) through the following mechanism:

• Semicircular Canals: There are three semi-circular canals, rotated 90 degrees relative to each other.
• Each canal is sensitive to acceleration in a different plane.
• The canals are filled with fluid (endolymph), which lags behind head movement, stimulating sensory hair cells.

Detecting Head Orientation (Tilt) via the Vestibular System

If the vestibular system is sensitive to acceleration, it can also detect the orientation (tilt) of the head because of its sensitivity to gravity. The otolith organs (utricle and saccule) contain dense structures (otoconia)...

Reading Section

1. C  11. B  21. C  31. A  41. D  51. A
2. B  12. C  22. D  32. C  42. ?
3. A  13. A  23. C  33. B  43. C
4. A  14. B  24. A  34. B  44. A
5. C  15. B  25. C  35. D  45. C
6. D  16. C  26. D  36. B  46. A
7. A  17. C  27. D  37. D  47. D
8. A  18. B  28. D  38. C  48. C
9. C  19. C  29. D  39. A  49. D
10. A 20. B  30. D  40. D  50. A

Writing and Language Section

1. D  11. B  21. C  31. C  41. C
2. C  12. A  22. B  32. A  42. ?
3. C  13. D  23. B  33. B  43. ?
4. B  14. A  24. D  34. D  44. ?
5. A  15. B  25. A  35. C
6. D  16. D  26. D  36. B
7. B  17. D  27. B  37. A
8. B  18. A  28. A  38. C
9. A  19. C  29. D  39. C
10. A 20. D  30. D  40. C

Math Sections

Math Section 3

1. C   11. B
2. D   12. A
3. B   13. A
4. D   14. C
5. A

Fundamental Astronomy Concepts

Angular Measurements & Units

1 degree = 60 arcminutes = 3600 arcseconds; 1 radian = 180/π degrees; 1 light year =

Understanding Angular Diameter

Angular diameter (or size) is the angle an object subtends, measured in units like degrees, arcminutes, radians, or arcseconds. The angular size of an object (α) is calculated as: α = D (diameter) / d (distance), where D and d must be in the same units.

Celestial Sphere & Earth's Motion

Circumpolar Stars & Polaris

Circumpolar stars are stars that appear to never set because they closely circle a celestial pole, such as Polaris (the North Star). The altitude of a celestial pole above the horizon is equal to your latitude.

• At 40° North latitude, the North Celestial

Numerical Methods for Solving Equations

1.1 Solving an Algebraic System

This code defines a function f(V) and then solves the system f([x,y,z]) = [x,y,z] to find its fixed points using the algsys command.

faux(x,y,z) := [(x^2)/2 + 1/3, x+y+z/4, x^2-y^2+(z^2)/4];
f(V) := faux(V[1], V[2], V[3]);

ecus : f([x,y,z]) - [x,y,z];
algsys(ecus, [x,y,z]), numer;

1.2 Fixed-Point Iteration Method

This block implements the fixed-point iteration method. It starts with an initial guess (seed) and iteratively applies the function f until the norm of the difference between successive iterations is smaller than a given tolerance (10^-14).

nor(V) := sqrt(V.V);
fpprec:100;

block(
  semilla:[0,0,0],
  while nor(f(semilla)-semilla) > 10^(-14) do 
    semilla:bfloat(

Understanding Solar Radiation

Direct radiation: Solar radiation received directly from the sun without being scattered by the atmosphere.

Diffuse radiation: Solar radiation received after its direction has been changed due to reflection and refraction in the atmosphere.

Total radiation is the sum of direct and diffuse radiation at the surface.

Solar Constant

The solar constant is the amount of energy received per unit time on a unit area perpendicular to the sun's direction at Earth's mean distance, outside the atmosphere. The currently accepted value is: S = 1.94 Ly min^-1 = 1368 W/m²

Absorption, Reflection, and Transmission

When radiation strikes a body, it can be absorbed, reflected, or transmitted. The ratio is: e + r + t = 1, where:

• e = absorptivity
• r

Oxygen Measurement Systems

Oxygen measurement systems, including electrochemical and zirconium oxide types, are crucial for determining the percentage of oxygen present in a gas concentration.

Electrochemical Oxygen Cell Operation

An electrochemical cell generates an electric potential, similar to a battery. The value of this potential is directly proportional to the oxygen concentration in the gas mixture.

Zirconia Cell Operation

The zirconia cell also generates an electric potential based on the oxygen level in the mixture, providing an accurate measurement of the oxygen percentage.

CO Analyzers for Combustion & Environmental Control

CO analyzers are essential for monitoring and controlling combustion processes and environmental emissions. Two...

Ideal vs. Practical Voltage Sources

Refraction of Light: Principles and Elements

Refraction of light is the change in direction experienced by light rays when they pass through a surface separating two media of different densities.

Key Elements of Light Refraction

• Incident Ray: The ray of light that reaches the surface in medium 1.
• Refracted Ray: The ray of light that has crossed the surface and moves in medium 2.
• Normal: An imaginary straight line perpendicular to the surface at the point of incidence.
• Incident Angle: The angle formed between the incident ray and the normal.
• Angle of Refraction: The angle formed by the refracted ray and the normal.

Conditions Governing Light Refraction

In the process of refraction, the following conditions apply:

• When light passes from a less dense medium