Introduction to Aerodynamics

There is a common misconceptions when it comes to Aerodynamics and Fluid Mechanics. Aerodynamics comes from the Greek for Aerios and contains two main conceptions, lighter than air known as Aerostatics, and heavier than air Aerodynamics.

Aerodynamics is the science describing forces on, and the resulting movement of objects though fluids, such as air.

Aerodynamics is a function of Fluid Mechanics, which like aerodynamics is broken into two main conceptions, Fluid Statics and Fluid Dynamics. [The schematic below should make for a better understand of this.

A fluid will keep moving as long as a force is present, the stress is proportional to the strain rate.

Properties of Fluids

It is known that water at 4℃ has a density of 1000kg/m^3. Density is defined as Rho, and changes in density are dependant upon temperature for liquids, and pressure and temperature for gases. This is known as the equation of state and separates aerodynamics/statics from hydrodynamics/statics. 

Air = 1.225 kg/m^3 (unless stated otherwise)

Water = 1000 kg/m^3 (unless stated otherwise)

In thermodynamics there is something called the Perfect Gas Law which is P = [rho]R*T. When you have the required data, you will find out that the R which is the Specific Gas Constant, for Air is 287.058 J/kgK [Joules/KilogramKelvin]

Always bare in mind that Gases are compressible and liquids generally are incompressible. 

Airliners generally fly at 12km above sea level, using the internal ISA charts, it can be established that the Pressure at this altitude is 19399 Pascals with the temperature 216.66 Kelvin. Therefore the density of the air is:

The Mach Number can be determined by [M=V/a] where 'a' is the speed of sound (SOS). The speed of sound for a perfect gas is:

Where Lamna, is the isentropic coefficient, which for Air is 1.4 [This is a constant]

The final part of the introduction to Aerodynamics is to understand Viscosity, this is defined as the "Stickiness" or "Thickness" of a fluid. This higher the number, the more "sticky."

Typical viscosity's are 1.81x10^-5 Pa/s for Air, and 1002x10^-3 for Water.

The Kinematic Viscosity is the same value, but without the effect of density, therefore V=μ/ρ [mu/rho]

This was a brief introduction to fluid mechanics and aerodynamics at Level 4, year one University, the next blog post will feature some more advanced features, and some higher level definitions. 

First Order Differential Equations.

First order differential equations are a lot more complex than ordinary differentials, the best way to identify a first order is shown below.

Integration - The Basics

Integration is the reverse of differentiation, and it has to be said it is a lot harder in my opinion. Integration is known as finding the area under a curve and although you can use graphical software and calculators to avoid complex formula's, it does help to have the knowledge to integrate using the classic pen and pencil.

Shown below is a few of the most common integrals

Differential Calculus - Examples

As promised here are some examples of differentiation which should clear up any confusion from the first topic "Diffential Calculus - The Basics" 

These first examples do not require any rules as they are simple equations and not combinations of functions. They can be solved by simply using the basic functions in the previous chapter.

Differential Calculus - The Basics

Welcome to the first differential calculus topic, shown below are some of the basic functions in differentiation which will be required to complete the unit.