In Aerospace Engineering, understanding the fundamentals of fluids is crucial for designing aircraft and for propulsion devices. The reason understanding fluids is important is because air can be considered as a fluid with its own special properties. When a plane flies through the sky, the air flows around the plane, creating lift and inducing drag. There are many different properties to air, and I assure we will talk about most if not all of them throughout this course. Enough said, let’s get started!
The first property we are going to talk about is pressure. If you have ever driven in a car and put your hand out of the window, you probably noticed a force pushing back; this is due to the air colliding with your hand, and this is a perfect example of pressure. Pressure is defined as the force per unit area and has units of Pascals (Pa) or $ \frac{N}{m^2} $ for SI, and $ \frac{lbs}{ft^2} $ for English. Pressure can be written as
[ 1 ]
$$ P = \frac{F}{A} $$
where P is pressure in Pa, F is force in N (Newtons), and A is the area in $ m^2 $.
Infinitesimal area in a gas under a force.
For differential increments of force and area, we can then write pressure as
[ 2 ]
$$ P = \lim_{dA \rightarrow 0} (\frac{dF}{dA}) $$
The next property that we will talk about is density. Density is the measure of mass per volume and has units $ \frac{kg}{m^3} $ for SI, and $ \frac{lbs}{ft^3} $ for English. I like to think of density as the classic experiment where you mix different oils in a beaker and when they settle, they will separate into different layers, with the densest layer on the bottom and the least dense layer on the top. We can write density as
[ 3 ]
$$ \rho = \frac{m}{V} $$
where $ \rho $ is density in $ \frac{kg}{m^3} $, m is mass in kg, and V is volume in $ m^3 $.
Infinitesimal volume in a gas volume.
If we were to take the limit of differential increments of mass and volume, then we could write density as
[ 4 ]
$$ \rho = \lim_{dV \rightarrow 0} (\frac{dm}{dV}) $$
The third property we will learn about is temperature. Temperature is proportional to the average molecular kinetic energy of a gas, and is always moving. Compared to liquid or solid states, gas has more energy by far; gas molecules are constantly colliding with one another and zipping around. Temperature has units of K (Kelvin) and °C (Celsius) for SI, and °R (Rankine) and °F (Fahrenheit) for English; it can be calculated using the Boltzmann constant and the average molecular KE of a gas.
[ 5 ]
$$ T = \frac{2}{3}\frac{KE}{k} $$
T is temperature in K, KE is average molecular kinetic energy of a gas in J (Joules), and k is the Boltzmann constant, where k = 1.38E-23 $ \frac{J}{K} $. Temperature is critical for most processes in aero and astrodynamics, especially for when we start talking about supersonics and hypersonics because the temperature increases greatly.
Now that we have an idea of the 3 fundamental properties of a flowing gas, let’s take a look at some air flowing around an airfoil.
Image of smoke streamlines passing around a Lissaman 7769 airfoil. Source: Dr. T.J. Mueller.
We will talk about them in much more detail as we go, but airfoils are cross sections of wings. They allow aerospace engineers to determine the properties of flight for a plane. As we can see from the image, there is airflow (using some smoke) going above and below the airfoil. Notice how the airflow going over top of the airfoil is closer to the top of the airfoil and the airflow going underneath the airfoil is further from the surface of the airfoil. This indicates there is more air underneath the airfoil than on top of the airfoil. We will break this down more as we go, but this is just a taste to see how air behaves around an airfoil. Studying streamlines is very useful for our field because they allow us to visualize the air patterns.