Bernoulli's equation is a fluid dynamics equation that has been derived from Bernoulli’s principles. Bernoulli’s principle states that increasing fluid speed occurs simultaneously with a decrease in pressure and the fluid’s potential energy. Bernoulli’s equation can be seen below:
There are various ways to determine Bernoulli’s principle from other engineering and physics principles. One of those is the law of conservation of energy. This states that through a fluid streamline, if there are no changes to the streamline, the sum of energy (kinetic, potential and internal) remain the same. Another is Newton’s Second Law of Motion. Newton’s Second Law states that F = ma which is derived from the rate of change of momentum of a body is directly proportional to the force applied, and this change in momentum takes place in the direction of the applied force.
So, what is Bernoulli’s equation used for? Here are a few applied examples:
Determine the fluid pressure at 2 different points in a pipework system.
Determine the fluid speed at a given point in a pipework system.
Find the velocity coming out of a water tank if the valve was opened.
Understand the force required to detach the roof of a house during strong wind.
Find the pressure required from a water system to feed enough water to a house which is on top of a hill.
There are many other examples. A great lecturer I have found who gives applied examples for fluid dynamics is Michel van Biezen. Head over to his channel if you require any additional help with your fluid dynamics course.
But, the primary question of this blog is how does this relate to the force of lift of an aircraft.
The general consensus for understanding lift is that the lower half of an aerofoil provides a shorter path and thus to meet up with the air flowing above the aerofoil, which has a much larger path, the flow of air must be faster. This is very similar to the Bernoulli effect.
There are a number of problems, however, with this theory. The most basic example of an issue with this theory is that there are symmetrical aerofoils that are capable of producing lift and why does an aircraft not fall to the floor during an airshow when it flies upside down?
Additionally, if you simulate the speed above and below an aerofoil, you will notice that the air molecules travel much faster above the wing to a point where they don’t meet the molecules below the wing at the trailing edge.
The real answer for where lift comes from stems from Newton's Third Law. To every action there is an equal and opposite reaction. When a plane is climbing or has a greater angle of attack the action is the air molecules striking the lower surface of the wing. The opposite reaction is that lift is then generated. The confusion comes through the fact that most of Bernoulli’s principles explains the theory of lift, but it is not entirely true.
So, how can we use Bernoulli’s equation in an aerospace example? Although not fundamentally exact, the following video demonstrates how we can determine a rough estimation of the surface area of a wing from our friend Michael van Biezen. The truth is that the large aerospace companies will not rely on any single fundamental principles to determine the shape or size of a wing but will use computational analysis in the form of CFD to determine how the wing is shapes. This is accompanied by intelligent manufacturing processes to obtain the most effective shape at the correct mass.
To conclude, we have determined that although Bernoulli’s equation is not the sole source of how lift is generated. However, we have learned that it is a valuable principle that can be applied in a generalised fashion to represent a method for how lift can be created from a fluid mechanics perspective.