The Bernoulli effect is key to our understanding of aerodynamics and crucial within aircraft design and motorsport. In motorsport, the engineers will want to generate downforce, pushing the car onto the road and providing more grip. In aerospace engineering, the aim is to produce lift to keep the plane in flight.
Some key terms we will need to understand before looking at the equation itself:
- Static Pressure (P) = The pressure exerted by a fluid which is not moving or flowing
- Usually what is meant when air pressure is referred to. Force exerted on the particles.
- Dynamic Pressure = The kinetic energy per unit volume of fluid (pv2/2)
- The difference between stagnation pressure and static pressure. If this value increases, static pressure goes down.
- Stagnation Pressure = Maximum pressure (static pressure + dynamic pressure)
- Also known as total pressure. This value remains constant when the height above sea level (and so density of air) is kept the same.
Bernoulli’s equation is:
P + pv2 + pgh = constant
- P = static pressure
- p = density
- v = velocity
- g = acceleration due to gravity
- h = height
Also written as:
Pressure + Dynamic pressure + density x height x acceleration due to gravity = Constant
Because pgh will remain constant if you stay in the same location, static pressure + dynamic pressure will be a constant in the same conditions. Dynamic pressure therefore can represent the loss in pressure due to velocity.
This means that as the relative velocity between the fluid and body is increases, the static pressure drops. This is incredibly important in aerodynamics and is an important principle to consider when attempting to produce lift or downforce.
The stagnation point is where the pressure is highest, the velocity therefore must be zero. Using the Bernoulli equation, we know that total pressure is constant so:
Pe + pv2e = P0 + pv20
Where e is any point and 0 is at the stagnation point.Velocity at the stagnation point is zero, so pv20 is equal to zero. This means that Pe + pv2e = P0
Because velocity is zero, the dynamic pressure is also zero, so static pressure is the highest value it can be. The static pressure is therefore also stagnation pressure. On a race car, stagnation points will result in high amounts of drag being produced, as the pressure resisting the motion of the car is highest.
In motorsport, downforce is incredibly important. It is produced by channeling fast moving air below the car and slow moving air above the car. The pressure difference will result in a downwards resultant force of very high magnitude, which pushes the car to the ground.
The front and rear wings are crucial to generating downforce on a Formula One car, but another key area which has been exploited by engineers in recent years has been the diffuser.
Go to my website www.f1now.co.uk for more on F1 aerodynamics.