The Bernoulli effect is key to our understanding of aerodynamics and crucial within Formula One. Generating the most downforce with the least drag is the challenge for the aerodynamicists. The equation links pressure with velocity and helps us gain a greater understanding of the airflow around the car.
Definitions:
Let’s start with some key definitions which we need to understand before we move on to the equation itself:
- Static Pressure (P) = The pressure exerted by a fluid which is not moving or flowing
- Usually what is meant when people refer to the air pressure. Force exerted on the particle from all directions.
- Dynamic Pressure = The kinetic energy per unit volume of fluid (pv2/2)
- The difference between stagnation and static pressure, as this value is increased, the static pressure will be reduced.
- Stagnation Pressure = Maximum pressure (static pressure + dynamic pressure)
- Also referred to as total pressure. This value remains constant when the height above sea level (and therefore density of air) is kept the same.
The Equation:
Bernoulli’s equation states that:
P + pv2 + pgh = constant
Where:
- P = static pressure
- p = density
- v = velocity
- g = acceleration due to gravity
- h = height
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 equal a constant if the environmental conditions are constant. Dynamic pressure therefore represents the loss in pressure due to velocity.
Therefore, as velocity increases, the pressure will decrease. This is incredibly important in aerodynamics and is the principal due to which lift and downforce can be generated.
Stagnation Pressure:
The stagnation point is when the velocity of the fluid is zero, this is the point where pressure is the highest:
Pe + pv2e = P0 + pv20
This is because velocity at the stagnation point is zero, so pv20 is equal to zero. This means that Pe + pv2e = P0
Therefore, at the stagnation point, the pressure is the highest because the dynamic pressure is equal to zero. On a Formula One car, stagnation points will result in drag being produced, as the pressure is at its highest and is resisting the movement of the car.
Generating downforce:
Downforce is generated by producing a region of low pressure underneath the object and high pressure above. The Bernoulli equation tells us that the slow moving air will have a higher pressure than the fast moving air. This is shown in the diagram above.
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. Read more about how they work here.