Bernoulli’s Principle

The continuity equation (conservation of mass) says that the quantity of fluid passing through a tube is equal to the amount of fluid passing through the tube.

The velocity of the fluid only changes if the diameter of the tube alters. Otherwise, the fluid is stable.

If the diameter is reduced, the velocity is increased.

Total Pressure

The diameter and velocity relationship is valid when the total pressure within the system is constant. Bernoulli’s Principle states:

p0=p + q

Where p0= total pressure, p= static pressure, and q= dynamic pressure. The hydrostatic term ρgz is neglected in the above equation if one assumes gravitational effects are negligible.

Velocity and Pressure Relationship

It is observed that static pressure is reduced at locations where the diameter is small and flow velocity is high.  

Therefore, while the total pressure within the system remains the same, p and q change negatively reciprocal towards each other.

This basic principle in aerodynamics helps understand how a wing produces lift.