Bernoulli's Principle

What is the relation of Bernoulli’s Principle?

Relates pressure to velocity in any fluid.

What happens to velocity as pressure decreases?

Velocity decreases

What type of flow is Bernoulli’s Principle valid for? Think foundations.

Incompressible Flow

What is the equation for Bernoulli’s principle that you can use at each point in a system?

P_static + (1/2)*density*v² = P_total

AKA

Internal Energy + Kinetic Energy = Total Energy

What are the assumptions of incompressible flow for Bernoulli’s?

1. Density is constant

2. Mass is conserved

3. Flow is steady

What is the limitation of density being constant?

Speed. M has to be below 0.3 otherwise it goes to compressible flow.

What is happening on the streamline with the assumption that mass is conserved?

At any point along one or multiple streamlines the mass flow is the same as it is at any other point along the same streamlines.

What is the significance of a reference point being upstream or infinity?

Bernoulli’s equation still works if all flow along all streamlines at the reference point has same total energy or pressure. AKA total energy is conserved.

With the assumption that flow is steady, what is another assumption that can be made?

Speed does not vary with time.

Why can’t it be assumed that the stagnation pressure should be the pressure of the atmosphere?

• Wing is colliding head-on with the air that is rushing through/around

• Stagnation Pressure = Atmospheric Pressure + Pressure of Collision (wing + fluid)

What is static pressure?

• Air is undisturbed (aka freestream)

• Doesn’t necessarily mean unmoving

Applications of Bernoulli’s Equation

1. Compute change in pressure along a streamline (velocity can vary)

2. Static pressure integrated along entire surface of airfoil gives total aerodynamics force on the airfoil (L, D)

3. Pitot tube on an aircraft to calculate velocity (for speedometer): measures static and total pressure and calculations are done with Bernoulli’s to get the velocity.