Bernoullis Equation

Topics covered in this session

1. Overview 2. Conservation of energy 3. Static Pressure in Airflow is Potential Energy 4. Dynamic Pressure in Airflow is Total Energy 5. Bernoullis Equation 6. Bernoullis Equation Applied to a Venturi Tube 7. Bernoullis Equation Applied to a Wing in Flight

WNTBPC Read ANA text pages 4 through 9, Bernoullis

principle and subsonic airflow, and Pilots Handbook of Aeronautical Knowledge (PHAK)

Watch this lecture Create your own notes in word, save it as a .pdf

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1. Overview Continuity equation explains why airflow on top of a

wing is faster than the airflow underneath the wing.

Once understanding Continuity, Bernoullis equation explains: Pressure on top of a wing is lower than the pressure

underneath the wing.

Bernoullis equation is based on the conservation of energy principle.

2. Conservation of Energy Bernoulli based on CONSERVATION OF ENERGY

principle. Energy level of a system remains constant

Energy neither created nor destroyed

Total energy TE = potential energy PE + kinetic energy KE = constant

TE = PE + KE = constant

Kinetic and Potential Energy

3. Static Pressure in Airflow is Potential Energy

Bernoulli transformed the general conservation of energy equation into airflow terms. In airflow, potential energy is static pressure.

PE = static pressure = Ps = p.

4. Dynamic Pressure in Airflow is Kinetic Energy

KE = dynamic pressure= PD = q.

= air density in slugs per cu. ft

v = true airspeed (TAS) velocity in fps

5. Total Pressure in Airflow is TOTAL ENERGY

TE = Total pressure, or H (head pressure) Pitot tube pitot head measuring total pressure

TE = total pressure = PT = H

Head pressure.

Pitot head pressure.

6. Bernoullis Equation Bernoullis Equation for conservation of energy in

subsonic airflow

Note: With no density changes, i.e., subsonic, constant

altitude, and are constant. So in qualitative terms, Bernoulli says that if the velocity increases, the pressure decreases and vice versa. This is the same as saying kinetic energy increases then potential energy decreases and vice versa.

7. Bernoullis Equation Applied to a venturi tube

In the venturi tube below, unlike the tubes previosuly drawn, the divergent area A3 is greater than the initial area A1.

8. Bernoullis Equation applied to a wing in flight