2.6 - Bernoulli’s Principle

Fluid Velocity and Pressure

• Bernoulli’s principle: When fluid velocity increases, pressure in the fluid decreases, and vice versa.
• A pressure difference produces a force from a higher-pressure region towards a lower-pressure region.
• Folded paper: Blowing beneath it increases air velocity there and lowers pressure, pressing it towards the table.
• Paper held in the hands: Blowing across its upper surface lowers pressure above it. Higher pressure below pushes it upwards.
• Two suspended balloons: Fast air between them lowers pressure in that space; higher surrounding pressure pushes them closer together.

Venturi Tube

• A Venturi tube has a narrow central section. The heights in vertical tubes A, B and C indicate pressure at X, Y and Z respectively.
• Smaller cross-sectional area gives higher flow velocity.
• From wide section X to narrow section Y: velocity increases and pressure decreases. The central column B is lower.
• From Y to wider section Z: velocity decreases and pressure increases.
• In the illustrated flow from X to Z, pressure at X exceeds pressure at Z, so column A is higher than column C.

Lift Force and Aerofoil

• Lift force results from a pressure difference caused by different air velocities.
• Ping pong ball in an inverted funnel: Fast air above the ball produces low pressure. Higher pressure below produces an upward resultant force that lifts it.
• Aerofoil: Faster airflow over the upper surface produces lower pressure; slower airflow below produces higher pressure. The difference supplies upward lift.
• Angle of attack also affects lift. The aerofoil exerts a force on the airflow; Newton’s Third Law gives a reaction force on the wing that contributes to lift.
• The four forces shown on an aeroplane are lift upwards, weight downwards, thrust from the jet engines and drag opposing motion.

Applications

Application	Effect shown
Bunsen burner	Gas and air mix at the air hole near a narrow gas outlet
Racing car	Splitter and spoiler produce a downward force
Football	A kick produces a curved path
Aeroplane	Aerofoil shape and angle of attack produce lift

• Paper-aeroplane flight also involves Bernoulli’s principle and Newton’s Third Law of Motion.