Applications of Bernoulli’s Principle Georgia CTAE Resource Network Curriculum Office Philip Ledford and Dr. Frank Flanders

Daniel Bernoulli Daniel Bernoulli was a Dutch-Swiss mathematician who is most known for his work in fluid mechanics and for his boom Hydrodynamica. Bernoulli came up with the equitation where: – is the fluid flow speed at a point on a streamline, speed – is the acceleration due to gravity, acceleration due to gravityacceleration due to gravity – is the elevation of the point above a reference plane, with the positive z-direction pointing upward — so in the direction opposite to the gravitational acceleration, elevation – is the pressure at the point, and pressure – is the density of the fluid at all points in the fluid. density

Bernoulli’s Equation What does it mean? In a simplified non-mathematical explanation, Bernoulli’s equation basically means that if velocity (the speed of motion) of a fluid increases, the pressure within (the force per unit area applied to an object) the fluid decreases. Bernoulli’s principle is used in aerodynamics and help explains how airplane get lift, and how race cars stay on the ground. It also has uses in lots of different machines such as a Hozon for agricultural use.

Hozon – Siphon Mixer A Hozon siphon mixer is used agriculturally to fertilize plants. This device operates somewhat with Bernoulli’s principle. Water flows through the device at a certain velocity. As you can see the water flows over tube where fertilizer is projected into the water.

Hozon – Siphon Mixer (con’t) This is where Bernoulli’s principle steps in. Because the water is flowing over the top of the fertilizer tube it creates pressure around the stream of moving water. This pressure around the stream of water causes the fertilizer to be projected upwards towards the stream of water.

Hozon – Siphon Mixer (con’t) Why doesn’t the water just spray into the fertilizer tube? The pressure of the stream is very low since it’s velocity is very high. But, the velocity around the out side of the stream of water is very low, thus causing the pressure outside the stream of water to be very high. The high pressure that is projecting fertilizer into the water doesn’t allow the water to enter the fertilizer tube.

Racecars! Racecars designs such as the ones the perform in the Indianapolis 500 use Bernoulli’s principle to keep the car on the ground, and allow the car to make sharper turns. Notice the shape of the spoiler.  The spoiler starts out thin and gradually curves upward. This causes the velocity to decrease and pressure to increase on the top.

Racecars! (cont’d) The spoiler of the car is shaped so that the velocity of air on the top of the spoiler is moving slower, thus creating more pressure on the top of the car pushing the car downward. The velocity of air on the bottom of the spoiler is much faster, thus having less pressure pushing upward on the car.

Airplanes  Notice the shape of the airplane’s wings. They are shaped opposite of a racecars spoiler. The top of an airplane’s wings are shaped so that the velocity of air moves faster over the top and slower on the bottom. Since the velocity of air is faster on top that means the pressure on top is low. The velocity of air is slower on the bottom so the pressure on bottom is greater helping give lift (the force that pulls an object outward, or upward.) to the airplane keeping it up in the air.

Airplane Wing The top of an airplane’s wing is shaped so that the velocity of air moves faster over the top and slower on the bottom. Since the velocity of air is faster on top that means the pressure on top is low. The velocity of air is slower on the bottom so the pressure on bottom is greater helping give lift to the airplane keeping it up in the air. * The same concept of low velocity and high pressure on the bottom of an airplane’s wings also applies to the wings of flying birds.

Summary What did we learn? Daniel Bernoulli was a Dutch-Swiss mathematician who came up with the principle of fluid mechanics known as Bernoulli’s Principle. Bernoulli’s principle basically states that as a fluid’s velocity increases the pressure within that fluid decreases.

Summary (con’t) Devices such as Hozon siphon mixers use Bernoulli’s principle to cause fertilizer to mix with water by the pressure of the water it is being mixed with. Racecars use a spoiler shaped so that pressure stays on top of the car holding down. Airplane wings are shaped opposite of racecars to have pressure on the bottom of the wing to give it lift.