Bernoullis Principle: Theorem, Equation and Formula

Bernoullis Principle can explain you how airplanes fly, why fast cars hug the road better, or why a shower curtain suddenly gets sucked toward you when you bathe?

All these odd little mysteries can be explained by one incredibly elegant concept in physics: Bernoullis Principle.

What is Bernoullis Principle?

Here’s the core idea:

As the speed of a fluid increases, the pressure within the fluid decreases.

Yes, it’s that simple—but it leads to mind-blowing applications.

This principle is named after Daniel Bernoulli, a Swiss physicist and mathematician who published it in 1738. He discovered that energy in a flowing fluid is conserved and can be transferred between pressure energy, kinetic energy (speed), and potential energy (height).

Let’s look at the mathematical form.

Bernoullis Equation

The principle is mathematically expressed as:

$ \displaystyle P + \frac{1}{2} \rho v^2 + \rho g h = \text{constant}$

Where:

• P = Pressure energy (in Pascals)
• $ \displaystyle ρ\rho$ = Density of the fluid (kg/m³)
• v = Speed or velocity of the fluid (m/s)
• g = Acceleration due to gravity (9.8 m/s²)
• h = Height above the reference level (m)

The three terms represent:

• Pressure energy
• Kinetic energy per unit volume
• Potential energy per unit volume

Together, they form the total mechanical energy of the fluid, and this total remains constant as long as the fluid is incompressible and there’s no friction (ideal fluid conditions).

Real-Life Examples and Applications of Bernoullis Principle

Let’s explore how Bernoulli’s Principle shows up in the real world:

1. How Airplanes Fly

The shape of an airplane wing—called an airfoil—is curved on top and flat on the bottom. As air flows over the curved top surface, it moves faster than the air underneath. According to Bernoulli’s Principle, this faster-moving air on top creates lower pressure. The higher pressure under the wing pushes the plane upward, generating lift.

This is how airplanes defy gravity and soar through the skies.

2. F1 Cars and Downforce

In Formula 1, race car designers use inverted airfoils to create downforce. Air travels faster over the bottom side of the car, generating lower pressure underneath and pushing the car down onto the track. This gives it more grip and stability at high speeds.

3. The Shower Curtain Mystery

When you take a hot shower, air moves quickly through the rising steam. This creates a low-pressure zone inside the shower. The higher pressure outside pushes the curtain inward, and suddenly it sticks to you! Yup, that’s Bernoulli’s magic at play.

4. Blowing Between Papers

Try this: Hold two sheets of paper close together and blow between them. Instead of spreading apart, they move closer together! That’s because the air between them moves faster, lowering the pressure between the sheets, and atmospheric pressure on the outer sides pushes them inward.

5. Venturi Meters and Fluid Flow

A Venturi meter is a device used to measure the flow rate of fluids in pipelines. It uses the principle that fluid speed increases in narrow sections, which decreases pressure. By comparing pressures at two points, the flow rate can be calculated—essential in industries like water supply and chemical processing.

How Bernoullis Principle Works: A Deeper Understanding

Let’s simplify the physics behind it.

Imagine a fluid (like air or water) flowing through a pipe that gets narrower in the middle. Since fluids are incompressible, the same amount of fluid must pass through every section of the pipe per second.

So, when the pipe narrows:

• The fluid speeds up
• The kinetic energy increases
• The pressure must decrease to conserve total energy

That’s Bernoullis Principle in action.

This interplay of pressure and speed is what allows:

• Wings to generate lift
• Chimneys to draw air upward
• Atomizers (like perfume sprays) to create a fine mist

Conditions for Bernoullis Principle to Apply

While it’s powerful, Bernoulli’s Principle has limitations. It only works under certain conditions:

In real-world applications, engineers make adjustments for turbulence, viscosity, and compressibility, especially in aerodynamics.

Bernoulli’s Principle vs Pascal’s Law

A Simple Classroom Experiment

Here’s a DIY demonstration:

You Need:

• A piece of paper (A4 size)
• Your breath

Try This:

1. Hold the paper by its short edge under your mouth.
2. Blow across the top of the paper.

Result? The paper lifts upward!

Why? Blowing air over the top lowers the pressure there, while the pressure below pushes the paper up. Bernoulli in action—live!

Summary: Key Takeaways

• Bernoulli’s Principle explains that faster fluid = lower pressure
• It is crucial for understanding lift, drag, fluid flow, and suction
• Common applications include airplanes, race cars, shower curtains, atomizers, and venturi meters
• Works under specific assumptions like steady, incompressible, and non-viscous flow

FAQs About Bernoullis Principle

Q1. Why does air pressure drop when fluid speed increases?

Because energy is conserved. If kinetic energy (speed) goes up, pressure energy must drop to keep the total constant.

Q2. Can Bernoullis Principle explain airplane flight alone?

Not entirely. Other factors like Newton’s Third Law, wing angle (angle of attack), and airflow behavior also contribute to lift.

Q3. Is Bernoullis Principle valid for all fluids?

It works best for incompressible, non-viscous fluids. In real-life gases and viscous fluids, corrections are often needed.

Bernoulli’s Principle is more than just a formula—it’s a key to unlocking the behavior of fluids in motion. From aviation to sports cars and from medical devices to perfume bottles, this principle makes our world work in surprisingly elegant ways.

Next time you’re on a flight or notice how a strong breeze lifts things up, you’ll know there’s a powerful law of physics at play—and now, you understand it!