Bernoulli’s Principle - Definition, Derivation, Solved Examples

Author at PW

January 23, 2026

Bernoullis principle is really important when we talk about dynamics. It is about how fast a fluid's moving and the pressure it has. When a fluid like water or air moves really fast, the pressure it has gets lower. This is a deal because it helps us understand what happens when fluids flow through pipes or over things like the wings of a plane. Bernoullis principle is key, to getting this right.

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Bernoulli’s Principle Formula and Equation

The Bernoullis principle equation is a way to figure out how energy works in moving fluids. It says that the energy from pressure the energy from moving and the energy from being in a place all added together stays the same for the Bernoullis principle equation, in a fluid that is moving smoothly and steadily and is not getting thicker or thinner and is not being slowed down by friction as long as you look at it along the path that the fluid is following for the Bernoullis principle equation.

The bernoulli's principle formula is typically written as:

P + ½ρv² + ρgh = constant

Where:

P: Static pressure of the fluid

ρ (rho): Density of the fluid

v: Velocity of fluid flow

g: Acceleration due to gravity

h: Elevation (height) of the point above a reference plane

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Derivation, Aviation, and Real-World Examples

To understand the bernoulli's principle aviation application, we must look at how wings (airfoils) are shaped. A wing is curved more on the top than on the bottom. According to the principle, air travels faster over the curved top surface, creating a region of lower pressure compared to the bottom. This pressure difference results in an upward force called lift.

Bernoulli’s Principle Example in Daily Life:

Venturi Meter: The Venturi Meter is a thing we use to see how fast stuff is moving through a pipe. When the pipe gets smaller the fluid inside starts moving fast and the pressure goes down. The Venturi Meter is really good, at measuring this flow rate.
Atomizers/Perfume Sprays: When you use Atomizers or Perfume Sprays something cool happens. Atomizers or Perfume Sprays work because when air moves really fast over the top of a tube it makes the pressure get low. This low pressure is what pulls the liquid up from the bottom of the tube in the Atomizers or Perfume Sprays. The air moving over the tube in the Atomizers or Perfume Sprays is, like a vacuum that sucks the liquid upward.
Bunsen Burner: High-velocity gas creates a low-pressure zone that draws in air for combustion.

Solved Example:

Question: Water flows through a horizontal pipe at a speed of 1 m/s with a pressure of 200,000 Pa. At a narrowed section, the speed increases to 2 m/s. Calculate the pressure at this section. (Density of water = 1000 kg/m³)

Ans. Since the pipe is horizontal, the height is constant (h1 = h2), so the potential energy terms cancel out

P1 + ½ρv1² = P2 + ½ρv2²

200,000 + ½(1000)(1)² = P2 + ½(1000)(2)²

200,000 + 500 = P2 + 2000

P2 = 200,500 - 2000 = 198,500 Pa

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Read More: Angle of Deviation in a Prism

FAQs related to Bernoulli’s Principle

1. What are the main assumptions of Bernoulli's principle?

Ans. The fluid must be incompressible, the flow must be steady (unchanging over time), the fluid should be non-viscous (no friction), and the flow must be along a streamline.

2. How does Bernoulli’s principle explain lift in aviation?

Ans. The bernoulli's principle aviation link is seen in the airfoil shape. Faster-moving air on the top of the wing creates lower pressure than the slower air underneath, pushing the wing upward.

3. What is the difference between static and dynamic pressure?

Ans. In the bernoulli's principle formula, P represents static pressure (exerted by the fluid at rest), while ½ρv² represents dynamic pressure (associated with the fluid's motion).