# Bernoulli’s Principle & Equation | Applications, Definition – Hydrodynamics

Bernoulli’s Principle Definition:
If an ideal liquid is flowing in streamlined flow, then total energy, i.e. sum of pressure energy, kinetic energy and potential energy per unit volume of the liquid remains constant at every cross-section of the tube.

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## Bernoulli’s Principle & Equation | Applications, Definition – Hydrodynamics

Bernoulli’s Principle Formula:
Mathematically,

p + $$\frac{1}{2}$$ ρv² + ρgh = constant

It can be expressed as, $$\frac{p}{\rho g}+\frac{v^{2}}{2 g}$$ + h = constant
where,
$$\frac{p}{\rho g}$$ = pressure head,
$$\frac{v^{2}}{2 g}$$ = velocity head,

For horizontal flow of liquid, p + $$\frac{1}{2}$$ ρv² = constant
where,
p is called static pressure and $$\frac{1}{2}$$ ρv² is called dynamic pressure.

• Therefore in horizontal flow of liquid, if p increases, v decreases and vice-versa.
• This theorem is applicable to ideal liquid, i.e. a liquid which is non-viscous incompressible and irrotational.

Applications of Bernoulli’s Theorem:

1. The action of carburetor, paintgun, scent sprayer, atomiser and insect sprayer is based on Bernoulli’s theorem.
2. The action of Bunsen’s burner, gas burner, oil stove and exhaust pump is also based on Bernoulli’s theorem.
3. Motion of a spinning ball (Magnus effect) is based on Bernoulli’s theorem.
4. Blowing of roofs by wind storms, attraction between two closely parallel moving boats, fluttering of a flag, etc are also based on Bernoulli’s theorem.
5. Bernoulli’s theorem helps in explaining blood flow in artery.
6. The working of an aeroplane is based on Bernoulli’s theorem.

Hydrodynamics:
In physics, hydrodynamics of fluid dynamics explains the mechanism of fluid such as flow of liquids and gases. It has a wide range of applications such as evaluating forces and momentum on aircraft, prediction of weather, etc.