Bernoulli’s Theorem

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Bernoulli’s Theorem

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.

Mathematically,

It can be expressed as

where, (p/ρ g) = pressure head, (v2/2g) = velocity head and h = gravitational head.
For horizontal flow of liquid,

  • where p is called static pressure and (1/2 ρv2) is called dynamic pressure.
  • Therefore in horizontal flow of liquid, if p increases, v decreases and vice-versa.
  • The 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, paint gun, scent sprayer atomizer insect sprayer is based on Bernoulli’s theorem.
  2. The action of Bunsen’s burner, gas burner, oil stove exhaust pump is also based on Bernoulli’s theorem.
  3. The motion of a spinning ball (Magnus effect) is based on Bernoulli theorem.
  4. Blowing of roofs by wind storms, the attraction between two close parallel moving boats, fluttering of a flag etc are also based Bernoulli’s theorem.

Venturimeter:

It is a device used for measuring the rate of flow of liquid t pipes. Its working is based on Bernoulli’s theorem.

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