Mathematically
It can be expressed as
where,( p / ρg) = pressure head,( v 2 / 2g) = velocity head and h = gravitational head.
For horizontal flow of liquid,
where, pis called static pressure and( 1 / 2 ρv 2) is called dynamic pressure.
The erefore in horizontal flow of liquid, if p increases, v decreases and Nce-versa.
The theorem is applicable to ideal liquid, i. e., a liquid which is nonviscous incompressible and irrotational.
Applications of Bernoulli’ s Theorem
1. The action of carburetor, paintgun, scent sprayer atomiser 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. Motion of a spinning ball( Magnus effect) is based on Bernoulli theorem.
4. Blowing of roofs by wind storms, attraction between two close parallel moving boats, fluttering of a flag etc are also based Bernoulli’ s theorem.