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(a) State Bernoulli's principle and prove it. (b)Explain any one application of it.
Carries 5 Marks
Class 11 CBSE
Answers
BERNOULLI'S PRINCIPLE
Bernoulli's principle states that an increase in the speed of a fluid occurs simultaneously with a decrease in pressure or a decrease in the fluid's potential energy.
★ " Total Initial energy equals to Total Final Energy " ★
DERIVATION OF BERNOULLI'S THEOREM :
→ Let the velocity, pressure and area of a fluid column at a point A be v₁, p, A₂
→ At Another point B be v₂, p₂, p₂ and A₂ .
Let the volume that is bounded by A and B be moved to M and N .
Let AM = L₁ and BN = L₂ .
Now if we can compress the fluid then we have,A₁L₁=A₂L₂
Net work done per volume = p₂ - p₁
• Kinetic energy per volume = 1/2 ρ v²
• Kinetic energy gained per volume = 1/2 ρ (v₂² - v₁²)
• Potential energy gained per volume = ρ g (h₂ - h₁)
• p₁ - p₂ = 1/2 ρ (v₂² - v₁²) + ρ g (h₂ - h₁)
p₁ - p₂ = 1/2 ρ v₂² - 1/2 ρ v₁² + ρ g h₂ - ρ g h₁
• p₁ + 1/2 ρ v₁² + ρ g h₁ = p₂ + 1/2 ρ v₂² + ρ g h₂
p + 1/2 ρ v + ρ g h = Constant
APPLICATIONS OF BERNOULLI'S PRINCIPLE
- Mechanism of the Airplanes
This Principle explains why airplane wings are curved along the top and why ships have to steer away from each other as they pass. The pressure above the wing is lower than below it, providing lift from underneath the wing.
- Blowing off roofs by wind Storms
During a tornado or hurricane, when a high speed wind blows over a straw or tin roof, it creates a low pressure (P) in accordance with Bernoulli’s principle.
- Magnus Effect
When a spinning ball is thrown, it deviates from its usual path in flight. This effect is called Magnus effect.
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