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| 1. |
Prove the Bernoulli theorem |
| Answer» The sum of pressure energy , kinetic energy and potential energy of liquid remains constant\xa0Bernoulli\'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.Derivation :\xa0Let the velocity, pressure and area of a fluid column at a point A be v₁,\xa0p and A₂ and at another point B be v₂,\xa0p₂,\xa0p₂ 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 = A₂L₂Net work done per volume = p₂ - p₁Kinetic energy per volume = 1/2\xa0ρ v²Kinetic energy gained per volume = 1/2\xa0ρ (v₂² - v₁²)\xa0Potential energy gained per volume =\xa0ρ g(h₂ - h₁)\xa0Now ,\xa0p₁ - p₂ = 1/2\xa0ρ (v₂² - v₁²) +\xa0ρ g(h₂ - h₁)\xa0p₁ - p₂ = 1/2\xa0ρ v₂² - 1/2\xa0ρ v₁² +\xa0ρ g h₂ -\xa0ρ g h₁p₁ + 1/2\xa0ρ v₁² +\xa0ρ g h₁ = p₂ +\xa01/2\xa0ρ v₂² +\xa0ρ g h₂p + 1/2\xa0ρ v +\xa0ρ g h = constant\xa0Applications :\xa0The top of the airplane wing is a little curved and the bottom is completely flat. But air travels across both parts of the wings simultaneously in the sky.The entire pitch of the baseball is working on the principle of Bernoulli’s theorem. The stitches of the ball can be seen forming a curve which makes it necessary for the pitcher to grip the ball’s seams.<br>Proving net see search kar loo becos bari hai aur time jada lag jaye ga<br>Bernoulli theorem states that the sum of pressure energy. Kinetic energy and potential energy per unit volume of an incompressible non viscous fluid in an streamlined irrational flow. | |