_________________________It states that when a non - Viscous LIQUID and INCOMPRESSIBLE liquid flows through a TUBE of non - uniform cross section area, then at each point, the total energy of the liquid ( Kinetic + Potential + Pressure energy ) per unit volume will remain constant. P + ρ v² + ρgh = constant :Consider an ideal liquid of density ρ,is flowing through the tube in streamline flow, then the force experienced by the liquid enters at the END in time t, F₁ = P₁ A₂Work done on the liquid at end X, W₁ = F₁ × v ₁ ∆tW₁ = P₁ A₁ ( v ₁ ∆t ) W₁ = P₁ ∆v₁ Similarly, work done by the liquid at end Y, W₂ = P₂ ∆v₂Net work done on the liquid, W = ( P₁ ∆v₁ ) - ( P₂ ∆v₂ ) From equation of continuity, A₁ V₁ = A₂ V₂ A₁ V₁ ∆t = A₂ V₂ ∆t∆v₁ = ∆v₂W = ( P₁ - P₂ ) ∆vW = ( P₁ - P₂ ) ---> ( i ) Kinetic Energy, ∆K = mv₂ ² - mv₁² Potential Energy, ∆P = mgh₂ - mgh₁Total energy of the liquid, ∆E = ∆K + ∆P ∆E = ( mv₂ ² - mv₁² ) + ( mgh₂ - mgh₁ ) From the law of conservation of energy, W = ∆E( P₁ - P₂ ) = ( mv₂² - mv₁² ) + ( mgh₂ - mgh₁ )( P₁ - P₂ ) = ρv₂² - frac{1}{2} ρv₁² + ρgh₂ -ρgh₁ P₁ + ρv₁² +ρgh₁ = P₂ + ρv₂² + ρgh₂ P + ρv² +ρgh = constant. _______________________________It states that during the streamlined flow of an ideal liquid ( incompressible, no-Viscous) through a pipe of varying Cross section, the product of area of cross - section and velocity of flow remains constant. AV = constant :Consider a liquid of density ρ flows through the tube XY, then volume of liquid enters at end v₁ = A₁v₁∆t and mass of the liquid enters at end X₁,m₁ = A₁v₁ ∆t ρSimilarly, mass of liquid going out through end y, m₂ = A₂ v₂ ∆t ρ According to law of conservation of mass, m₁ = m₂ A₁v₁ ∆t ρ = A₂ v₂ ∆t ρ A₁v₁ = A₂ v₂ AV = constant. _______________________________It is the flow of liquid in which each particle of the liquid passing through a point travels along the same path and with same velocity as the preceding particle passing through the same point. _______________________________