An ideal fluid of density flows steadily through a horizontal pipe of varying cross-section. At a wider section of the pipe, the cross-sectional area is A and the fluid velocity is v . At a narrower section, the cross-sectional area reduces to A 2 . The pressure difference (P₁ - P₂) between the wider and narrower sections is :

Step-by-step solution

Let the wider section be denoted by subscript 1 and the narrower section by subscript 2 . From the equation of continuity: A₁ v₁ = A₂ v₂ A(v) = ( A 2 ) v₂ v₂ = 2v Applying Bernoulli's equation for a horizontal pipe ( h₁ = h₂ ): P₁ + 1 2 v₁^2 = P₂ + 1 2 v₂^2 Rearranging to find the pressure difference (P₁ - P₂) : P₁ - P₂ = 1 2 v₂^2 - 1 2 v₁^2 P₁ - P₂ = 1 2 (2v)^2 - 1 2 (v)^2 P₁ - P₂ = 1 2 (4v^2 - v^2) = 3 2 v^2 Answer: 3 2 v^2