Water flows steadily through a horizontal pipe that contains a constriction. The cross-sectional area of the wider section of the pipe is twice that of the narrower section. The pressure difference between the wider and narrower sections is 6.0 10^3 Pa . Given the density of water is 1000 kg m ⁻³ , the velocity of water in the narrower section is _________ m s ⁻¹ .

Step-by-step solution

Let the cross-sectional areas of the wider and narrower sections be A₁ and A₂ respectively, and the velocities be v₁ and v₂ . Given that A₁ = 2A₂ . From the equation of continuity: A₁v₁ = A₂v₂ 2A₂v₁ = A₂v₂ v₁ = v₂ 2 Applying Bernoulli's equation for a horizontal pipe: P₁ + 1 2 v₁² = P₂ + 1 2 v₂² The pressure difference is P = P₁ - P₂ = 6.0 10³ Pa . P₁ - P₂ = 1 2 (v₂² - v₁²) Substitute v₁ = v₂ 2 and = 1000 kg m ⁻³ : 6.0 10³ = 1 2 1000 (v₂² - v₂² 4 ) 6000 = 500 3 4 v₂² 6000 = 375 v₂² v₂² = 6000 375 = 16 v₂ = 4 m s ⁻¹