A horizontal pipeline carries water in a stream-line flow. At a point along the pipe, where the cross-sectional area is 10 ~cm ^2 , the velocity of water is 1 ~m / s and pressure is 2000 Pa . The pressure of water at another point where the cross-sectional area 5 ~cm ^2 is [ Given density of water =1000 ~kg / m ^3 ]

Step-by-step solution

The equation of continuity gives A₁ v₁ = A₂ v₂ for incompressible flow. With A₁ = 10 10⁻⁴ , m ^2 and A₂ = 5 10⁻⁴ , m ^2 , while v₁ = 1 , m/s , it follows that v₂ = A₁ A₂ v₁ = 10 10⁻⁴ 5 10⁻⁴ 1 = 2 , m/s . For a horizontal pipeline, Bernoulli’s equation simplifies to P₁ + 1 2 v₁^2 = P₂ + 1 2 v₂^2 , where = 1000 , kg/m ^3 and P₁ = 2000 , Pa . Substituting known values: 2000 + 1 2 1000 1^2 = 2000 + 500 = 2500 , Pa and 1 2 1000 2^2 = 2000 , Pa . Solving yields P₂ = 2500 - 2000 = 500 , Pa . The pressure at the constricte