Flow speed of the fluid through a non-uniform pipe increases from 1 m/sec to 3 m/sec. If change in P.E. is zero, then pressure difference between two points will be: (density of the fluid = 1000 kg/m3).

Explanation

According to Bernoulli's equation, the pressure difference between two points in a fluid is related to the change in velocity of the fluid and the density of the fluid.The equation is given as:P1 + (1/2)ρv1² = P2 + (1/2)ρv2²where P1 and P2 are the pressures at two different points in the pipe, v1 and v2 are the velocities at those points, and ρ is the density of the fluid.In this problem, we are given that the change in potential energy is zero, which means that we can neglect the potential energy term in Bernoulli's equation.Also, the density of the fluid is given as 1000 kg/m³.Using Bernoulli's equation, we can write:P1 + (1/2)ρv1² = P2 + (1/2)ρv2²Since the change in potential energy is zero, the pressure difference between the two points is given by:ΔP = P1 - P2 = (1/2)ρ(v2² - v1²)Substituting the given values, we get:ΔP = (1/2) x 1000 x (3² - 1²)ΔP = 4000 N/m²Therefore, the pressure difference between the two points is 4000 N/m². Option D is the correct answer.