An incompressible fluid is flowing through a vertical pipe with a constriction. The wide section is 2.00 cm in diameter and is at the top of the pipe. The pressure of the fluid in the wide section at the top is 200 kPa. The velocity of the fluid in the wide section is 4.00 m/s. The narrow section is located 2.00 m below the wide section. What is the diameter of the narrow section, if the pressure of the fluid in the narrow section is equal to the pressure in the wide section? (density of the fluid is 1,000 kg/m³) A) 1.47 cm B) 1.20 cm C) 1.10 cm D) 0.90 cm E) 0.75 cm

Question

Quizplus · Accepted Answer

To solve this problem, we can use the Bernoulli's equation and the continuity equation for incompressible fluids. The continuity equation states that A1V1 = A2V2, where A is the cross-sectional area and V is the velocity of the fluid. The Bernoulli's equation for a fluid element moving from the wide section (1) to the narrow section (2) can be simplified as P1 + 0.5ρV1^2 + ρgh1 = P2 + 0.5ρV2^2 + ρgh2, given that P1 = P2 and h2 = h1 - 2.00 m. Solving these equations simultaneously allows us to find the velocity in the narrow section and subsequently the diameter of the narrow section. The correct diameter that satisfies these conditions is 1.47 cm.

An Incompressible Fluid Is Flowing Through a Vertical Pipe with a Constriction