Water (density = 1*10³ kg/m³) flows at 10 m/s through a pipe with radius 0.040 m. The pipe goes up to the second floor of the building, 2.0 m higher, and the pressure remains unchanged. What is the radius of the pipe on the second floor?

Question

Quizplus · Accepted Answer

Bernoulli's equation: P + 1/2ρv^2 + ρgh = constant. Since the pressure remains unchanged, we have: 1/2ρv^2 + ρgh = constant. Thus, v^2 + 2gh = constant. Since the velocity is inversely proportional to the cross-sectional area, we have: A1v1^2 = A2v2^2. Thus, A1/A2 = v2^2/v1^2 = (h1/h2)^2. Since h1 = 0 and h2 = 2.0 m, we have: A1/A2 = (0/2.0)^2 = 0. Thus, A2 = A1. Since the area is proportional to the square of the radius, we have: r2^2 = r1^2. Thus, r2 = r1 = 0.040 m.

Water (Density = 1*103 Kg/m3) Flows at 10 M/s Through

Water (Density = 1*10³ Kg/m³) Flows at 10 M/s Through