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? A) 0.045 m B) 0.034 m C) 0.015 m D) 0.012 m

Question

Quizplus · Accepted Answer

Bernoulli's equation: P + 1/2ρv^2 + ρgh = constant. Since the pressure remains unchanged, 1/2ρv^2 + ρgh = constant. Thus, v^2 + 2gh = constant. So, v1^2 = v2^2 + 2g(h2 - h1). v1 = 10 m/s, h2 - h1 = 2.0 m, g = 9.8 m/s^2. Thus, v2 = 8.9 m/s. The continuity equation: A1v1 = A2v2. Thus, A2 = A1v1/v2 = πr1^2v1/v2 = π(0.040 m)^2(10 m/s)/(8.9 m/s) = 0.0179 m^2. Thus, r2 = 0.045 m.

Water (Density = 1 × 103 Kg/m3)flows at 10 M/s

Water (Density = 1 × 10³ Kg/m³)flows at 10 M/s