Water (density = 1.00 × 10³ kg/m³)flows at 7.2 m/s through a pipe with radius 0.025 m.The pipe goes up to the second floor of the building,2.00 m higher,and the pressure remains unchanged.What is the radius of the pipe on the second floor? A)0.019 m B)0.036 m C)0.0013 m D)0.23 m E)0.022 m

Question

Quizplus · Accepted Answer

Using Bernoulli's Equation:
1/2ρv1² + ρgh1 + P1 = 1/2ρv2² + ρgh2 + P2
Assuming h1 = 0, P1 = P2, and solving for v2:
v2 = sqrt(2gh2 + (v1²/2))
At the second floor, the volume flow rate must remain constant:
A1v1 = A2v2
pi(0.025²)(7.2) = pi(r²)(sqrt(2g(2)))
r = 0.036 m

Water (Density = 1