Water (density = 1 ´ 10³ kg/m³)flows at 10 m/s through a pipe with radius 0.030 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)0.046 m B)0.034 m C)0.015 m D)0.012 m

Question

Quizplus · Accepted Answer

We can use Bernoulli's equation:

P1 + ½ρv1^2 + ρgh1 = P2 + ½ρv2^2 + ρgh2

Where P is pressure, ρ is density, v is velocity, g is acceleration due to gravity, and h is height.

Since the pressure remains unchanged, we can drop the P1 and P2 terms. Also, since the water is flowing horizontally, we can drop the h1 and h2 terms.

Thus, we are left with:

½ρv1^2 = ½ρv2^2

We can solve for v2:

v2 = v1*(r1/r2)^2

Where r1 is the original radius of the pipe and r2 is the radius of the pipe on the second floor.

Plugging in the given values:

10 = v1*(0.030/r2)^2

Solving for r2:

r2 = 0.034 m

Therefore, the answer is B) 0.034 m.

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

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