FIGURE 15-11
-Water flows in the horizontal pipe shown in Figure 15-11. At A the diameter is 6.00 cm and at B the diameter is 5.00 cm. The fluid in the manometer is oil, which has a density of 800 kg/m³. The manometer reading h is 10.0 cm. What is the speed of the water at B?

Question

FIGURE 15-11 FIGURE 15-11 -Water flows in the horizontal pipe shown in Figure 15-11. At A the diameter is 6.00 cm and at B the diameter is 5.00 cm. The fluid in the manometer is oil, which has a density of 800 kg/m<sup>3</sup>. The manometer reading h is 10.0 cm. What is the speed of the water at B? A) 0.195 m/s B) 1.55 m/s C) 1.74 m/s D) 8.70 m/s E) 11.4 m/s

FIGURE 15-11 -Water flows in the horizontal pipe shown in Figure 15-11. At A the diameter is 6.00 cm and at B the diameter is 5.00 cm. The fluid in the manometer is oil, which has a density of 800 kg/m<sup>3</sup>. The manometer reading h is 10.0 cm. What is the speed of the water at B? A) 0.195 m/s B) 1.55 m/s C) 1.74 m/s D) 8.70 m/s E) 11.4 m/s

-Water flows in the horizontal pipe shown in Figure 15-11. At A the diameter is 6.00 cm and at B the diameter is 5.00 cm. The fluid in the manometer is oil, which has a density of 800 kg/m³. The manometer reading h is 10.0 cm. What is the speed of the water at B?

Quizplus · Accepted Answer

Using Bernoulli's equation between points A and B:
P + (1/2)ρv1^2 + ρgh1 = P + (1/2)ρv2^2 + ρgh2
Canceling out the pressure terms and using the fact that h1 - h2 = h:
(1/2)ρv1^2 + ρgh1 = (1/2)ρv2^2 + ρgh2
(1/2)ρv1^2 + ρgh = (1/2)ρv2^2 + ρgh1 - h
Simplifying:
v2^2 = v1^2 + 2gh - 2gh1
v2^2 = (2)(9.81 m/s^2)(0.100 m) + (2)(9.81 m/s^2)(0.060 m)
v2^2 = 2.94 m^2/s^2
v2 = 1.74 m/s (rounded to two significant figures)

FIGURE 15-11 -Water Flows in the Horizontal Pipe Shown in Figure 15-11