FIGURE 15-18
-Water flows through the 30.0-cm diameter pipe shown in Figure 15-18. An open tube is flush with an opening in the pipe at A and enters the pipe at B and is bent along the centerline of the pipe to face the oncoming flow. Water enters the tube and rises until the hydrostatic pressure in the tube balances the pressure at the mouth of the tube. Because no more water enters the tube, the speed of the water just outside the mouth of the tube is zero m/s. What is the manometer reading if the speed of the water in the pipe is 1.20 m/s? The manometer fluid is oil with a density of 800 kg/m³.

Question

FIGURE 15-18

-Water flows through the 30.0-cm diameter pipe shown in Figure 15-18. An open tube is flush with an opening in the pipe at A and enters the pipe at B and is bent along the centerline of the pipe to face the oncoming flow. Water enters the tube and rises until the hydrostatic pressure in the tube balances the pressure at the mouth of the tube. Because no more water enters the tube, the speed of the water just outside the mouth of the tube is zero m/s. What is the manometer reading if the speed of the water in the pipe is 1.20 m/s? The manometer fluid is oil with a density of 800 kg/m³.

Quizplus · Accepted Answer

The correct answer is A because the pressure at the mouth of the tube is equal to the hydrostatic pressure in the tube, which is equal to the density of the oil times the height of the oil in the tube. The height of the oil in the tube is equal to the difference in pressure between the mouth of the tube and the point in the pipe where the tube enters the pipe, which is equal to the dynamic pressure of the water in the pipe. The dynamic pressure of the water in the pipe is equal to half the density of the water times the square of the speed of the water in the pipe. Therefore, the height of the oil in the tube is equal to half the density of the water times the square of the speed of the water in the pipe divided by the density of the oil. Plugging in the given values, we get:h = (1/2)(1000 kg/m^3)(1.20 m/s)^2 / (800 kg/m^3) = 0.918 m = 91.8 cmTherefore, the manometer reading is 91.8 cm, which is closest to choice A, 9.18 cm.

FIGURE 15-18 -Water Flows Through the 30.0-Cm Diameter Pipe Shown in Figure