Question

8. (10 points extra credit) Consider the figure shown below. It shows a U-shaped mercury manometer (a device for detecting pressure differences) that is attached to a pipe along which water is flowing from left to right. The water pipe has a circular cross-section. At A the diameter of the water pipe is 5.6 cm and the speed of the water is 2.80 m/s. At B the diameter of the pipe is 3 cm. The fluid in the manometer is mercury, which has a density of 13600 kg/m3. What is h, the reading on the manometer (the difference between the height of mercury on either side of the U-tube)? [The acceleration due to gravity is 9.81 m/s2. The density of water is 1000 kg/m².] manometer - A - water pipe

Answer 1

de = 5.6cm = 0.056 m da = 3cm = 0.03m Y = 0.028m r2 = 0.015m V = 2.8 mis 2 = 2 From equation of continuity A, U = A₂ 4₂ 1828 = T & 2 = 820, (0.028) 2 x 2 8 = 9.756 m/s Y? (0.015)? From Bernoullis theorem we have ΟΥ -1,2 - (9.756}}.8) 39 = h 29 ag - 29 29 h = 87. 34 = 4.4565m (9.756)2-(-8)2 29 2x9.8

inside the monometer tube fluid is mercato inside the monometer tube fluid is mercures Hence 4.4565 1000 x 4.456 = 0.328 m. 13600 Th= 32.768 cm