A pressurized cylindrical tank, 5.0 m in diameter, contains water which emerges

Question

A pressurized cylindrical tank, 5.0 m in diameter, contains water which emerges from the pipe at point C, with a velocity of 84 m/s. Point A is 10 m above point B and point C is 3 m above point B. The area of the pipe at point B is 0.08 m^2 and the pipe narrows to an area of 0.07 m^2 at point C. Assume the water is an ideal fluid in laminar flow. The density of water is 1000 kg/m^3. In Figure 13.3, the rate at which the water level is falling in the tank, in mm/s, is closest to: 160 250 210 340 300

Explanation / Answer

Bernoulli’s equation
p/ + gy + v²/2 = constant
P/ + gy + v²/2 = p/ + gy + v²/2
(P - p)/ = (v² - v²) / 2 + g(y - y)
gh = (v² - v²) / 2 + g(y - y)
h = (v² - v²) / 2g + (y - y)
10 = (v² - v²) / 2g + 3
(v² - v²) / 2g = 7
(v² - v²) = 137.2--------------1
A v = A v
8 v = 7 v
Substituting in 1
63 v² = 137.2
v = 21.17 m /s
A v = 8*10^-2*21.17 m^3 /s
h/s = 8*10^-2*21.17 / (3.14*2.5^2) = 0.08629 m/s
=86.29 mm/s

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