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

Question

A pressurized cylindrical tank, 5.0m in diameter, contains water which emerges from the pipe at point C, with a velocity of 14 m/s Point A is 10m above point B and point C is 3m above point B. The area of the pipe at point B is 8?10?2 m^2 and the pipe narrows to an area of 1?10?2 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 the figure, the rate at which the water level is falling in the tank, in mm/s is closest to: a) 4.9mm/s b) 6.0mm/s c) 7.1mm/s d) 3.8mm/s

Explanation / Answer

consider level of point B at datum line

now, from equation of continuity between point B and C:

area at B * velocity at B = area at C * velocity at C

velocity at B = 7 m/s

now, we know that Bernaulli's equation is :
p/ + v2/2 + gz = constant

where,

p=pressure

=density

v=velocity

g=acceleration due to gravity = 10 m/s2

z=height

now, applying Bernaulli's equation at points B and C we get :

(pB/1000) + (49/2) = (pC/1000) + (196/2) + 30

(pB - pC)/1000 = 103.5 N/m2

now, applying Bernaulli's equation at points A and B we get :

(pA/1000) + (vA2/2) + 100 = (pB/1000) + (49/2)

(pB - pA)/1000 = 124.5 + (vA2/2)

as pressure at point A and C are same (both being atmospheric pressure)

pA = pC

103.5 = 124.5 + (vA2/2)

- 21 = (vA2/2)

negative sign represents the direction

vA2 = 42

vA = 6.48074 m/s

therefore, the rate at which the water level is falling in the tank, in m/s is closest to: b) 6.0m/s

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