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Social ScienceProblem 5: A pressurized tank of water has a 10-cm-diameter nozzle at the bottom, where theliquid discharges to the atmosphere. The liquid level is 2.5 m above the outlet and the tankdiameter can be assumed to be much larger than the diameter of the discharge nozzle. The airpressure in the space above the liquid is 250 kPa (absolute) while the atmospheric pressure is100 kPa. Neglecting frictional effects, determine the rate of discharge (kg/sec) of liquid from thetank when the liquid level is 2.5m.Air250 kPa25 m10 cm
What forms of conservation laws apply to this
problem? (Write out as well as you can)
a. Conservation of Energy:
b. Conservation of Mass:
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Problem 5: A pressurized tank of water has a 10-cm-diameter nozzle at the bottom, where the liquid discharges to the atmosphere. The liquid level is 2.5 m above the outlet and the tank diameter can be assumed to be much larger than the diameter of the discharge nozzle. The air pressure in the space above the liquid is 250 kPa (absolute) while the atmospheric pressure is 100 kPa. Neglecting frictional effects, determine the rate of discharge (kg/sec) of liquid from the tank when the liquid level is 2.5m. Air 250 kPa 25 m 10 cm
Expert Answer
Let above the liquid surface as point 1 and point 2 as just after the nozzle.
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P-250kPa Z1 2.5m 10 cm Z2 0 P2-100 kPa
Bernoulli’s equation is considered as the principle of conservation of energy in fluid flow. Applying Bernoulli’s equation between points 1 and 2.
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V. +Z2 2g Р. +Z Pg 2g Pg Where and V is velocity of fluid at 1 and 2 respectively The dia of tank too much larger than diameter of nozzle. hence the velocity at 1 can be neglected. .И, 0.
Now, plugging the values in Bernoulli’s equation. ...
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100 X103V +0 250 x 103 0 +2.5 2g 1000g 2g 1000g 174.525 2 100 2 2 250 +2.5 g V 2x174.525 2g g V 349.05 250 2.5g 100 + 2 V 349.05 18.683 m/sec 250 2.5x9.81 -100 2 V. 250 24.525-100 = 2
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