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A pressurized 2-rn-diameter tank of water has a 10-cm-diameter orifice at the bottom, where water discharges to the atmosphere. The water level initially is 3 m above the outlet. The tank air pressure above the water level is maintained at 450 kPa absolute and the atmospheric pressure is 100 kPa. Neglecting frictional effects, determine (a) how long it will take for half of the water in the tank to be discharged and (b) the water level in the tank after 10 s.
(a)
The time required for half discharge of water from tank.
Answer to Problem 103P
The time required for half discharge of water from tank is
Explanation of Solution
Given information:
The pressurized tank diameter is
Write the expression for the Bernoulli's Equation.
Here, the density of water is
Write the expression for the area of orifice.
Here, the diameter of orifice is
Write the expression for the volume flow rate through orifice.
Here, the time is
Substitute
Write the expression for volume of water in tank.
Here, the diameter of tank is
Write the expression for time required in half discharge.
Calculations:
Substitute
Substitute
Substitute
Substitute
Conclusion:
The time required for half discharge of water from tank is
(b)
The water level in tank after
Answer to Problem 103P
The water level in tank after
Explanation of Solution
Given information:
The pressurized tank diameter is
Write the expression for volume discharge in
Write the expression for the volume of water remaining after
Write the expression for remaining volume in tank.
Here, the height of remaining volume is
Calculations:
Substitute
Substitute
Substitute
Conclusion:
The water level in tank after
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Chapter 5 Solutions
Fluid Mechanics Fundamentals And Applications
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