Concept explainers
The water supply of a building is fed through a main pipe 6.00 cm in diameter. A 2.00-cm-diameter faucet tap, located 2.00 m above the main pipe, is observed to fill a 25.0-L container in 30.0 s. (a) What is the speed at which the water leaves the faucet? (b) What is the gauge pressure in the 6-cm main pipe? Assume the faucet is the only “leak” in the building.
(a)
The speed at which the water leaves the faucet.
Answer to Problem 14.80AP
The speed at which the water leaves the faucet is
Explanation of Solution
Given info: The diameter of main pipe is
Formula to calculate the flow rate of the water is,
Here,
Substitute
Thus the flow rate of the water is
Formula to calculate the area of the faucet is,
Here,
Substitute
Thus the area of the faucet pipe is
Formula to calculate the flow rate of the water is,
Here,
Rearrange the above expression for
Substitute
Conclusion:
Therefore, the speed at which the water leaves the faucet is
(b)
The gauge pressure in the main pipe.
Answer to Problem 14.80AP
The gauge pressure in the main pipe is
Explanation of Solution
Given info: The diameter of main pipe is
Formula to calculate the area of main pipe is,
Here,
Substitute
Thus the area of the main pipe is
Write the continuity equation,
Here,
Rearrange the above expression for
Substitute
Thus, the speed of the water leaves at the main pipe is
The difference between the heights of the pipe is,
Here,
Formula to calculate the gauge pressure is,
Here,
Write the Bernoulli’s theorem,
Here,
Rearrange the above equation for
Substitute
Substitute
Conclusion:
Therefore, the gauge pressure in the main pipe is
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Chapter 14 Solutions
EBK PHYSICS FOR SCIENTISTS AND ENGINEER
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