Concept explainers
(a)
The speed with which the water leaves the faucet.
(a)
Answer to Problem 80AP
The speed with which the water leaves the faucet is
Explanation of Solution
Given that the diameter of the faucet tap is
The flow rate of water through the pipe is always a constant. Write the expression for the volume flow rate of the water.
Here,
Write the expression for the flow rate in terms of area of the pipe.
Here,
Equate the right hand sides of equations (I) and (II).
Write the expression for the cross sectional area of the faucet tap in terms of its diameter.
Here,
Use equation (IV) in (III) and solve for
Conclusion:
Substitute
Therefore, the speed with which the water leaves the faucet is
(b)
The gauge pressure in the main pipe.
(b)
Answer to Problem 80AP
The gauge pressure in the main pipe is
Explanation of Solution
Given that the diameter of the faucet tap is
Consider two points 1 and 2 such that point 1 is in the entrance pipe and point 2 is in the faucet tap.
Write the continuity equation for the flow of water through points 1 and 2.
Here,
Rewrite equation (VI) in terms of the diameters of the pipes and solve for
Write Bernaulli’s equation for the give flow.
Here,
Since,
Conclusion:
Substitute
Substitute
Therefore, the gauge pressure in the main pipe is
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Chapter 14 Solutions
Physics for Scientists and Engineers with Modern, Revised Hybrid (with Enhanced WebAssign Printed Access Card for Physics, Multi-Term Courses)
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