(a)
The frictional force exerted on the stopper by the nozzle.
(a)
Answer to Problem 44P
The frictional force exerted on the stopper by the nozzle is
Explanation of Solution
Given that the diameter of the hose is
Consider two points, point 1 at the free surface of the water in the tank and point 2 inside the nozzle.
Apply Bernoulli’s theorem to the given situation.
Here,
Reduce the expression (I) for
Since the pressure
The total force acting on the stopper must be zero.
Here,
Write the expression for the force exerted by water on the stopper.
Here,
Write the expression for the force exerted by air on the stopper.
Use equation (V), and (VI) in (IV) and solve for
Write the expression for the cross sectional area of the nozzle.
Here,
Use equation (III), and (VIII) in (VII).
Conclusion:
Substitute
Therefore, the frictional force exerted on the stopper by the nozzle is
(b)
The mass of water flows through the nozzle in
(b)
Answer to Problem 44P
The mass of water flows through the nozzle in
Explanation of Solution
Equation (II) gives the pressure difference at both ends of the stopper.
When the stopper is removed, the pressure on both points become atmospheric pressure
Write the expression for the mass of water leaving the nozzle.
Here,
Write the expression for the volume of water leaving the nozzle with speed
Use equation (XII) and (VIII) in (XI).
Conclusion:
Substitute
Substitute
Therefore, the mass of water flows through the nozzle in
(c)
The gauge pressure of the flowing water in the hose just behind the nozzle.
(c)
Answer to Problem 44P
The gauge pressure of the flowing water in the hose just behind the nozzle is
Explanation of Solution
Write the continuity equation for the flow of water through the hose and nozzle.
Here,
Solve equation (XIV) for
Rewrite equation (XV) in terms of the diameters of the hose and nozzle.
Rewrite equation (II) for the current situation, such that
Since the gauge pressure
Conclusion:
Substitute
Substitute
Therefore, the gauge pressure of the flowing water in the hose just behind the nozzle is
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Chapter 14 Solutions
Physics For Scientists And Engineers With Modern Physics, 9th Edition, The Ohio State University
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