A village maintains a large tank with ail open top, containing water for emergencies. The water can drain from the tank through a hose of diameter 6.60 cm. The hose ends with a nozzle of diameter 2.20 cm. A rubber stopper is inserted into the nozzle. The water level in the lank is kept 7.50 m above the nozzle. (a) Calculate the friction force exerted on the stopper by the nozzle. (b) The stopper is removed. What mass of water flows from the nozzle in 2.00 h? (c) Calculate the gauge pressure of the flowing water in the hose just behind the nozzle.
(a)
The friction force which is exerted on the stopper by the nozzle.
Answer to Problem 14.44P
The friction force which is exerted on the stopper by the nozzle is
Explanation of Solution
Given info: The diameter of a hose is
Write the equation for Bernoulli’s equation.
Here,
The velocity at the free surface
Substitute
Write the equation for forces in equilibrium.
Here,
Substitute
Write the formula for area of nozzle.
Here,
Substitute
The density of water is
Substitute
Conclusion:
Therefore, the friction force which is exerted on the stopper by the nozzle is
(b)
The mass of water flows from the nozzle.
Answer to Problem 14.44P
The mass of water flows from the nozzle is
Explanation of Solution
Given info: The diameter of a hose is
Write the equation of mass flow rate.
Here,
Write the equation of velocity at the nozzle from Bernoulli’s equation at the point of hose and nozzle.
Substitute
Thus, the velocity at the nozzle is
Substitute
Conclusion:
Therefore, the mass of water flows from the nozzle is
(c)
The gauge pressure of the flowing water in the hose just behind the nozzle.
Answer to Problem 14.44P
The gauge pressure of the flowing water in the hose just behind the nozzle is
Explanation of Solution
Given info: The diameter of a hose is
Write the equation for Bernoulli’s equation in the hose and the point of nozzle.
The level is same at the hose and the nozzle.
Substitute
Write the equation of continuity equation.
Here,
Substitute
Thus, the value of velocity
Substitute
Conclusion:
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
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