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Review. In a water pistol, a piston drives water through a large tube of area A1 into a smaller tube of area A2 as shown in Figure P14.46. The radius of the large tube is 1.00 cm and that of the small tube is 1.00 mm. The smaller tube is 3.00 cm above the larger tube. (a) If the pistol is fired horizontally at a height of 1.50 m, determine the time interval required for the water to travel from the nozzle to the ground. Neglect air resistance and assume atmospheric pressure is 1.00 atm. (b) If the desired range of the stream is 8.00 m, with what speed v2 must the stream leave the nozzle? (c) At what speed v1 must the plunger be moved to achieve the desired range? (d) What is the pressure at the nozzle? (e) Find the pressure needed in the larger tube. (f) Calculate the force that must be exerted on the trigger to achieve the desired range. (The force that must be exerted is due to pressure over and above atmospheric pressure.)
Figure P14.46
(a)
The time required for the water to travel from the nozzle to the ground.
Answer to Problem 14.78AP
The time required for the water to travel from the nozzle to the ground is
Explanation of Solution
The radius of the large tube is
Formula to calculate the time interval is,
Here,
Substitute
Conclusion:
Therefore, the time required for the water to travel from the nozzle to the ground is
(b)
The speed of the stream to leave the nozzle if the range of the stream is
Answer to Problem 14.78AP
The speed of the stream to leave the nozzle is
Explanation of Solution
Formula to calculate the speed of the stream to leave the nozzle is,
Here,
Substitute
Conclusion:
Therefore, the speed of the stream to leave the nozzle is
(c)
The speed of the plunger is moved to achieve the range of
Answer to Problem 14.78AP
The speed of the plunger is
Explanation of Solution
By continuity equation at the plunger and exit point of the nozzle is,
Here,
Formula to calculate the area of the large tube is,
Here,
Formula to calculate the area of the small tube is,
Here,
Substitute
`
Substitute
Conclusion:
Therefore, the speed of the plunger is
(d)
The pressure at the nozzle.
Answer to Problem 14.78AP
The pressure at the nozzle is
Explanation of Solution
The pressure at the nozzle is equal to the atmospheric pressure.
The atmospheric pressure is equal to the
Conclusion:
Therefore, the pressure at the nozzle is
(e)
The pressure needed in the large tube.
Answer to Problem 14.78AP
The pressure needed in the large tube is
Explanation of Solution
Apply the Bernoulli’s equation at point
Here,
Substitute
Conclusion:
Therefore, the pressure needed in the large tube is
(f)
The force exerted on the trigger to achieve the range of
Answer to Problem 14.78AP
The force exerted on the trigger to achieve the range of
Explanation of Solution
Formula to calculate the force exerted on the trigger is,
Here,
Substitute
Substitute
Conclusion:
Therefore, the force exerted on the trigger to achieve the range of
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