Bundle: Physics for Scientists and Engineers with Modern Physics, Loose-leaf Version, 9th + WebAssign Printed Access Card, Multi-Term
Bundle: Physics for Scientists and Engineers with Modern Physics, Loose-leaf Version, 9th + WebAssign Printed Access Card, Multi-Term
9th Edition
ISBN: 9781305932302
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
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Chapter 14, Problem 78AP

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

Chapter 14, Problem 78AP, Review. In a water pistol, a piston drives water through a large tube of area A1 into a smaller tube

(a)

Expert Solution
Check Mark
To determine

The time required for the water to travel from the nozzle to the ground.

Answer to Problem 78AP

The time required for the water to travel from the nozzle to the ground is 0.553s .

Explanation of Solution

Given info: The radius of the large tube is 1.00cm and radius of the small tube is 1.00mm . The smaller tube is 3.00cm above the larger tube, the pistol is fired at a height 1.50m with the horizontal.

Formula to calculate the time interval is,

t=2hg

Here,

h is the height of the pistol above the horizontal.

g is the acceleration due to gravity.

Substitute 1.50m for h and 9.81m/s2 for g to find t .

t=2×1.50m9.81m/s2=0.553s

Conclusion:

Therefore, the time required for the water to travel from the nozzle to the ground is 0.553s .

(b)

Expert Solution
Check Mark
To determine

The speed of the stream to leave the nozzle if the range of the stream is 8.00m .

Answer to Problem 78AP

The speed of the stream to leave the nozzle is 14.46m/s if the range of the stream is 8.00m .

Explanation of Solution

Given info: The radius of the large tube is 1.00cm and radius of the small tube is 1.00mm . The smaller tube is 3.00cm above the larger tube, the pistol is fired at a height 1.50m with the horizontal.

Formula to calculate the speed of the stream to leave the nozzle is,

v2=dt

Here,

d is the range of the stream.

v2 is the speed of the stream to leave the nozzle.

Substitute 8.00m for d and 0.553s for t to find v2 .

v2=8.00m0.553s=14.46m/s

Conclusion:

Therefore, the speed of the stream to leave the nozzle is 14.46m/s if the range of the stream is 8.00m .

(c)

Expert Solution
Check Mark
To determine

The speed of the plunger is moved to achieve the range of 8.00m .

Answer to Problem 78AP

The speed of the plunger is 0.1446m/s to achieve the range of 8.00m .

Explanation of Solution

Given info: The radius of the large tube is 1.00cm and radius of the small tube is 1.00mm . The smaller tube is 3.00cm above the larger tube, the pistol is fired at a height 1.50m with the horizontal.

By continuity equation at the plunger and exit point of the nozzle is,

A1v1=A1v2 (I)

Here,

A1 is the area of the large tube

A2 is the area of the smaller tube.

v1 is the speed of the plunger.

Formula to calculate the area of the large tube is,

A1=πr12

Here,

r1 is the radius of the large tube.

Formula to calculate the area of the small tube is,

A2=πr22

Here,

r2 is the radius of the small tube.

Substitute πr12 for A1 and πr22 for A2 in equation (I).

` πr12×v1=πr22×v2v1=r22×v2r12

Substitute 1.00cm for r1 , 1.00mm for r2 and 14.46m/s for v2 to find v1 .

v1=(1.00mm×1m1000mm)2×14.46m/s(1.00cm×1m100cm)2=0.1446m/s

Conclusion:

Therefore, the speed of the plunger is 0.1446m/s to achieve the range of 8.00m .

(d)

Expert Solution
Check Mark
To determine

The pressure at the nozzle.

Answer to Problem 78AP

The pressure at the nozzle is 101325Pa .

Explanation of Solution

Given info: The radius of the large tube is 1.00cm and radius of the small tube is 1.00mm . The smaller tube is 3.00cm above the larger tube, the pistol is fired at a height 1.50m with the horizontal.

The pressure at the nozzle is equal to the atmospheric pressure.

The atmospheric pressure is equal to the 101325Pa , hence the pressure at the muzzle is equal to the 101325Pa .

Conclusion:

Therefore, the pressure at the nozzle is 101325Pa .

(e)

Expert Solution
Check Mark
To determine

The pressure needed in the large tube.

Answer to Problem 78AP

The pressure needed in the large tube is 205860Pa .

Explanation of Solution

Given info: The radius of the large tube is 1.00cm and radius of the small tube is 1.00mm . The smaller tube is 3.00cm above the larger tube, the pistol is fired at a height 1.50m with the horizontal.

Apply the Bernoulli’s equation at point 1 and point 2 .

P1+12ρv12+ρgy1=P2+12ρv22+ρgy2

  • P1 is the pressure in the large tube.
  • y1 is the elevation at point 1 .
  • P2 is the pressure at the exit point of the nozzle.
  • y2 is the elevation at point 2 .
  • ρ is the density of the water.
  • g is the acceleration due to gravity.

Substitute 0 for y1 , 0.1446m/s for v1 , 101325Pa for P2 , 14.46m/s for v2 , 1000kg/m3 for ρ and 0 for y2 to find P1 .

P1+121000kg/m3×(0.1446m/s)2+ρg(0)=101325Pa+121000kg/m3×(14.46m/s)2+ρg(0)P1=101325Pa+121000kg/m3((14.46m/s)2(0.1446m/s)2)=205860Pa

Conclusion:

Therefore, the pressure needed in the large tube is 205860Pa .

(f)

Expert Solution
Check Mark
To determine

The force exerted on the trigger to achieve the range of 8.00m .

Answer to Problem 78AP

The force exerted on the trigger to achieve the range of 8.00m is 35.84N .

Explanation of Solution

Given info: The radius of the large tube is 1.00cm and radius of the small tube is 1.00mm . The smaller tube is 3.00cm above the larger tube, the pistol is fired at a height 1.50m with the horizontal.

Formula to calculate the force exerted on the trigger is,

F=(P1P2)×A1

  • F is the force exerted on the trigger.

Substitute πr12 for A1 in the above expression.

F=(P1P2)×πr12

Substitute 1.00cm for r1 , 101325Pa for P2 , 205860Pa for P1 to find F .

F=(205860Pa101325Pa)×π(1.00cm×1m100cm)2=35.84N

Conclusion:

Therefore, the force exerted on the trigger to achieve the range of 8.00m is 35.84N .

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Chapter 14 Solutions

Bundle: Physics for Scientists and Engineers with Modern Physics, Loose-leaf Version, 9th + WebAssign Printed Access Card, Multi-Term

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