Principles of Physics: A Calculus-Based Text
Principles of Physics: A Calculus-Based Text
5th Edition
ISBN: 9781133104261
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
bartleby

Concept explainers

bartleby

Videos

Question
Book Icon
Chapter 15, Problem 69P

(a)

To determine

The speed at which the water leaves the faucet.

(a)

Expert Solution
Check Mark

Answer to Problem 69P

The speed at which the water leaves the faucet is 2.65 m/s .

Explanation of Solution

Write the equation for the volume flow rate.

  Q=ΔVΔt        (I)

Here, Q is the volume flow rate, ΔV is the volume of liquid flowed in time interval Δt .

Write the equation for the volume flow rate in terms of the speed of the water.

  Q=Av

Here, A is the area through which the liquid moves and v is the speed of the liquid.

Rewrite the above equation for v .

  v=QA        (II)

Write the equation for A .

  A=πd24

Here, d is the diameter of the faucet tap.

Put the above equation in equation (II).

  v=Qπd24=4Qπd2        (III)

Conclusion:

Substitute 25 L for ΔV and 30.0 s for Δt in equation (I) to find Q .

  Q=25.0 L1000 cm31.0 L30.0 s=833 cm3/s

Substitute 833 cm3/s for Q and 2.00 cm for d in equation (III) to find v .

  v=4(833 cm3/s)π(2.00 cm)2=265 cm/s1 m100 cm=2.65 m/s

Therefore, the speed at which the water leaves the faucet is 2.65 m/s.

(b)

To determine

The gauge pressure in the 6 cm main pipe.

(b)

Expert Solution
Check Mark

Answer to Problem 69P

The gauge pressure in the 6 cm main pipe is 2.31×104 Pa.

Explanation of Solution

Take point 1 to be in the entrance pipe and point 2 to be at the faucet pipe.

Write the continuity equation of fluids.

  A1v1=A2v2

Here, A1 is the area of the entrance pipe, v1 is the speed of the water at point 1, A2 is the area of the faucet pipe and v2 is the speed of the water at point 2.

Rewrite the above equation for v1.

  v1=A2v2A1        (IV)

Write the equation for A2 .

  A2=πd224

Here, d2 is the diameter of the faucet tap.

Write the equation for A1 .

  A1=πd124

Here, d1 is the diameter of the entrance pipe.

Put the above two equations in equation (IV).

  v1=(πd224)v2(πd124)=(d2d1)2v2        (V)

Write the Bernoulli’s equation.

  P1+12ρv12+ρgy1=P2+12ρv22+ρgy2

Here, P1 is the pressure at the point 1, ρ is the density of the fluid, g is the acceleration due to gravity, y1 is the height of the point 1 above the reference position, P2 is the pressure at the point 2 and y2 is the height of the point 2 above the reference position.

Rearrange the above equation.

  P1P2=(12ρv2212ρv12)+(ρgy2ρgy1)=12ρ(v22v12)+ρg(y2y1)        (VI)

Write the equation for gauge pressure.

  Pgauge=P1P2

Here, Pgauge is the gauge pressure.

Put the above equation in equation (VI).

  Pgauge=12ρ(v22v12)+ρg(y2y1)        (VII)

Conclusion:

The density of water is 1000 kg/m3 , value of g is 9.80 m/s2 and the value of v2 is found to be 2.65 m/s in part (a).

Substitute 2.00 cm for d2 , 6.00 cm for d1 and 2.65 m/s for v2 in equation (V) to find v1 .

  v1=(2.00 cm6.00 cm)2(2.65 m/s)=0.295 m/s

Substitute 1000 kg/m3 for ρ , 2.65 m/s for v2 , 0.295 m/s for v1 , 9.80 m/s2 for g and 2.00 m for y2y1 in equation (VII) to find Pgauge .

  Pgauge=12(1000 kg/m3)[(2.65 m/s)2(0.295 m/s)2]+(1000 kg/m3)(9.80 m/s2)(2.00 m)=2.31×104 Pa

Therefore, the gauge pressure in the 6 cm main pipe is 2.31×104 Pa.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Chapter 15 Solutions

Principles of Physics: A Calculus-Based Text

Ch. 15 - A solid iron sphere and a solid lead sphere of the...Ch. 15 - Prob. 6OQCh. 15 - Prob. 7OQCh. 15 - Prob. 8OQCh. 15 - An ideal fluid flows through a horizontal pipe...Ch. 15 - Prob. 10OQCh. 15 - Prob. 11OQCh. 15 - A small piece of steel is tied to a block of wood....Ch. 15 - A piece of unpainted porous wood barely floats in...Ch. 15 - Prob. 14OQCh. 15 - A water supply maintains a constant rate of flow...Ch. 15 - Prob. 1CQCh. 15 - Because atmospheric pressure is about 105 N/m2 and...Ch. 15 - Two thin-walled drinking glasses having equal base...Ch. 15 - Prob. 4CQCh. 15 - Prob. 5CQCh. 15 - Prob. 6CQCh. 15 - Prob. 7CQCh. 15 - Prob. 8CQCh. 15 - Prob. 9CQCh. 15 - Prob. 10CQCh. 15 - Prob. 11CQCh. 15 - Prob. 12CQCh. 15 - (a) Is the buoyant force a conservative force? (b)...Ch. 15 - An empty metal soap dish barely floats in water. A...Ch. 15 - Prob. 15CQCh. 15 - How would you determine the density of an...Ch. 15 - Prob. 17CQCh. 15 - Place two cans of soft drinks, one regular and one...Ch. 15 - Prob. 19CQCh. 15 - Prob. 1PCh. 15 - A 50.0-kg woman wearing high-heeled shoes is...Ch. 15 - Prob. 3PCh. 15 - Prob. 4PCh. 15 - Prob. 5PCh. 15 - The small piston of a hydraulic lift (Fig. P15.6)...Ch. 15 - A container is filled to a depth of 20.0 cm with...Ch. 15 - Prob. 8PCh. 15 - (a) Calculate the absolute pressure at an ocean...Ch. 15 - (a) A very powerful vacuum cleaner has a hose 2.86...Ch. 15 - What must be the contact area between a suction...Ch. 15 - Prob. 12PCh. 15 - Review. The tank in Figure P15.13 is filled with...Ch. 15 - Review. The tank in Figure P15.13 is filled with...Ch. 15 - Prob. 15PCh. 15 - Prob. 16PCh. 15 - Mercury is poured into a U-tube as shown in Figure...Ch. 15 - Prob. 18PCh. 15 - A backyard swimming pool with a circular base of...Ch. 15 - A tank with a flat bottom of area A and vertical...Ch. 15 - Prob. 21PCh. 15 - A Styrofoam slab has thickness h and density s....Ch. 15 - A table-tennis ball has a diameter of 3.80 cm and...Ch. 15 - The gravitational force exerted on a solid object...Ch. 15 - A 10.0-kg block of metal measuring 12.0 cm by 10.0...Ch. 15 - Prob. 26PCh. 15 - Prob. 27PCh. 15 - Prob. 28PCh. 15 - How many cubic meters of helium are required to...Ch. 15 - Prob. 30PCh. 15 - A plastic sphere floats in water with 50.0% of its...Ch. 15 - The weight of a rectangular block of low-density...Ch. 15 - Decades ago, it was thought that huge herbivorous...Ch. 15 - Prob. 34PCh. 15 - Prob. 35PCh. 15 - A light balloon is filled with 400 m3 of helium at...Ch. 15 - A horizontal pipe 10.0 cm in diameter has a smooth...Ch. 15 - Prob. 38PCh. 15 - A large storage tank with an open top is filled to...Ch. 15 - Review. Old Faithful Geyser in Yellowstone...Ch. 15 - (a) A water hose 2.00 cm in diameter is used to...Ch. 15 - Water flows through a fire hose of diameter 6.35...Ch. 15 - Prob. 43PCh. 15 - Prob. 44PCh. 15 - A village maintains a large tank with an open top,...Ch. 15 - Prob. 46PCh. 15 - Figure P15.47 shows a stream of water in steady...Ch. 15 - An airplane is cruising at altitude 10 km. The...Ch. 15 - The Bernoulli effect can have important...Ch. 15 - Prob. 50PCh. 15 - Prob. 51PCh. 15 - Prob. 52PCh. 15 - Prob. 53PCh. 15 - Prob. 54PCh. 15 - Prob. 55PCh. 15 - Prob. 56PCh. 15 - Prob. 57PCh. 15 - Prob. 58PCh. 15 - Review. A copper cylinder hangs at the bottom of a...Ch. 15 - Prob. 60PCh. 15 - An incompressible, nonviscous fluid is initially...Ch. 15 - In about 1657, Otto von Guericke, inventor of the...Ch. 15 - A 1.00-kg beaker containing 2.00 kg of oil...Ch. 15 - A beaker of mass mb containing oil of mass mo and...Ch. 15 - Prob. 65PCh. 15 - Prob. 66PCh. 15 - A U-tube open at both ends is partially filled...Ch. 15 - Prob. 68PCh. 15 - Prob. 69PCh. 15 - The spirit-in-glass thermometer, invented in...
Knowledge Booster
Background pattern image
Physics
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.
Similar questions
SEE MORE QUESTIONS
Recommended textbooks for you
Text book image
Physics for Scientists and Engineers, Technology ...
Physics
ISBN:9781305116399
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Text book image
Principles of Physics: A Calculus-Based Text
Physics
ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Text book image
Physics for Scientists and Engineers: Foundations...
Physics
ISBN:9781133939146
Author:Katz, Debora M.
Publisher:Cengage Learning
Text book image
College Physics
Physics
ISBN:9781938168000
Author:Paul Peter Urone, Roger Hinrichs
Publisher:OpenStax College
Text book image
University Physics Volume 1
Physics
ISBN:9781938168277
Author:William Moebs, Samuel J. Ling, Jeff Sanny
Publisher:OpenStax - Rice University
Text book image
Physics for Scientists and Engineers
Physics
ISBN:9781337553278
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Fluids in Motion: Crash Course Physics #15; Author: Crash Course;https://www.youtube.com/watch?v=fJefjG3xhW0;License: Standard YouTube License, CC-BY