Physics for Scientists and Engineers (AP Edition)
Physics for Scientists and Engineers (AP Edition)
9th Edition
ISBN: 9781133953951
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
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Chapter 14, Problem 14.50P

Review. Old Faithful Geyser in Yellowstone National Park erupts at approximately one-hour intervals, and the height of the water column reaches 40.0 m (Fig. P14.25). (a) Model the rising stream as a series of separate droplets. Analyze the free-fall motion of one of the droplets to determine the speed at which the water leaves the ground. (b) What If? Model the rising stream as an ideal fluid in streamline flow. Use Bernoulli’s equation to determine the speed of the water as it leaves ground level. (c) How does the answer from part (a) compare with the answer from part (b)? (d) What is the pressure (above atmospheric) in the heated underground chamber if its depth is 175 m? Assume the chamber is large compared with the geyser’s vent.

Figure P14.25

Chapter 14, Problem 14.50P, Review. Old Faithful Geyser in Yellowstone National Park erupts at approximately one-hour intervals,

(a)

Expert Solution
Check Mark
To determine

The speed at which the water leaves the ground when it is modeled as separate droplets.

Answer to Problem 14.50P

The speed at which the water leaves the ground when it is modeled as separate droplets is 28m/s.

Explanation of Solution

The height of the water column is 40.0m.

For the free fall, the equation of motion for upward flight is,

    vf2=vi22gh

Here, vf is the speed of water at the top of the column, vi is the speed of water leaving the ground, g is the acceleration due to gravity and h is the height of the water column.

Substitute 0m/s for vf, 9.8m/s2 for g and 40.0m for h to find vi.

    0=vi22×9.8m/s2×40.0mvi=784m2/s2=28m/s    

Conclusion:

Therefore, the speed at which the water leaves the ground when it is modeled as separate droplets is 28m/s.

(b)

Expert Solution
Check Mark
To determine

The speed of water as it leaves the ground using Bernoulli’s equation.

Answer to Problem 14.50P

The speed of water as it leaves the ground using Bernoulli’s equation is 28.0m/s.

Explanation of Solution

Apply Bernoulli’s equation at the ground level and at the top of the column.

    P0+12ρv12+ρgy1=P0+12ρv22+ρgy212ρv12+ρgy1=12ρv22+ρgy212(v12v22)=g(y2y1)v12v22=2g(y2y1)

Here, P0 is the atmospheric pressure, ρ is the density of water, v1 is the speed of water leaving the ground, v2 is the speed of water at the top of the column, h1 is the height of the bottom of the column from the ground and h2 is the height of the top of the column from the ground.

Substitute 0m/s for v2, 9.8m/s2 for g, 0m for y1 and 40.0m for y2 to find v1.

    v120=2×9.8m/s2(40.0m0m)v1=784m2/s2=28.0m/s

Conclusion:

Therefore, the speed of water as it leaves the ground using Bernoulli’s equation is 28.0m/s.

(c)

Expert Solution
Check Mark
To determine

The answer obtained in part (a) with the answer obtained in part (b).

Answer to Problem 14.50P

Both the models are consistence with each other as the speed of water leaving the ground is same in both models.

Explanation of Solution

Along a streamline for an ideal fluid, the sum of the pressure, kinetic energy per unit volume and the potential energy per unit volume is same at all the points.

The speed of the water leaving the ground obtained in both part (a) as well as in part (b) is 28m/s.

This shows that the both the models are consistence with each other.

Conclusion:

Therefore, both the models are consistence with each other as the speed of water leaving the ground is same in both models.

(d)

Expert Solution
Check Mark
To determine

The pressure in the heated underground chamber.

Answer to Problem 14.50P

The pressure in the heated underground chamber is 2.11MPa.

Explanation of Solution

Apply the Bernoulli’s equation between the chamber and the geyser vent.

    P0+12ρv12+ρgy1=P+12ρv32+ρgy3

Here, P is the pressure in the heated underground chamber, v3 is the speed of water in the heated underground chamber and y3 is the depth of the heated underground chamber.

Substitute 0m for y1 and 0m/s for v3 in the above equation.

    P0+12ρv12+ρg(0)=P+12ρ(0)+ρgy3PP0=12ρ(v122gy3)

Substitute 1000kg/m3, 28m/s for v1, 9.8m/s2 for g and 175m for y3 in the above equation.

    PP0=12(1000kg/m3){(28m/s)22×9.8m/s2×(175m)}=12(1000kg/m3)×4214m2/s2=2.11×106Pa×106MPa1Pa=2.11MPa

Conclusion:

Therefore, the pressure in the heated underground chamber is 2.11MPa.

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Chapter 14 Solutions

Physics for Scientists and Engineers (AP Edition)

Ch. 14 - A solid iron sphere and a solid lead sphere of the...Ch. 14 - Prob. 14.7OQCh. 14 - One of the predicted problems due to global...Ch. 14 - A boat develops a leak and, after its passengers...Ch. 14 - A small piece of steel is tied to a block of wood....Ch. 14 - A piece of unpainted porous wood barely floats in...Ch. 14 - A person in a boat floating in a small pond throws...Ch. 14 - Rank the buoyant forces exerted on the following...Ch. 14 - A water supply maintains a constant rate of flow...Ch. 14 - A glass of water contains floating ice cubes. When...Ch. 14 - An ideal fluid flows through a horizontal pipe...Ch. 14 - When an object is immersed in a liquid at rest,...Ch. 14 - Two thin-walled drinking glasses having equal base...Ch. 14 - Because atmospheric pressure is about 105 N/m2 and...Ch. 14 - A fish rests on the bottom of a bucket of water...Ch. 14 - You are a passenger on a spacecraft. For your...Ch. 14 - Prob. 14.6CQCh. 14 - Prob. 14.7CQCh. 14 - If you release a ball while inside a freely...Ch. 14 - (a) Is the buoyant force a conservative force? (b)...Ch. 14 - All empty metal soap dish barely floats in water....Ch. 14 - Prob. 14.11CQCh. 14 - Prob. 14.12CQCh. 14 - Prob. 14.13CQCh. 14 - Does a ship float higher in the water of an inland...Ch. 14 - Prob. 14.15CQCh. 14 - Prob. 14.16CQCh. 14 - Prairie dogs ventilate their burrows by building a...Ch. 14 - Prob. 14.18CQCh. 14 - Prob. 14.19CQCh. 14 - A large man sits on a four-legged chair with his...Ch. 14 - Prob. 14.2PCh. 14 - A 50.0-kg woman wearing high-heeled shoes is...Ch. 14 - Estimate the total mass of the Earths atmosphere....Ch. 14 - Calculate the mass of a solid gold rectangular bar...Ch. 14 - (a) A wry powerful vacuum cleaner has a hose 2.86...Ch. 14 - The spring of the pressure gauge shown in Figure...Ch. 14 - The small piston of a hydraulic lift (Fig. P14.8)...Ch. 14 - What must be the contact area between a suction...Ch. 14 - A swimming pool has dimensions 30.0 m 10.0 m and...Ch. 14 - (a) Calculate the absolute pressure at the bottom...Ch. 14 - Prob. 14.12PCh. 14 - Prob. 14.13PCh. 14 - A container is filled to a depth of 20.0 cm with...Ch. 14 - Review. 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The...Ch. 14 - The human brain and spinal cord are immersed in...Ch. 14 - Blaise Pascal duplicated Torricellis barometer...Ch. 14 - Prob. 14.22PCh. 14 - A backyard swimming pool with a circular base of...Ch. 14 - A tank with a flat bottom of area A and vertical...Ch. 14 - A table-tennis ball has a diameter of 3.80 cm and...Ch. 14 - Prob. 14.26PCh. 14 - A 10.0-kg block of metal measuring 12.0 cm by 10.0...Ch. 14 - A light balloon is filled with 400 m3 of helium at...Ch. 14 - A cube of wood having an edge dimension of 20.0 cm...Ch. 14 - The United States possesses the ten largest...Ch. 14 - A plastic sphere floats in water with 50.0% of its...Ch. 14 - A spherical vessel used for deep-sea exploration...Ch. 14 - A wooden block of volume 5.24 104 m3 floats in...Ch. 14 - The weight of a rectangular block of low-density...Ch. 14 - A large weather balloon whose mass is 226 kg is...Ch. 14 - A hydrometer is an instrument used to determine...Ch. 14 - Refer to Problem 16 and Figure P14.16. A...Ch. 14 - On October 21, 2001, Ian Ashpole of the United...Ch. 14 - How many cubic meters of helium are required to...Ch. 14 - Water flowing through a garden hose of diameter...Ch. 14 - A large storage tank, open at the top and filled...Ch. 14 - Prob. 14.42PCh. 14 - Prob. 14.43PCh. 14 - A village maintains a large tank with ail open...Ch. 14 - A legendary Dutch boy saved Holland by plugging a...Ch. 14 - Water falls over a dam of height h with a mass...Ch. 14 - Water is pumped up from the Colorado River to...Ch. 14 - In ideal flow, a liquid of density 850 kg/m3 moves...Ch. 14 - The Venturi tube discussed in Example 14.8 and...Ch. 14 - Review. Old Faithful Geyser in Yellowstone...Ch. 14 - An airplane is cruising al altitude 10 km. The...Ch. 14 - An airplane has a mass of 1.60 104 kg, and each...Ch. 14 - Prob. 14.53PCh. 14 - The Bernoulli effect can have important...Ch. 14 - Prob. 14.55PCh. 14 - Decades ago, it was thought that huge herbivorous...Ch. 14 - (a) Calculate the absolute pressure at an ocean...Ch. 14 - Prob. 14.58APCh. 14 - A spherical aluminum ball of mass 1.26 kg contains...Ch. 14 - Prob. 14.60APCh. 14 - Review. Figure P14.61 shows a valve separating a...Ch. 14 - The true weight of an object can be measured in a...Ch. 14 - Water is forced out of a fire extinguisher by air...Ch. 14 - Review. Assume a certain liquid, with density 1...Ch. 14 - Prob. 14.65APCh. 14 - Prob. 14.66APCh. 14 - Prob. 14.67APCh. 14 - A common parameter that can be used to predict...Ch. 14 - Evangelista Torricelli was the first person to...Ch. 14 - Review. With reference to the dam studied in...Ch. 14 - A 1.00-kg beaker containing 2.00 kg of oil...Ch. 14 - A beaker of mass mb containing oil of mass mu and...Ch. 14 - In 1983, the United States began coining the...Ch. 14 - Review. A long, cylindrical rod of radius r is...Ch. 14 - Prob. 14.75APCh. 14 - The spirit-in-glass thermometer, invented in...Ch. 14 - Prob. 14.77APCh. 14 - Review. In a water pistol, a piston drives water...Ch. 14 - Prob. 14.79APCh. 14 - The water supply of a building is fed through a...Ch. 14 - A U-tube open at both ends is partially filled...Ch. 14 - A woman is draining her fish tank by siphoning the...Ch. 14 - The hull of an experimental boat is to be lifted...Ch. 14 - Prob. 14.84APCh. 14 - An ice cube whose edges measure 20.0 mm is...Ch. 14 - Why is the following situation impossible? A barge...Ch. 14 - Show that the variation of atmospheric pressure...
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