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Conceptual questions

You can squirt water a considerably greater distance by placing your thumb over the end of a garden hose and then releasing, than by leaving it completely uncovered. Explain how this works.

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Water is shot nearly vertically upward in a decorative fountain and the stream is observed to broaden as it rises. Conversely, a stream of water falling straight down from a faucet narrows. Explain why, and discuss whether surface tension enhances or reduces the effect in each case.

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Look back to [link] . Answer the following two questions. Why is P o size 12{P rSub { size 8{o} } } {} less than atmospheric? Why is P o size 12{P rSub { size 8{o} } } {} greater than P i size 12{P rSub { size 8{i} } } {} ?

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Give an example of entrainment not mentioned in the text.

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Many entrainment devices have a constriction, called a Venturi, such as shown in [link] . How does this bolster entrainment?

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Figure shows a venturi tube, a cylindrical tube broader at both the ends and narrow in the middle. The narrow part is labeled as venturi constriction. The flow of fluid is shown as horizontal arrows along the length of the tube toward the right. The flow lines are closer in the center and spread apart at both the ends. There is an opening on the top portion of the narrow section for the entrained fluid to enter.
A tube with a narrow segment designed to enhance entrainment is called a Venturi. These are very commonly used in carburetors and aspirators.

Some chimney pipes have a T-shape, with a crosspiece on top that helps draw up gases whenever there is even a slight breeze. Explain how this works in terms of Bernoulli's principle.

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Is there a limit to the height to which an entrainment device can raise a fluid? Explain your answer.

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Why is it preferable for airplanes to take off into the wind rather than with the wind?

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Roofs are sometimes pushed off vertically during a tropical cyclone, and buildings sometimes explode outward when hit by a tornado. Use Bernoulli's principle to explain these phenomena.

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Why does a sailboat need a keel?

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It is dangerous to stand close to railroad tracks when a rapidly moving commuter train passes. Explain why atmospheric pressure would push you toward the moving train.

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Water pressure inside a hose nozzle can be less than atmospheric pressure due to the Bernoulli effect. Explain in terms of energy how the water can emerge from the nozzle against the opposing atmospheric pressure.

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A perfume bottle or atomizer sprays a fluid that is in the bottle. ( [link] .) How does the fluid rise up in the vertical tube in the bottle?

A perfume bottle with a spray cap.
Atomizer: perfume bottle with tube to carry perfume up through the bottle. (credit: Antonia Foy, Flickr)

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If you lower the window on a car while moving, an empty plastic bag can sometimes fly out the window. Why does this happen?

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Problems&Exercises

Verify that pressure has units of energy per unit volume.

P = Force Area , ( P ) units = N/m 2 = N m/m 3 = J/m 3 = energy/volume alignl { stack { size 12{P= { {"Force"} over {"Area"} } ,} {} #size 12{ \( P \) rSub { size 8{"units"} } ="N/m" rSup { size 8{2} } =N cdot "m/m" rSup { size 8{3} } ="J/m" rSup { size 8{3} } } {} # ="energy/volume" {}} } {}

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Suppose you have a wind speed gauge like the pitot tube shown in [link] (b). By what factor must wind speed increase to double the value of h size 12{h} {} in the manometer? Is this independent of the moving fluid and the fluid in the manometer?

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If the pressure reading of your pitot tube is 15.0 mm Hg at a speed of 200 km/h, what will it be at 700 km/h at the same altitude?

184 mm Hg

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Calculate the maximum height to which water could be squirted with the hose in [link] example if it: (a) Emerges from the nozzle. (b) Emerges with the nozzle removed, assuming the same flow rate.

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Every few years, winds in Boulder, Colorado, attain sustained speeds of 45.0 m/s (about 100 mi/h) when the jet stream descends during early spring. Approximately what is the force due to the Bernoulli effect on a roof having an area of 220 m 2 size 12{"220"`m rSup { size 8{2} } } {} ? Typical air density in Boulder is 1 . 14 kg/m 3 size 12{1 "." "14"`"kg/m" rSup { size 8{3} } } {} , and the corresponding atmospheric pressure is 8 . 89 × 10 4 N/m 2 size 12{8 "." "89" times "10" rSup { size 8{4} } `"N/m" rSup { size 8{2} } } {} . (Bernoulli's principle as stated in the text assumes laminar flow. Using the principle here produces only an approximate result, because there is significant turbulence.)

2 . 54 × 10 5 N size 12{2 "." "54" times "10" rSup { size 8{5} } " N"} {}

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(a) Calculate the approximate force on a square meter of sail, given the horizontal velocity of the wind is 6.00 m/s parallel to its front surface and 3.50 m/s along its back surface. Take the density of air to be 1.29 kg /m 3 size 12{1 "." "29"`"kg/m" rSup { size 8{3} } } {} . (The calculation, based on Bernoulli's principle, is approximate due to the effects of turbulence.) (b) Discuss whether this force is great enough to be effective for propelling a sailboat.

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(a) What is the pressure drop due to the Bernoulli effect as water goes into a 3.00-cm-diameter nozzle from a 9.00-cm-diameter fire hose while carrying a flow of 40.0 L/s? (b) To what maximum height above the nozzle can this water rise? (The actual height will be significantly smaller due to air resistance.)

(a) 1 . 58 × 10 6 N/m 2 size 12{1 "." "58" times "10" rSup { size 8{6} } " N/m" rSup { size 8{2} } } {}

(b) 163 m

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(a) Using Bernoulli's equation, show that the measured fluid speed v for a pitot tube, like the one in [link] (b), is given by

v = 2 ρ gh ρ 1 / 2 , size 12{v= left ( { {2 { {ρ}} sup { ' }gh} over {ρ} } right ) rSup { size 8{ {1} slash {2} } } } {}

where h size 12{h} {} is the height of the manometer fluid, ρ size 12{ { {ρ}} sup { ' }} {} is the density of the manometer fluid, ρ size 12{ρ} {} is the density of the moving fluid, and g size 12{g} {} is the acceleration due to gravity. (Note that v size 12{v} {} is indeed proportional to the square root of h size 12{h} {} , as stated in the text.) (b) Calculate v size 12{v} {} for moving air if a mercury manometer's h size 12{h} {} is 0.200 m.

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Test prep for ap courses

At what depth beneath the surface of the lake is the pressure in the water equal to twice atmospheric pressure?

  1. 10 m
  2. 100 m
  3. 1000 m
  4. 10,000 m

(a)

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A pump provides pressure to the lower end of a long pipeline that supplies water from a reservoir to a house located on a hill 150 m vertically upward from the lower end of the pipe (where the water is initially at rest before being pumped). The pipeline has a constant diameter of 3.5 cm, and the upper end of the pipeline is open to the atmosphere. What pressure must the pump provide for water to flow from the upper end of the pipeline at a rate of 5.0 m/s?

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According to Bernoulli's equation, if the pressure in a given fluid is constant and the kinetic energy per unit volume of a fluid increases, which of the following is true?

  1. The potential energy per unit volume of the fluid decreases.
  2. The potential energy per unit volume of the fluid increases.
  3. The fluid must no longer be considered incompressible.
  4. The flow rate of the fluid increases.

(a)

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Consider the following circumstances within a fluid, and determine the answer using Bernoulli's equation. (a) The pressure and kinetic energy per unit volume along a fluid path increases. What must be true about the potential energy per unit volume of the fluid along the fluid path? Explain. (b) The pressure along a fluid path increases, and the kinetic energy per unit volume remains constant. What must be true about the potential energy per unit volume of the fluid along the fluid path? Explain.

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Questions & Answers

A spherica, concave shaving mirror has a radius of curvature of 32 cm .what is the magnification of a persons face. when it is 12cm to the left of the vertex of the mirror
Alona Reply
A weather vane is some sort of directional arrow parallel to the ground that may rotate freely in a horizontal plane. A typical weather vane has a large cross-sectional area perpendicular to the direction the arrow is pointing, like a “One Way” street sign. The purpose of the weather vane is to indicate the direction of the wind. As wind blows pa
Kavita Reply
If a prism is fully imersed in water then the ray of light will normally dispersed or their is any difference?
Anurag Reply
the same behavior thru the prism out or in water bud abbot
Ju
If this will experimented with a hollow(vaccum) prism in water then what will be result ?
Anurag
What was the previous far point of a patient who had laser correction that reduced the power of her eye by 7.00 D, producing a normal distant vision power of 50.0 D for her?
Jaydie Reply
What is the far point of a person whose eyes have a relaxed power of 50.5 D?
Jaydie
What is the far point of a person whose eyes have a relaxed power of 50.5 D?
Jaydie
A young woman with normal distant vision has a 10.0% ability to accommodate (that is, increase) the power of her eyes. What is the closest object she can see clearly?
Jaydie
29/20 ? maybes
Ju
In what ways does physics affect the society both positively or negatively
Princewill Reply
how can I read physics...am finding it difficult to understand...pls help
rerry Reply
try to read several books on phy don't just rely one. some authors explain better than other.
Ju
And don't forget to check out YouTube videos on the subject. Videos offer a different visual way to learn easier.
Ju
hope that helps
Ju
I have a exam on 12 february
David Reply
what is velocity
Jiti
the speed of something in a given direction.
Ju
what is a magnitude in physics
Jiti Reply
Propose a force standard different from the example of a stretched spring discussed in the text. Your standard must be capable of producing the same force repeatedly.
Giovani Reply
What is meant by dielectric charge?
It's Reply
what happens to the size of charge if the dielectric is changed?
Brhanu Reply
omega= omega not +alpha t derivation
Provakar Reply
u have to derivate it respected to time ...and as w is the angular velocity uu will relace it with "thita × time""
Abrar
do to be peaceful with any body
Brhanu Reply
the angle subtended at the center of sphere of radius r in steradian is equal to 4 pi how?
Saeed Reply
if for diatonic gas Cv =5R/2 then gamma is equal to 7/5 how?
Saeed
define variable velocity
Ali Reply
Practice Key Terms 2

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Source:  OpenStax, College physics for ap® courses. OpenStax CNX. Nov 04, 2016 Download for free at https://legacy.cnx.org/content/col11844/1.14
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