Review Figure 11-6 Answer the Following Questions What Happened Betwwen Input and Input

fourteen Fluid Mechanics

fourteen Affiliate Review

Key Terms

absolute pressure

sum of gauge force per unit area and atmospheric pressure level

Archimedes' principle

buoyant force on an object equals the weight of the fluid information technology displaces

Bernoulli's equation

equation resulting from applying conservation of free energy to an incompressible frictionless fluid: p + 1 2 ρ v 2 + ρ yard h = constant , p+12ρv2+ρgh=constant, throughout the fluid

Bernoulli's principle

Bernoulli'south equation applied at abiding depth:

p i + ane 2 ρ v 2 i = p 2 + 1 2 ρ v 2 two p1+12ρv12=p2+12ρv22

buoyant strength

net upward force on any object in any fluid due to the pressure divergence at dissimilar depths

density

mass per unit of measurement volume of a substance or object

flow rate

abbreviatedQ, it is the volumeV that flows past a particular point during a timet, or Q = d V / d t Q=dV/dt

fluids

liquids and gases; a fluid is a state of matter that yields to shearing forces

gauge pressure

pressure relative to atmospheric pressure

hydraulic jack

simple machine that uses cylinders of different diameters to distribute force

hydrostatic equilibrium

state at which h2o is not flowing, or is static

ideal fluid

fluid with negligible viscosity

laminar flow

type of fluid menses in which layers practice not mix

Pascal's principle

alter in force per unit area applied to an enclosed fluid is transmitted undiminished to all portions of the fluid and to the walls of its container

Poiseuille'southward law

rate of laminar flow of an incompressible fluid in a tube: Q = ( p 2 − p 1 ) π r four 8 η l . Q=(p2−p1)πr48ηl.

Poiseuille's law for resistance

resistance to laminar menstruation of an incompressible fluid in a tube: R = eight η 50 π r 4 R=8ηlπr4

pressure level

strength per unit area exerted perpendicular to the area over which the force acts

Reynolds number

dimensionless parameter that tin can reveal whether a item menstruum is laminar or turbulent

specific gravity

ratio of the density of an object to a fluid (usually water)

turbulence

fluid flow in which layers mix together via eddies and swirls

turbulent flow

type of fluid flow in which layers mix together via eddies and swirls

viscosity

measure of the internal friction in a fluid

Key Equations

Density of a sample at constant density	ρ = m V ρ=mV
Force per unit area	p = F A p=FA
Pressure at a depthh in a fluid of abiding density	p = p 0 + ρ chiliad h p=p0+ρgh
Change of pressure with height in a constant-density fluid	d p d y = − ρ g dpdy=−ρg
Absolute pressure	p abs = p thou + p atm pabs=pg+patm
Pascal'south principle	F ane A one = F 2 A 2 F1A1=F2A2
Volume menstruum rate	Q = d V d t Q=dVdt
Continuity equation (constant density)	A 1 v 1 = A 2 v 2 A1v1=A2v2
Continuity equation (general grade)	ρ ane A one v 1 = ρ 2 A ii v ii ρ1A1v1=ρ2A2v2
Bernoulli'due south equation	p + 1 ii ρ v 2 + ρ g y = constant p+12ρv2+ρgy=abiding
Viscosity	η = F L v A η=FLvA
Poiseuille's law for resistance	R = eight η l π r four R=8ηlπr4
Poiseuille's law	Q = ( p 2 − p 1 ) π r four viii η 50 Q=(p2−p1)πr48ηl

Summary

xiv.1 Fluids, Density, and Pressure level

• A fluid is a state of affair that yields to sideways or shearing forces. Liquids and gases are both fluids. Fluid statics is the physics of stationary fluids.
• Density is the mass per unit of measurement volume of a substance or object, divers as ρ = m / V . ρ=m/Five.  The SI unit of density is kg/m 3 . kg/m3.
• Pressure level is the force per unit perpendicular expanse over which the force is applied, p = F / A . p=F/A.  The SI unit of force per unit area is the pascal: i Pa = 1 N/yard 2 1Pa=1N/m2 .
• Pressure level due to the weight of a liquid of constant density is given past p = ρ g h p=ρgh , wherep is the pressure,h is the depth of the liquid, ρ ρ  is the density of the liquid, andchiliad is the acceleration due to gravity.

14.2 Measuring Pressure

• Estimate pressure is the pressure level relative to atmospheric pressure.
• Accented force per unit area is the sum of judge pressure level and atmospheric pressure.
• Open-tube manometers have U-shaped tubes and one end is always open. They are used to measure pressure. A mercury barometer is a device that measures atmospheric force per unit area.
• The SI unit of pressure is the pascal (Pa), but several other units are commonly used.

xiv.3 Pascal's Principle and Hydraulics

• Pressure is force per unit area.
• A modify in pressure applied to an enclosed fluid is transmitted undiminished to all portions of the fluid and to the walls of its container.
• A hydraulic system is an enclosed fluid system used to exert forces.

14.iv Archimedes' Principle and Buoyancy

• Buoyant force is the net up force on any object in any fluid. If the buoyant force is greater than the object's weight, the object volition rise to the surface and bladder. If the buoyant force is less than the object's weight, the object volition sink. If the buoyant force equals the object's weight, the object can remain suspended at its present depth. The buoyant force is ever nowadays and interim on whatever object immersed either partially or entirely in a fluid.
• Archimedes' principle states that the buoyant force on an object equals the weight of the fluid it displaces.

14.five Fluid Dynamics

• Flow charge per unitQ is divers as the volumeV flowing past a betoken in fourth dimensiont, or Q = d V d t Q=dVdt  whereV is volume andt is time. The SI unit of measurement of flow charge per unit is yard 3 /s, m3/s,  merely other rates can be used, such as L/min.
• Period rate and velocity are related by Q = A v Q=Av  whereA is the cross-sectional area of the flow andv is its average velocity.
• The equation of continuity states that for an incompressible fluid, the mass flowing into a pipe must equal the mass flowing out of the pipe.

14.6 Bernoulli's Equation

• Bernoulli's equation states that the sum on each side of the post-obit equation is constant, or the same at any two points in an incompressible frictionless fluid:

  p i + 1 2 ρ v 2 1 + ρ g h 1 = p 2 + ane ii ρ v two ii + ρ g h 2 . p1+12ρv12+ρgh1=p2+12ρv22+ρgh2.

• Bernoulli's principle is Bernoulli'south equation applied to situations in which the elevation of the fluid is constant. The terms involving depth (or tiptoph) subtract out, yielding

  p 1 + 1 2 ρ v 2 1 = p 2 + ane 2 ρ v ii 2 . p1+12ρv12=p2+12ρv22.

• Bernoulli'south principle has many applications, including entrainment and velocity measurement.

xiv.7 Viscosity and Turbulence

• Laminar flow is characterized by smooth flow of the fluid in layers that do not mix.
• Turbulence is characterized by eddies and swirls that mix layers of fluid together.
• Fluid viscosity η η  is due to friction within a fluid.
• Menstruation is proportional to pressure difference and inversely proportional to resistance:
• The pressure level drop caused by flow and resistance is given past p ii – p 1 = R Q p2–p1=RQ .
• The Reynolds number Northward R NR  can reveal whether menstruation is laminar or turbulent. Information technology is N R = 2 ρ v r η NR=2ρvrη .
• For North R NR  below about 2000, flow is laminar. For Due north R NR  above almost 3000, period is turbulent. For values of Northward R NR  betwixt 2000 and 3000, it may be either or both.

Conceptual Questions

14.1 Fluids, Density, and Pressure

1.

Which of the following substances are fluids at room temperature and atmospheric pressure: air, mercury, water, glass?

2 .

Why are gases easier to compress than liquids and solids?

3.

Explain how the density of air varies with altitude.

4 .

The image shows a glass of ice water filled to the brim. Will the water overflow when the ice melts? Explicate your answer.

5.

How is pressure related to the sharpness of a pocketknife and its ability to cut?

vi .

Why is a force exerted by a static fluid on a surface always perpendicular to the surface?

seven.

Imagine that in a remote location almost the North Pole, a chunk of water ice floats in a lake. Adjacent to the lake, a glacier with the same volume as the floating ice sits on country. If both chunks of water ice should melt due to rise global temperatures, and the melted water ice all goes into the lake, which one would crusade the level of the lake to rising the most? Explicate.

eight .

In ballet, dancingen pointe (on the tips of the toes) is much harder on the toes than normal dancing or walking. Explain why, in terms of force per unit area.

ix.

Atmospheric pressure exerts a large force (equal to the weight of the atmosphere higher up your trunk—about 10 tons) on the top of your trunk when you are lying on the beach sunbathing. Why are yous able to go up?

10 .

Why does atmospheric pressure decrease more apace than linearly with altitude?

11.

The epitome shows how sandbags placed effectually a leak outside a river levee can effectively stop the flow of h2o under the levee. Explain how the small amount of h2o within the cavalcade of sandbags is able to balance the much larger torso of water behind the levee.

12 .

Is there a net forcefulness on a dam due to atmospheric pressure? Explain your respond.

thirteen.

Does atmospheric force per unit area add to the gas pressure in a rigid tank? In a toy balloon? When, in full general, does atmospheric force per unit area non affect the total pressure in a fluid?

14 .

You tin can break a potent vino bottle past pounding a cork into information technology with your fist, just the cork must press direct confronting the liquid filling the bottle—there can be no air between the cork and liquid. Explain why the canteen breaks only if in that location is no air between the cork and liquid.

14.2 Measuring Pressure

15.

Explicate why the fluid reaches equal levels on either side of a manometer if both sides are open to the atmosphere, even if the tubes are of unlike diameters.

14.iii Pascal's Principle and Hydraulics

xvi .

Suppose the master cylinder in a hydraulic organization is at a greater acme than the cylinder information technology is controlling. Explicate how this volition touch on the force produced at the cylinder that is being controlled.

14.four Archimedes' Principle and Buoyancy

17.

More forcefulness is required to pull the plug in a total bathtub than when it is empty. Does this contradict Archimedes' principle? Explain your answer.

18 .

Practise fluids exert buoyant forces in a "weightless" environment, such as in the space shuttle? Explain your answer.

19.

Volition the aforementioned ship bladder higher in salt water than in freshwater? Explain your answer.

20 .

Marbles dropped into a partially filled bathtub sink to the bottom. Part of their weight is supported past buoyant strength, yet the downwards force on the lesser of the tub increases by exactly the weight of the marbles. Explain why.

14.5 Fluid Dynamics

21.

Many figures in the text testify streamlines. Explain why fluid velocity is greatest where streamlines are closest together. (Hint: Consider the relationship betwixt fluid velocity and the cross-sectional area through which the fluid flows.)

fourteen.six Bernoulli'due south Equation

22 .

Yous can squirt water from a garden hose a considerably greater altitude by partially covering the opening with your pollex. Explain how this works.

23.

Water is shot about vertically upward in a decorative fountain and the stream is observed to augment as it rises. Conversely, a stream of h2o falling straight down from a faucet narrows. Explain why.

24 .

Look back to Figure xiv.29. Answer the following two questions. Why is p o po  less than atmospheric? Why is p o po  greater than p i pi ?

25.

A tube with a narrow segment designed to enhance entrainment is called aVenturi, such every bit shown below. Venturis are very commonly used in carburetors and aspirators. How does this structure bolster entrainment?

26 .

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

27.

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

28 .

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

29.

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

30 .

It is unsafe to stand shut to railroad tracks when a apace moving driver train passes. Explicate why atmospheric pressure would push yous toward the moving train.

31.

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

32 .

David rolled downwardly the window on his car while driving on the superhighway. An empty plastic bag on the floor promptly flew out the window. Explicate why.

33.

Based on Bernoulli's equation, what are three forms of energy in a fluid? (Note that these forms are bourgeois, unlike heat transfer and other dissipative forms non included in Bernoulli's equation.)

34 .

The old condom boot shown below has 2 leaks. To what maximum acme tin the water squirt from Leak ane? How does the velocity of h2o emerging from Leak 2 differ from that of Leak i? Explain your responses in terms of free energy.

35.

Water pressure inside a hose nozzle can be less than atmospheric force per unit area due to the Bernoulli result. Explicate in terms of energy how the water tin can emerge from the nozzle against the opposing atmospheric pressure.

14.7 Viscosity and Turbulence

36 .

Explain why the viscosity of a liquid decreases with temperature, that is, how might an increment in temperature reduce the effects of cohesive forces in a liquid? Also explain why the viscosity of a gas increases with temperature, that is, how does increased gas temperature create more collisions betwixt atoms and molecules?

37.

When paddling a canoe upstream, it is wisest to travel as near to the shore as possible. When canoeing downstream, information technology is mostly better to stay most the eye. Explain why.

38 .

Plumbing usually includes air-filled tubes near water faucets (meet the following figure). Explicate why they are needed and how they work.

39.

Doppler ultrasound can be used to measure out the speed of blood in the body. If there is a partial constriction of an avenue, where would y'all expect blood speed to be greatest: at or after the constriction? What are the two distinct causes of higher resistance in the constriction?

40 .

Sink drains frequently have a device such as that shown below to help speed the flow of h2o. How does this work?

Issues

xiv.1 Fluids, Density, and Pressure level

41.

Aureate is sold by the troy ounce (31.103 thou). What is the book of 1 troy ounce of pure gilt?

42 .

Mercury is ordinarily supplied in flasks containing 34.five kg (about 76 lb.). What is the book in liters of this much mercury?

43.

What is the mass of a deep breath of air having a book of ii.00 50? Discuss the effect taking such a jiff has on your body's volume and density.

44 .

A straightforward method of finding the density of an object is to measure its mass and then measure its volume by submerging it in a graduated cylinder. What is the density of a 240-g rock that displaces 89.0 cm 3 89.0cm3  of water? (Note that the accuracy and applied applications of this technique are more than limited than a multifariousness of others that are based on Archimedes' principle.)

45.

Suppose you have a java mug with a circular cross-section and vertical sides (uniform radius). What is its within radius if it holds 375 g of coffee when filled to a depth of vii.l cm? Presume coffee has the same density every bit h2o.

46 .

A rectangular gasoline tank tin hold fifty.0 kg of gasoline when full. What is the depth of the tank if it is 0.500-m wide past 0.900-m long? (b) Discuss whether this gas tank has a reasonable volume for a passenger car.

47.

A trash compactor tin can compress its contents to 0.350 times their original volume. Neglecting the mass of air expelled, by what factor is the density of the rubbish increased?

48 .

A 2.l-kg steel gasoline can holds 20.0 L of gasoline when full. What is the average density of the full gas tin, taking into account the volume occupied by steel too equally by gasoline?

49.

What is the density of eighteen.0-karat gilt that is a mixture of 18 parts gold, v parts silver, and 1 part copper? (These values are parts by mass, not volume.) Assume that this is a unproblematic mixture having an average density equal to the weighted densities of its constituents.

50 .

The tip of a blast exerts tremendous pressure when hitting by a hammer because it exerts a large strength over a small-scale area. What force must exist exerted on a nail with a circular tip of i.00-mm diameter to create a pressure of iii.00 × ten 9 Northward/m 2 ? 3.00×109N/m2?  (This high pressure level is possible because the hammer striking the nail is brought to balance in such a brusk distance.)

51.

A drinking glass tube contains mercury. What would be the height of the column of mercury which would create pressure equal to 1.00 atm?

52 .

The greatest ocean depths on Earth are plant in the Marianas Trench near the Philippines. Calculate the force per unit area due to the sea at the lesser of this trench, given its depth is xi.0 km and bold the density of seawater is constant all the way down.

53.

Verify that the SI unit of h ρ k hρg  is N/chiliad 2 North/m2 .

54 .

What pressure is exerted on the bottom of a gas tank that is 0.500-m wide and 0.900-one thousand long and tin can hold 50.0 kg of gasoline when full?

55.

A dam is used to hold back a river. The dam has a height H = 12 m H=12m  and a width W = x m . Due west=10m.  Assume that the density of the water is ρ = thousand kg/chiliad 3 . ρ=1000kg/m3.  (a) Determine the internet force on the dam. (b) Why does the thickness of the dam increase with depth?

14.2 Measuring Pressure

56 .

Observe the gauge and absolute pressures in the balloon and peanut jar shown in Figure 14.12, assuming the manometer continued to the balloon uses water and the manometer connected to the jar contains mercury. Limited in units of centimeters of h2o for the airship and millimeters of mercury for the jar, taking h = 0.0500 m h=0.0500m  for each.

57.

How tall must a water-filled manometer exist to measure blood pressure as high as 300 mm Hg?

58 .

Assuming bicycle tires are perfectly flexible and back up the weight of bicycle and passenger past pressure alone, calculate the total surface area of the tires in contact with the footing if a bicycle and rider have a total mass of fourscore.0 kg, and the gauge force per unit area in the tires is three.50 × 10 5 Pa three.50×105Pa .

14.iii Pascal's Principle and Hydraulics

59.

How much pressure is transmitted in the hydraulic organization considered in Example 14.3? Express your answer in atmospheres.

60 .

What force must be exerted on the master cylinder of a hydraulic elevator to back up the weight of a 2000-kg car (a large car) resting on a second cylinder? The master cylinder has a 2.00-cm diameter and the second cylinder has a 24.0-cm diameter.

61.

A host pours the remnants of several bottles of wine into a jug later a party. The host then inserts a cork with a 2.00-cm bore into the canteen, placing it in direct contact with the vino. The host is amazed when the host pounds the cork into place and the bottom of the jug (with a xiv.0-cm diameter) breaks away. Summate the actress forcefulness exerted against the bottom if he pounded the cork with a 120-N force.

62 .

A certain hydraulic organisation is designed to exert a force 100 times as large every bit the one put into it. (a) What must be the ratio of the expanse of the cylinder that is being controlled to the area of the master cylinder? (b) What must be the ratio of their diameters? (c) By what factor is the altitude through which the output force moves reduced relative to the distance through which the input forcefulness moves? Assume no losses due to friction.

63.

Verify that piece of work input equals piece of work output for a hydraulic system assuming no losses due to friction. Do this by showing that the distance the output force moves is reduced past the same cistron that the output forcefulness is increased. Assume the book of the fluid is constant. What effect would friction inside the fluid and between components in the system have on the output strength? How would this depend on whether or non the fluid is moving?

14.4 Archimedes' Principle and Buoyancy

64 .

What fraction of ice is submerged when it floats in freshwater, given the density of h2o at 0 °C 0°C  is very close to thou kg/one thousand iii 1000kg/m3 ?

65.

If a person's body has a density of 995 kg/m 3 995kg/m3 , what fraction of the body volition exist submerged when floating gently in (a) freshwater? (b) In table salt water with a density of 1027 kg/m 3 1027kg/m3 ?

66 .

A stone with a mass of 540 m in air is found to take an apparent mass of 342 g when submerged in water. (a) What mass of h2o is displaced? (b) What is the book of the stone? (c) What is its average density? Is this consistent with the value for granite?

67.

Archimedes' principle can exist used to calculate the density of a fluid as well as that of a solid. Suppose a chunk of iron with a mass of 390.0 g in air is found to have an apparent mass of 350.5 k when completely submerged in an unknown liquid. (a) What mass of fluid does the fe readapt? (b) What is the volume of atomic number 26, using its density as given in Table 14.1? (c) Calculate the fluid's density and place information technology.

68 .

Calculate the buoyant forcefulness on a ii.00-L helium balloon. (b) Given the mass of the safety in the balloon is 1.fifty k, what is the net vertical force on the airship if it is permit go? Neglect the volume of the prophylactic.

69.

What is the density of a woman who floats in fresh water with four.00 % 4.00%  of her book in a higher place the surface? (This could exist measured by placing her in a tank with marks on the side to measure how much water she displaces when floating and when held under water.) (b) What percent of her volume is to a higher place the surface when she floats in seawater?

70 .

A homo has a mass of lxxx kg and a density of 955 kg/thou 3 955kg/m3  (excluding the air in his lungs). (a) Calculate his volume. (b) Find the buoyant force air exerts on him. (c) What is the ratio of the buoyant force to his weight?

71.

A simple compass can be made by placing a small bar magnet on a cork floating in water. (a) What fraction of a obviously cork will exist submerged when floating in water? (b) If the cork has a mass of x.0 g and a 20.0-g magnet is placed on it, what fraction of the cork will be submerged? (c) Will the bar magnet and cork bladder in ethyl booze?

72 .

What percentage of an atomic number 26 anchor'southward weight will be supported by buoyant strength when submerged in salt water?

73.

Referring to Figure 14.xx, show that the buoyant strength on the cylinder is equal to the weight of the fluid displaced (Archimedes' principle). You may assume that the buoyant strength is F 2 − F one F2−F1  and that the ends of the cylinder accept equal areas A A . Note that the volume of the cylinder (and that of the fluid it displaces) equals ( h 2 − h 1 ) A (h2−h1)A .

74 .

A 75.0-kg man floats in freshwater with 3.00% of his book above h2o when his lungs are empty, and five.00% of his volume above water when his lungs are full. Calculate the volume of air he inhales—chosen his lung capacity—in liters. (b) Does this lung volume seem reasonable?

fourteen.v Fluid Dynamics

75.

What is the average flow charge per unit in cm 3 /southward cm3/southward  of gasoline to the engine of a automobile traveling at 100 km/h if it averages x.0 km/L?

76 .

The heart of a resting adult pumps blood at a rate of five.00 50/min. (a) Convert this to cm 3 /due south cm3/due south . (b) What is this rate in m 3 /southward m3/due south ?

77.

The Huka Falls on the Waikato River is i of New Zealand's most visited natural tourist attractions. On boilerplate, the river has a flow rate of about 300,000 L/south. At the gorge, the river narrows to 20-grand wide and averages 20-g deep. (a) What is the average speed of the river in the gorge? (b) What is the average speed of the water in the river downstream of the falls when it widens to 60 k and its depth increases to an average of 40 m?

78 .

(a) Approximate the time it would take to fill a individual pond pool with a capacity of fourscore,000 Fifty using a garden hose delivering 60 L/min. (b) How long would it take if you could divert a moderate size river, flowing at 5000 one thousand 3 /s 5000m3/s  into the pool?

79.

What is the fluid speed in a fire hose with a 9.00-cm diameter carrying lxxx.0 L of water per 2d? (b) What is the flow rate in cubic meters per second? (c) Would your answers be different if common salt water replaced the fresh water in the fire hose?

80 .

Water is moving at a velocity of 2.00 yard/southward through a hose with an internal diameter of 1.60 cm. (a) What is the flow rate in liters per 2d? (b) The fluid velocity in this hose'south nozzle is 15.0 g/s. What is the nozzle's inside diameter?

81.

Testify that the speed of an incompressible fluid through a constriction, such as in a Venturi tube, increases by a factor equal to the foursquare of the gene by which the diameter decreases. (The antipodal applies for flow out of a constriction into a larger-diameter region.)

82 .

Water emerges straight downwards from a faucet with a 1.eighty-cm diameter at a speed of 0.500 m/southward. (Because of the structure of the faucet, there is no variation in speed across the stream.) (a) What is the flow rate in cm 3 /s cm3/due south ? (b) What is the bore of the stream 0.200 m below the faucet? Neglect any furnishings due to surface tension.

14.6 Bernoulli'due south Equation

83.

Verify that pressure has units of energy per unit book.

84 .

Suppose you take a wind speed gauge like the pitot tube shown in Figure xiv.32. By what factor must wind speed increase to double the value ofh in the manometer? Is this contained of the moving fluid and the fluid in the manometer?

85.

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

86 .

Every few years, winds in Bedrock, Colorado, reach sustained speeds of 45.0 g/s (nigh 100 mph) when the jet stream descends during early spring. Approximately what is the force due to the Bernoulli equation on a roof having an area of 220 thou 2 220m2 ? Typical air density in Boulder is 1.14 kg/m 3 1.14kg/m3 , and the respective atmospheric pressure is 8.89 × 10 4 North/m ii eight.89×104N/m2 . (Bernoulli's principle as stated in the text assumes laminar flow. Using the principle hither produces only an approximate result, because there is pregnant turbulence.)

87.

What is the pressure drop due to the Bernoulli Effect as water goes into a 3.00-cm-bore nozzle from a 9.00-cm-diameter burn down hose while carrying a flow of 40.0 L/s? (b) To what maximum height above the nozzle can this h2o rise? (The actual tiptop volition be significantly smaller due to air resistance.)

88 .

(a) Using Bernoulli's equation, show that the measured fluid speed5 for a pitot tube, like the ane in Figure 14.32(b), is given past 5 = ( 2 ρ ′ thou h ρ ) 1 / 2 five=(2ρ′ghρ)1/2 , whereh is the height of the manometer fluid, ρ ′ ρ′  is the density of the manometer fluid, ρ ρ  is the density of the moving fluid, andone thousand is the acceleration due to gravity. (Note that5 is indeed proportional to the square root ofh, as stated in the text.) (b) Calculatev for moving air if a mercury manometer'sh is 0.200 g.

89.

A container of water has a cross-sectional area of A = 0.i m 2 A=0.1m2 . A piston sits on top of the water (see the following figure). There is a spout located 0.15 one thousand from the bottom of the tank, open up to the atmosphere, and a stream of water exits the spout. The cross exclusive expanse of the spout is A s = 7.0 × 10 −iv k two As=7.0×10−4m2 . (a) What is the velocity of the water as it leaves the spout? (b) If the opening of the spout is located 1.5 m above the ground, how far from the spout does the water hit the flooring? Ignore all friction and dissipative forces.

xc .

A fluid of a abiding density flows through a reduction in a pipe. Detect an equation for the change in pressure, in terms of v 1 , A 1 , A 2 v1,A1,A2 , and the density.

14.7 Viscosity and Turbulence

91.

(a) Summate the retarding force due to the viscosity of the air layer between a cart and a level air track given the following information: air temperature is 20 °C 20°C , the cart is moving at 0.400 m/s, its surface area is 2.50 × 10 −ii g ii , 2.50×ten−2m2,  and the thickness of the air layer is 6.00 × ten −v m half-dozen.00×10−5m . (b) What is the ratio of this strength to the weight of the 0.300-kg cart?

92 .

The arterioles (minor arteries) leading to an organ tuck in order to subtract catamenia to the organ. To shut down an organ, blood flow is reduced naturally to i.00% of its original value. By what cistron do the radii of the arterioles constrict?

93.

A spherical particle falling at a terminal speed in a liquid must have the gravitational forcefulness balanced by the drag strength and the buoyant force. The buoyant forcefulness is equal to the weight of the displaced fluid, while the elevate force is causeless to exist given past Stokes Law, F s = 6 π r η v . Fs=6πrηv.  Evidence that the terminal speed is given by v = ii R 2 1000 9 η ( ρ s − ρ 1 ) v=2R2g9η(ρs−ρ1) , whereR is the radius of the sphere, ρ due south ρs  is its density, and ρ i ρ1  is the density of the fluid, and η η  the coefficient of viscosity.

94 .

Using the equation of the previous problem, discover the viscosity of motor oil in which a steel ball of radius 0.eight mm falls with a terminal speed of 4.32 cm/south. The densities of the ball and the oil are vii.86 and 0.88 1000/mL, respectively.

95.

A skydiver will reach a terminal velocity when the air drag equals his or her weight. For a skydiver with a large body, turbulence is a factor at high speeds. The elevate strength so is approximately proportional to the square of the velocity. Taking the drag force to be F D = i 2 ρ A v ii , FD=12ρAv2,  and setting this equal to the skydiver's weight, find the terminal speed for a person falling "spread eagle."

96 .

(a) Verify that a 19.0% decrease in laminar menstruum through a tube is caused past a 5.00% decrease in radius, assuming that all other factors remain constant. (b) What increase in flow is obtained from a v.00% increase in radius, again assuming all other factors remain constant?

97.

When physicians diagnose arterial blockages, they quote the reduction in menstruum charge per unit. If the flow rate in an avenue has been reduced to 10.0% of its normal value by a blood clot and the boilerplate pressure difference has increased by 20.0%, by what factor has the clot reduced the radius of the avenue?

98 .

An oil gusher shoots crude oil 25.0 m into the air through a pipe with a 0.100-k diameter. Neglecting air resistance but non the resistance of the pipe, and assuming laminar catamenia, calculate the pressure at the entrance of the fifty.0-m-long vertical pipe. Take the density of the oil to exist 900 kg/yard 3 900kg/m3  and its viscosity to be 1.00 ( N/m 2 ) ⋅ due south 1.00(N/m2)⋅s  (or one.00 Pa ⋅ s 1.00Pa⋅southward ). Note that you must take into account the pressure due to the 50.0-m column of oil in the pipe.

99.

Concrete is pumped from a cement mixer to the place it is being laid, instead of being carried in wheelbarrows. The flow charge per unit is 200 L/min through a 50.0-m-long, eight.00-cm-diameter hose, and the pressure at the pump is viii.00 × 10 6 Due north/m 2 8.00×106N/m2 . (a) Calculate the resistance of the hose. (b) What is the viscosity of the concrete, assuming the menses is laminar? (c) How much power is being supplied, bold the point of employ is at the same level as the pump? You may fail the power supplied to increment the concrete'southward velocity.

100 .

Verify that the menstruation of oil is laminar for an oil gusher that shoots rough oil 25.0 m into the air through a piping with a 0.100-m bore. The vertical pipe is fifty grand long. Have the density of the oil to be 900 kg/m 3 900kg/m3  and its viscosity to be ane.00 ( N/one thousand two ) ⋅ s 1.00(N/m2)⋅southward (or 1.00 Pa ⋅ s 1.00Pa⋅southward ).

101.

Calculate the Reynolds numbers for the flow of water through (a) a nozzle with a radius of 0.250 cm and (b) a garden hose with a radius of 0.900 cm, when the nozzle is attached to the hose. The menstruation rate through hose and nozzle is 0.500 50/s. Tin the flow in either possibly exist laminar?

102 .

A burn down hose has an inside diameter of half dozen.forty cm. Suppose such a hose carries a flow of forty.0 50/s starting at a gauge pressure of 1.62 × 10 half dozen N/chiliad 2 one.62×106N/m2 . The hose goes 10.0 m upwards a ladder to a nozzle having an inside diameter of iii.00 cm. Calculate the Reynolds numbers for flow in the fire hose and nozzle to show that the flow in each must be turbulent.

103.

At what flow rate might turbulence begin to develop in a water main with a 0.200-m diameter? Presume a 20 °C 20°C temperature.

Boosted Problems

104 .

Before digital storage devices, such as the retention in your cell phone, music was stored on vinyl disks with grooves with varying depths cutting into the disk. A phonograph used a needle, which moved over the grooves, measuring the depth of the grooves. The pressure exerted past a phonograph needle on a record is surprisingly large. If the equivalent of 1.00 one thousand is supported by a needle, the tip of which is a circle with a 0.200-mm radius, what pressure level is exerted on the tape in Pa?

105.

Water towers shop water above the level of consumers for times of heavy apply, eliminating the need for loftier-speed pumps. How high in a higher place a user must the water level be to create a gauge pressure of 3.00 × 10 5 N/m 2 three.00×105N/m2 ?

106 .

The aqueous humour in a person's eye is exerting a force of 0.300 Northward on the i.10 -cm two one.10-cm2  area of the cornea. What pressure is this in mm Hg?

107.

(a) Catechumen normal blood pressure readings of 120 over 80 mm Hg to newtons per meter squared using the relationship for pressure due to the weight of a fluid ( p = h ρ grand ) (p=hρg)  rather than a conversion factor. (b) Explicate why the claret pressure of an infant would likely exist smaller than that of an developed. Specifically, consider the smaller peak to which blood must exist pumped.

108 .

Pressure cookers accept been around for more than 300 years, although their utilise has profoundly declined in recent years (early on models had a nasty addiction of exploding). How much forcefulness must the latches holding the chapeau onto a pressure cooker be able to withstand if the circular hat is 25.0 cm 25.0cm  in diameter and the gauge pressure inside is 300 atm? Fail the weight of the chapeau.

109.

Bird bones have air pockets in them to reduce their weight—this also gives them an average density significantly less than that of the bones of other animals. Suppose an ornithologist weighs a bird bone in air and in water and finds its mass is 45.0 g and its apparent mass when submerged is 3.60 g (presume the bone is watertight). (a) What mass of water is displaced? (b) What is the book of the bone? (c) What is its average density?

110 .

In an immersion measurement of a adult female's density, she is found to have a mass of 62.0 kg in air and an credible mass of 0.0850 kg when completely submerged with lungs empty. (a) What mass of h2o does she displace? (b) What is her volume? (c) Calculate her density. (d) If her lung capacity is 1.75 50, is she able to float without treading water with her lungs filled with air?

111.

Some fish have a density slightly less than that of water and must exert a force (swim) to stay submerged. What force must an 85.0-kg grouper exert to stay submerged in table salt water if its body density is 1015 kg/m 3 ? 1015kg/m3?

112 .

The homo circulation system has approximately 1 × 10 9 1×109  capillary vessels. Each vessel has a diameter of about 8 μ m 8μm . Bold cardiac output is 5 Fifty/min, decide the average velocity of blood flow through each capillary vessel.

113.

The flow rate of blood through a 2.00 × 10 −6 m 2.00×ten−6m -radius capillary is iii.eighty × 10 nine cm 3 /southward 3.80×109cm3/due south . (a) What is the speed of the claret flow? (b) Assuming all the blood in the body passes through capillaries, how many of them must in that location be to deport a total flow of 90.0 cm 3 /s 90.0cm3/s  ?

114 .

The left ventricle of a resting adult's heart pumps claret at a flow charge per unit of 83.0 cm 3 /s 83.0cm3/s , increasing its pressure by 110 mm Hg, its speed from goose egg to xxx.0 cm/s, and its height by v.00 cm. (All numbers are averaged over the entire heartbeat.) Summate the full power output of the left ventricle. Note that most of the power is used to increase claret pressure.

115.

A sump pump (used to drain water from the basement of houses built below the water table) is draining a flooded basement at the rate of 0.750 50/s, with an output pressure of three.00 × 10 v Northward/g 2 3.00×105N/m2 . (a) The water enters a hose with a 3.00-cm inside bore and rises 2.50 grand above the pump. What is its pressure at this bespeak? (b) The hose goes over the foundation wall, losing 0.500 thou in meridian, and widens to iv.00 cm in diameter. What is the pressure level now? You may neglect frictional losses in both parts of the problem.

116 .

A glucose solution existence administered with an 4 has a flow rate of four.00 cm 3 /min four.00cm3/min . What will the new catamenia rate be if the glucose is replaced by whole blood having the same density but a viscosity 2.l times that of the glucose? All other factors remain constant.

117.

A small artery has a length of i.1 × 10 −3 1000 ane.ane×10−3m  and a radius of 2.5 × 10 −5 m ii.v×ten−5m . If the force per unit area drop across the artery is 1.iii kPa, what is the flow rate through the artery? (Assume that the temperature is 37 °C 37°C .)

118 .

Angioplasty is a technique in which arteries partially blocked with plaque are dilated to increment blood flow. By what factor must the radius of an avenue be increased in order to increase blood flow past a factor of 10?

119.

Suppose a blood vessel's radius is decreased to 90.0% of its original value by plaque deposits and the body compensates by increasing the pressure difference forth the vessel to keep the menstruum rate constant. By what factor must the pressure departure increase? (b) If turbulence is created by the obstruction, what additional effect would information technology have on the period rate?

Challenge Problems

120 .

The force per unit area on the dam shown early on in the problems section increases with depth. Therefore, there is a internet torque on the dam. Find the cyberspace torque.

121.

The temperature of the atmosphere is not ever constant and can increase or decrease with height. In a neutral temper, where there is not a significant amount of vertical mixing, the temperature decreases at a rate of approximately 6.v One thousand per km. The magnitude of the decrease in temperature every bit tiptop increases is known as the lapse rate ( Γ ) . (Γ).  (The symbol is the upper case Greek letter of the alphabet gamma.) Assume that the surface force per unit area is p 0 = 1.013 × 10 5 Pa p0=1.013×105Pa  where T = 293 G T=293K  and the lapse rate is ( − Γ = 6.5 K km ) (−Γ=6.5Kkm) . Guess the pressure level 3.0 km above the surface of Earth.

122 .

A submarine is stranded on the bottom of the bounding main with its hatch 25.0 m below the surface. Calculate the force needed to open the hatch from the inside, given information technology is circular and 0.450 m in bore. Air pressure level inside the submarine is 1.00 atm.

123.

Logs sometimes bladder vertically in a lake because one end has become water-logged and denser than the other. What is the average density of a uniform-bore log that floats with twenty.0% of its length higher up h2o?

124 .

Scurrilous con artists have been known to correspond gilt-plated tungsten ingots as pure gold and sell them at prices much beneath gold value merely high above the toll of tungsten. With what accurateness must you be able to mensurate the mass of such an ingot in and out of water to tell that it is almost pure tungsten rather than pure aureate?

125.

The within book of a house is equivalent to that of a rectangular solid 13.0 g broad by 20.0 m long past 2.75 grand loftier. The firm is heated by a forced air gas heater. The main uptake air duct of the heater is 0.300 one thousand in diameter. What is the average speed of air in the duct if it carries a volume equal to that of the house's interior every 15 minutes?

126 .

A garden hose with a diameter of 2.0 cm is used to fill a bucket, which has a book of 0.10 cubic meters. Information technology takes ane.2 minutes to make full. An adjustable nozzle is attached to the hose to subtract the diameter of the opening, which increases the speed of the water. The hose is held level to the ground at a height of ane.0 meters and the diameter is decreased until a bloom bed three.0 meters away is reached. (a) What is the volume menstruation charge per unit of the water through the nozzle when the diameter is ii.0 cm? (b) What is the speed of the water coming out of the hose? (c) What does the speed of the water coming out of the hose need to be to reach the flower bed 3.0 meters away? (d) What is the diameter of the nozzle needed to reach the flower bed?

127.

A frequently quoted rule of pollex in aircraft design is that wings should produce about chiliad North of lift per square meter of wing. (The fact that a wing has a tiptop and bottom surface does not double its expanse.) (a) At takeoff, an aircraft travels at lx.0 k/s, so that the air speed relative to the bottom of the wing is 60.0 k/s. Given the sea level density of air as i.29 kg/thousand 3 1.29kg/m3 , how fast must it move over the upper surface to create the ideal lift? (b) How fast must air move over the upper surface at a cruising speed of 245 thou/southward and at an altitude where air density is 1-quaternary that at body of water level? (Note that this is non all of the shipping's lift—some comes from the body of the airplane, some from engine thrust, and then on. Furthermore, Bernoulli's principle gives an approximate answer because flow over the fly creates turbulence.)

128 .

2 pipes of equal and constant diameter leave a water pumping station and dump water out of an open up end that is open to the atmosphere (see the following figure). The water enters at a pressure of two atmospheres and a speed of ( v 1 = 1.0 grand/s ) (v1=one.0m/southward) . I pipage drops a height of 10 one thousand. What is the velocity of the water equally the h2o leaves each piping?

129.

Fluid originally flows through a tube at a rate of 100 cm iii /s 100cm3/due south . To illustrate the sensitivity of flow rate to various factors, calculate the new flow rate for the following changes with all other factors remaining the aforementioned as in the original conditions. (a) Pressure difference increases by a gene of 1.50. (b) A new fluid with 3.00 times greater viscosity is substituted. (c) The tube is replaced by one having 4.00 times the length. (d) Another tube is used with a radius 0.100 times the original. (eastward) Nonetheless another tube is substituted with a radius 0.100 times the original and half the length, and the pressure departure is increased by a cistron of ane.50.

130 .

During a marathon race, a runner'due south blood flow increases to ten.0 times her resting rate. Her blood's viscosity has dropped to 95.0% of its normal value, and the blood pressure difference across the circulatory organization has increased by 50.0%. By what gene has the average radii of her blood vessels increased?

131.

Water supplied to a house by a h2o main has a pressure of three.00 × 10 5 North/m 2 three.00×105N/m2  early on a summer day when neighborhood use is low. This pressure produces a menstruation of 20.0 Fifty/min through a garden hose. Afterwards in the day, pressure level at the exit of the water principal and entrance to the house drops, and a flow of only 8.00 50/min is obtained through the same hose. (a) What pressure is now being supplied to the house, assuming resistance is abiding? (b) By what factor did the catamenia rate in the h2o primary increment in club to cause this decrease in delivered pressure? The pressure level at the entrance of the water main is 5.00 × 10 5 N/one thousand 2 5.00×105N/m2 , and the original flow rate was 200 L/min. (c) How many more users are at that place, assuming each would consume 20.0 L/min in the morn?

132 .

Gasoline is piped undercover from refineries to major users. The menses rate is three.00 × x −2 m iii /due south 3.00×ten−2m3/s  (nearly 500 gal/min), the viscosity of gasoline is ane.00 × ten −3 ( N/m 2 ) ⋅ due south 1.00×10−3(N/m2)⋅s , and its density is 680 kg/m 3 . 680kg/m3.  (a) What minimum diameter must the pipe take if the Reynolds number is to be less than 2000? (b) What force per unit area departure must be maintained along each kilometer of the pipe to maintain this flow rate?

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Source: https://opentextbc.ca/universityphysicsv1openstax/chapter/14-chapter-review/

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