(III) A 3.65-kg block of wood (SG =0.50) floats on water.

The approximate volume of the granite monolith known as El Capitan in Yosemite National Park (Fig.1047) is about 10 What is its approximate mass

What is the approximate mass of air in a living room 5.6 m * 3.6 m * 2.4 m?

If you tried to smuggle gold bricks by filling your backpack, whose dimensions are what would its mass be?

State your mass and then estimate your volume. [Hint: Because you can swim on or just under the surface of the water in a swimming pool, you have a pretty good idea of your density.]

A bottle has a mass of 35.00 g when empty and 98.44 g when filled with water. When filled with another fluid, the mass is 89.22 g. What is the specific gravity of this other fluid?

(II) If 4.0 L of antifreeze solution (specific gravity = 0.80) is added to 5.0 L of water to make a 9.0-L mixture, what is the specific gravity of the mixture?

The Earth is not a uniform sphere, but has regions of varying density. Consider a simple model of the Earth divided into three regionsinner core, outer core, and mantle. Each region is taken to have a unique constant density (the average density of that region in the real Earth): (a) Use this model to predict the average density of the entire Earth. (b) If the radius of the Earth is 6380 km and its mass is determine the actual average density of the Earth and compare it (as a percent difference)with the one you determined in (a).

Estimate the pressure needed to raise a column of water to the same height as a 46-m-tall pine tree

What is the difference in blood pressure (mm-Hg) between the top of the head and bottom of the feet of a 1.75-m-tall person standing vertically?

(I) (a) Calculate the total force of the atmosphere acting on the top of a table that measures \(1.7 \ \mathrm m \times 2.6 \ \mathrm m\) (b) What is the total force acting upward on the underside of the table?

How high would the level be in an alcohol barometer at normal atmospheric pressure?

How high would the level be in an alcohol barometer at normal atmospheric pressure?

In a movie, Tarzan evades his captors by hiding under water for many minutes while breathing through a long, thin reed. Assuming the maximum pressure difference his lungs can manage and still breathe is calculate the deepest he could have been

(II) The maximum gauge pressure in a hydraulic lift is 17.0 atm. What is the largest-size vehicle (kg) it can lift if the diameter of the output line is 25.5 cm?

(II) The gauge pressure in each of the four tires of an automobile is 240 kPa. If each tire has a “footprint” of \(190\ cm^2\) (area touching the ground), estimate the mass of the car.

(a) Determine the total force and the absolute pressure on the bottom of a swimming pool 28.0 m by 8.5 m whose uniform depth is 1.8 m. (b) What will be the pressure against the side of the pool near the bottom?

A house at the bottom of a hill is fed by a full tank of water 6.0 m deep and connected to the house by a pipe that is 75 m long at an angle of 61 from the horizontal (Fig. 1049). (a) Determine the water gauge pressure at the house. (b) How high could the water shoot if it came vertically out of a broken pipe in front of the house?

Water and then oil (which dont mix) are poured into a tube, open at both ends. They come to equilibrium as shown in Fig. 1050. What is the density of the oil? [Hint: Pressures at points a and b are equal. Why?]

How high would the atmosphere extend if it were of uniform density throughout, equal to half the present density at sea level?

Determine the minimum gauge pressure needed in the water pipe leading into a building if water is to come out of a faucet on the fourteenth floor, 44 m above that pipe.

Determine the minimum gauge pressure needed in the water pipe leading into a building if water is to come out of a faucet on the fourteenth floor, 44 m above that pipe.

An open-tube mercury manometer is used to measure the pressure in an oxygen tank. When the atmospheric pressure is 1040 mbar, what is the absolute pressure (in Pa) in the tank if the height of the mercury in the open tube is (a) 18.5 cm higher, (b) 5.6 cm lower, than the mercury in the tube connected to the tank? See Fig. 107a.

What fraction of a piece of iron will be submerged when it floats in mercury?

A geologist finds that a Moon rock whose mass is 9.28 kg has an apparent mass of 6.18 kg when submerged in water. What is the density of the rock?

A crane lifts the 18,000-kg steel hull of a sunken ship out of the water. Determine (a) the tension in the cranes cable when the hull is fully submerged in the water, and (b) the tension when the hull is completely out of the water

A spherical balloon has a radius of 7.15 m and is filled with helium. How large a cargo can it lift, assuming that the skin and structure of the balloon have a mass of 930 kg? Neglect the buoyant force on the cargo volume itself.

What is the likely identity of a metal (see Table 101) if a sample has a mass of 63.5 g when measured in air and an apparent mass of 55.4 g when submerged in water?

Calculate the true mass (in vacuum) of a piece of aluminum whose apparent mass is 4.0000 kg when weighed in air

Because gasoline is less dense than water, drums containing gasoline will float in water. Suppose a 210-L steel drum is completely full of gasoline. What total volume of steel can be used in making the drum if the gasoline-filled drum is to float in fresh water?

A scuba diver and her gear displace a volume of 69.6 L and have a total mass of 72.8 kg. (a) What is the buoyant force on the diver in seawater? (b) Will the diver sink or float?

(II) The specific gravity of ice is 0.917, whereas that of seawater is 1.025. What percent of an iceberg is above the surface of the water?

(II) Archimedes’ principle can be used to determine the specific gravity of a solid using a known liquid (Example 10–8). The reverse can be done as well. (a) As an example, a 3.80-kg aluminum ball has an apparent mass of 2.10 kg when submerged in a particular liquid: calculate the density of the liquid. (b) Determine a formula for finding the density of a liquid using this procedure.

(II) A 32-kg child decides to make a raft out of empty 1.0-L soda bottles and duct tape. Neglecting the mass of the duct tape and plastic in the bottles, what minimum number of soda bottles will the child need to be able stay dry on the raft?

An undersea research chamber is spherical with an external diameter of 5.20 m. The mass of the chamber, when occupied, is 74,400 kg. It is anchored to the sea bottom by a cable. What is (a) the buoyant force on the chamber, and (b) the tension in the cable?

A 0.48-kg piece of wood floats in water but is found to sink in alcohol in which it has an apparent mass of 0.047 kg. What is the SG of the wood?

A two-component model used to determine percent body fat in a human body assumes that a fraction of the bodys total mass m is composed of fat with a density of and that the remaining mass of the body is composed of fat-free tissue with a density of If the specific gravity of the entire bodys density is X, show that the percent body fat is given by

(II) On dry land, an athlete weighs 70.2 kg. The same athlete, when submerged in a swimming pool and hanging from a scale, has an “apparent weight” of 3.4 kg. Using Example 10–8 as a guide, (a) find the total volume V of the submerged athlete. (b) Assume that when submerged, the athlete’s body contains a residual volume \(V_R = 1.3 \times 10^{-3}\ m^3\) of air (mainly in the lungs). Taking \(V - V_R\) to be the actual volume of the athlete’s body, find the body’s specific gravity, SG. (c) What is the athlete’s percent body fat assuming it is given by the formula (495/SG) - 450?

How many helium-filled balloons would it take to lift a person? Assume the person has a mass of 72 kg and that each helium-filled balloon is spherical with a diameter of 33 cm.

A scuba tank, when fully submerged, displaces 15.7 L of seawater. The tank itself has a mass of 14.0 kg and, when full, contains 3.00 kg of air. Assuming only its weight and the buoyant force act on the tank, determine the net force (magnitude and direction) on the fully submerged tank at the beginning of a dive (when it is full of air) and at the end of a dive (when it no longer contains any air).

A 3.65-kg block of wood floats on water. What minimum mass of lead, hung from the wood by a string, will cause the block to sink?

A 12-cm-radius air duct is used to replenish the air of a room every 12 min. How fast does the air flow in the duct?

Calculate the average speed of blood flow in the major arteries of the body, which have a total cross- sectional area of about Use the data of Example 1012.

How fast does water flow from a hole at the bottom of a very wide, 4.7-m-deep storage tank filled with water? Ignore viscosity.

Show that Bernoullis equation reduces to the hydrostatic variation of pressure with depth (Eq. 103b) when there is no flow (v1 = v2 = 0).

(II) What is the volume rate of flow of water from a 1.85-cm-diameter faucet if the pressure head is 12.0 m?

A fish tank has dimensions 36 cm wide by 1.0 m long by 0.60 m high. If the filter should process all the water in the tank once every 3.0 h, what should the flow speed be in the 3.0-cm-diameter input tube for the filter?

What gauge pressure in the water pipes is necessary if a fire hose is to spray water to a height of 16 m?

A (inside) diameter garden hose is used to fill a round swimming pool 6.1 m in diameter. How long will it take to fill the pool to a depth of 1.4 m if water flows from the hose at a speed of 0.40 ms?

(II) A 180-km/h wind blowing over the flat roof of a house causes the roof to lift off the house. If the house is \(6.2 \ \mathrm m \times 12.4 \ \mathrm m\) in size, estimate the weight of the roof. Assume the roof is not nailed down.

A 6.0-cm-diameter horizontal pipe gradually narrows to 4.5 cm. When water flows through this pipe at a certain rate, the gauge pressure in these two sections is 33.5 kPa and 22.6 kPa, respectively. What is the volume rate of flow?

Estimate the air pressure inside a category 5 hurricane, where the wind speed is (Fig. 10 300 kmh 52).

What is the lift (in newtons) due to Bernoullis principle on a wing of area if the air passes over the top and bottom surfaces at speeds of and 150 m/s, respectively?

Water at a gauge pressure of 3.8 atm at street level flows into an office building at a speed of through a pipe 5.0 cm in diameter. The pipe tapers down to 2.8 cm in diameter by the top floor, 16 m above (Fig. 1053), where the faucet has been left open. Calculate the flow velocity and the gauge pressure in the pipe on the top floor. Assume no branch pipes and ignore viscosity

(II) Show that the power needed to drive a fluid through a pipe with uniform cross-section is equal to the volume rate of flow, Q, times the pressure difference, \(P_1-P_2\). Ignore viscosity.

(III) In Fig. 10–54, take into account the speed of the top surface of the tank and show that the speed of fluid leaving an opening near the bottom is \(v_1=\sqrt{\frac{2gh}{(1-A^2 _1 / A^2 _2 )}}\), where \(h = y_2 - y_1\), and \(A_1\) and \(A_2\) are the areas of the opening and of the top surface, respectively. Assume \(A_1 << A_2\) so that the flow remains nearly steady and laminar.

(a) Show that the flow speed measured by a venturi meter (see Fig. 1029) is given by the relation (b) A venturi meter is measuring the flow of water; it has a main diameter of 3.5 cm tapering down to a throat diameter of 1.0 cm. If the pressure difference is measured to be 18 mm-Hg, what is the speed of the water entering the venturi throat?

A fire hose exerts a force on the person holding it. This is because the water accelerates as it goes from the hose through the nozzle. How much force is required to hold a 7.0-cm-diameter hose delivering through a 0.75-cm-diameter nozzle?

A viscometer consists of two concentric cylinders, 10.20 cm and 10.60 cm in diameter. A liquid fills the space between them to a depth of 12.0 cm. The outer cylinder is fixed, and a torque of keeps the inner cylinder turning at a steady rotational speed of What is the viscosity of the liquid?

Engine oil (assume SAE 10, Table 103) passes through a fine 1.80-mm-diameter tube that is 10.2 cm long. What pressure difference is needed to maintain a flow rate of 6.2 mL/min?

A gardener feels it is taking too long to water a garden with a hose. By what factor will the time be cut using a hose instead? Assume nothing else is changed.

What diameter must a 15.5-m-long air duct have if the ventilation and heating system is to replenish the air in a room every 15.0 min? Assume the pump can exert a gauge pressure of 0.710 * 103 atm

(II) What must be the pressure difference between the two ends of a 1.6-km section of pipe, 29 cm in diameter, if it is to transport oil \((\rho = 950\ kg/m^3,\ \eta = 0.20\ Pa \cdot s)\) at a rate of \(650\ cm^3/s\)?

Poiseuilles equation does not hold if the flow velocity is high enough that turbulence sets in. The onset of turbulence occurs when the Reynolds number, Re, exceeds approximately 2000. Re is defined as where is the average speed of the fluid, is its density, is its viscosity, and r is the radius of the tube in which the fluid is flowing. (a) Determine if blood flow through the aorta is laminar or turbulent when the average speed of blood in the aorta during the resting part of the hearts cycle is about (b) During exercise, the blood-flow speed approximately doubles. Calculate the Reynolds number in this case, and determine if the flow is laminar or turbulent.

Assuming a constant pressure gradient, if blood flow is reduced by 65%, by what factor is the radius of a blood vessel decreased?

Calculate the pressure drop per cm along the aorta using the data of Example 1012 and Table 103.

Calculate the pressure drop per cm along the aorta using the data of Example 1012 and Table 103.

(I) If the force F needed to move the wire in Fig. 10–34 is \(3.4 \times 10^{-3}\ N\), calculate the surface tension \(\gamma\) of the enclosed fluid. Assume \(\ell = 0.070\ m\).

(I) Calculate the force needed to move the wire in Fig. 10–34 if it holds a soapy solution (Table 10–4) and the wire is 21.5 cm long.

The surface tension of a liquid can be determined by measuring the force F needed to just lift a circular platinum ring of radius r from the surface of the liquid. (a) Find a formula for in terms of F and r. (b) At 30C, if and calculate for the tested liquid

If the base of an insects leg has a radius of about and the insects mass is 0.016 g, would you expect the six-legged insect to remain on top of the water? Why or why not?

(III) Estimate the diameter of a steel needle that can just barely remain on top of water due to surface tension.

A physician judges the health of a heart by measuring the pressure with which it pumps blood. If the physician mistakenly attaches the pressurized cuff around a standing patients calf (about 1 m below the heart) instead of the arm (Fig. 1042), what error (in Pa) would be introduced in the hearts blood pressure measurement?

A 3.2-N force is applied to the plunger of a hypodermic needle. If the diameter of the plunger is 1.3 cm and that of the needle is 0.20 mm, (a) with what force does the fluid leave the needle? (b) What force on the plunger would be needed to push fluid into a vein where the gauge pressure is 75 mm- Hg? Answer for the instant just before the fluid starts to move

Intravenous transfusions are often made under gravity, as shown in Fig. 1055. Assuming the fluid has a density of at what height h should the bottle be placed so the liquid pressure is (a) 52 mm-Hg, and (b) (c) If the blood pressure is 75 mm-Hg above atmospheric pressure, how high should the bottle be placed so that the fluid just barely enters the vein?

A beaker of water rests on an electronic balance that reads 975.0 g. A 2.6-cm-diameter solid copper ball attached to a string is submerged in the water, but does not touch the bottom. What are the tension in the string and the new balance reading?

Estimate the difference in air pressure between the top and the bottom of the Empire State Building in New York City. It is 380 m tall and is located at sea level. Express as a fraction of atmospheric pressure at sea level.

A hydraulic lift is used to jack a 960-kg car 42 cm off the floor. The diameter of the output piston is 18 cm, and the input force is 380 N. (a) What is the area of the input piston? (b) What is the work done in lifting the car 42 cm? (c) If the input piston moves 13 cm in each stroke, how high does the car move up for each stroke? (d) How many strokes are required to jack the car up 42 cm? (e) Show that energy is conserved.

When you ascend or descend a great deal when driving in a car, your ears pop, which means that the pressure behind the eardrum is being equalized to that outside. If this did not happen, what would be the approximate force on an eardrum of area if a change in altitude of 1250 m takes place?

Giraffes are a wonder of cardiovascular engineering. Calculate the difference in pressure (in atmospheres) that the blood vessels in a giraffes head must accommodate as the head is lowered from a full upright position to ground level for a drink. The height of an average giraffe is about 6 m.

How high should the pressure head be if water is to come from a faucet at a speed of Ignore viscosity.

Suppose a person can reduce the pressure in his lungs to gauge pressure. How high can water then be sucked up a straw?

A bicycle pump is used to inflate a tire. The initial tire (gauge) pressure is 210 kPa (30 psi). At the end of the pumping process, the final pressure is 310 kPa (45 psi). If the diameter of the plunger in the cylinder of the pump is 2.5 cm, what is the range of the force that needs to be applied to the pump handle from beginning to end?

Estimate the pressure on the mountains underneath the Antarctic ice sheet, which is typically 2 km thick.

A simple model (Fig. 1056) considers a continent as a block floating in the mantle rock around it Assuming the continent is 35 km thick (the average thickness of the Earths continental crust), estimate the height of the continent above the surrounding mantle rock.

A ship, carrying fresh water to a desert island in the Caribbean, has a horizontal cross-sectional area of at the waterline. When unloaded, the ship rises 8.25 m higher in the sea. How much water was delivered?

A raft is made of 12 logs lashed together. Each is 45 cm in diameter and has a length of 6.5 m. How many people can the raft hold before they start getting their feet wet, assuming the average person has a mass of 68 kg? Do not neglect the weight of the logs. Assume the specific gravity of wood is 0.60.

Estimate the total mass of the Earths atmosphere, using the known value of atmospheric pressure at sea level.

During each heartbeat, approximately of blood is pushed from the heart at an average pressure of 105 mm-Hg. Calculate the power output of the heart, in watts, assuming 70 beats per minute.

Four lawn sprinkler heads are fed by a 1.9-cm-diameter pipe. The water comes out of the heads at an angle of 35 above the horizontal and covers a radius of 6.0 m. (a) What is the velocity of the water coming out of each sprinkler head? (Assume zero air resistance.) (b) If the output diameter of each head is 3.0 mm, how many liters of water do the four heads deliver per second? (c) How fast is the water flowing inside the 1.9-cm-diameter pipe?

One arm of a tube (open at both ends) contains water, and the other alcohol. If the two fluids meet at exactly the bottom of the and the alcohol is at a height of 16.0 cm, at what height will the water be?

The contraction of the left ventricle (chamber) of the heart pumps blood to the body. Assuming that the inner surface of the left ventricle has an area of \(82\ cm^2\) and the maximum pressure in the blood is 120 mm-Hg, estimate the force exerted by the ventricle at maximum pressure.

An airplane has a mass of and the air flows past the lower surface of the wings at If the wings have a surface area of how fast must the air flow over the upper surface of the wing if the plane is to stay in the air?

A drinking fountain shoots water about 12 cm up in the air from a nozzle of diameter 0.60 cm (Fig. 1057). The pump at the base of the unit (1.1 m below the nozzle) pushes water into a 1.2-cm- diameter supply pipe that goes up to the nozzle. What gauge pressure does the pump have to provide? Ignore the viscosity; your answer will therefore be an underestimate.

A hurricane-force wind of blows across the face of a storefront window. Estimate the force on the window due to the difference in air pressure inside and outside the window. Assume the store is airtight so the inside pressure remains at 1.0 atm. (This is why you should not tightly seal a building in preparation for a hurricane.)

Blood is placed in a bottle 1.40 m above a 3.8-cm-long needle, of inside diameter 0.40 mm, from which it flows at a rate of What is the viscosity of this blood?

You are watering your lawn with a hose when you put your finger over the hose opening to increase the distance the water reaches. If you are holding the hose horizontally, and the distance the water reaches increases by a factor of 4, what fraction of the hose opening did you block?

A copper (Cu) weight is placed on top of a 0.40-kg block of wood floating in water, as shown in Fig. 1058. What is the mass of the copper if the top of the wood block is exactly at the waters surface?

You need to siphon water from a clogged sink. The sink has an area of and is filled to a height of 4.0 cm. Your siphon tube rises 45 cm above the bottom of the sink and then descends 85 cm to a pail as shown in Fig. 1059. The siphon tube has a diameter of 2.3 cm. (a) Assuming that the water level in the sink has almost zero velocity, use Bernoullis equation to estimate the water velocity when it enters the pail. (b) Estimate how long it will take to empty the sink. Ignore viscosity

If cholesterol buildup reduces the diameter of an artery by 25%, by what % will the blood flow rate be reduced, assuming the same pressure difference?

Problem 1MCQ You hold a piece of wood in one hand and a piece of iron in the other. Both pieces have the same volume, and you hold them fully under water at the same depth. At the moment you let go of them, which one experiences the greater buoyancy force? (a) The piece of wood. (b) The piece of iron. (c) They experience the same buoyancy force. (d)More information is needed.

Problem 1P The approximate volume of the granite monolith known as El Capitan in Yosemite National Park (Fig.10–47) is about \(10^8\mathrm{\ m}^3\). What is its approximate mass? ________________ Equation Transcription: Text Transcription: 10^{8} m^{3}

Problem 1Q If one material has a higher density than another, must the molecules of the first be heavier than those of the second? Explain.

Problem 1SL A 5.0-kg block and 4.0 kg of water in a 0.50-kg container are placed symmetrically on a board that can balance at the center (Fig. 10–60). A solid aluminum cube of sides 10.0 cm is lowered into the water. How much of the aluminum must be under water to make this system balance? How would your answer change for a lead cube of the same size? Explain. (See Sections 10–7 and 9–1.)

Problem 2MCQ Three containers are filled with water to the same height and have the same surface area at the base, but the total weight of water is different for each (Fig. 10–46). In which container does the water exert the greatest force on the bottom of the container? (a) Container A. (b) Container B. (c) Container C. (d) All three are equal.

Problem 2P (I) What is the approximate mass of air in a living room 5.6 m X 3.6 m X 2.4 m?

Problem 2Q Consider what happens when you push both a pin and the blunt end of a pen against your skin with the same force. Decide what determines whether your skin is cut—the net force applied to it or the pressure.

Problem 3MCQ Beaker A is filled to the brim with water. Beaker B is the same size and contains a small block of wood which floats when the beaker is filled with water to the brim. Which beaker weighs more? (a) Beaker A. (b) Beaker B. (c) The same for both.

Problem 3P (I) If you tried to smuggle gold bricks by filling your backpack, whose dimensions are 54 cm X 31 cm X 22 cm, what would its mass be?

Problem 3Q A small amount of water is boiled in a 1-gallon metal can. The can is removed from the heat and the lid put on. As the can cools, it collapses and looks crushed. Explain.

In working out his principle, Pascal showed dramatically how force can be multiplied with fluid pressure. He placed a long, thin tube of radius r = 0.30 cm vertically into a wine barrel of radius R = 21 cm, Fig. 10-62. He found that when the barrel was filled with water and the tube filled to a height of 12 m, the barrel burst. Calculate (a) the mass of water in the tube, and (b) the net force exerted by the water in the barrel on the lid just before rupture.

Problem 4MCQ Why does an ocean liner float? (a) It is made of steel, which floats. (b) Its very big size changes the way water supports it. (c) It is held up in the water by large Styrofoam compartments. (d) The average density of the ocean liner is less than that of seawater. (e) Remember the Titanic—ocean liners do not float.

(I) State your mass and then estimate your volume. [Hint: Because you can swim on or just under the surface of the water in a swimming pool, you have a pretty good idea of your density.]

Problem 4Q An ice cube floats in a glass of water filled to the brim. What can you say about the density of ice? As the ice melts, will the water overflow? Explain.

Problem 5MCQ A rowboat floats in a swimming pool, and the level of the water at the edge of the pool is marked. Consider the following situations. (i) The boat is removed from the water. (ii) The boat in the water holds an iron anchor which is removed from the boat and placed on the shore. For each situation, the level of the water will (a) rise. (b) fall. (c) stay the same.

(II) A bottle has a mass of 35.00 g when empty and 98.44 g when filled with water. When filled with another fluid, the mass is 89.22 g.What is the specific gravity of this other fluid?

Will an ice cube float in a glass of alcohol?Why or why not?

Problem 6MCQ You put two ice cubes in a glass and fill the glass to the rim with water. As the ice melts, the water level (a) drops below the rim. (b) rises and water spills out of the glass. (c) remains the same. (d) drops at first, then rises until a little water spills out.

Problem 6P (II) If 4.0 L of antifreeze solution (specific gravity = 0.80) is added to 5.0 L of water to make a 9.0-L mixture, what is the specific gravity of the mixture?

Problem 6Q A submerged can of Coke® will sink, but a can of Diet Coke® will float. (Try it!) Explain.

Problem 6SL What approximations are made in the derivation of Bernoulli’s equation? Qualitatively, how do you think Bernoulli’s equation would change if each of these approximations was not made? (See Sections 10–8, 10–9, 10–11, and 10–12.)

Problem 7MCQ Hot air is less dense than cold air. Could a hot-air balloon be flown on the Moon, where there is no atmosphere? (a) No, there is no cold air to displace, so no buoyancy force would exist. (b) Yes, warm air always rises, especially in a weak gravitational field like that of the Moon. (c) Yes, but the balloon would have to be filled with helium instead of hot air.

(III) The Earth is not a uniform sphere, but has regions of varying density. Consider a simple model of the Earth divided into three regions—inner core, outer core, and mantle. Each region is taken to have a unique constant density (the average density of that region in the real Earth): (a) Use this model to predict the average density of the entire Earth. (b) If the radius of the Earth is 6380 km and its mass is \(5.98 \times 10^{24}\ kg\), determine the actual average density of the Earth and compare it (as a percent difference) with the one you determined in (a).

Problem 7Q Why don’t ships made of iron sink?

An object that can float in both water and in oil (whose density is less than that of water) experiences a buoyant force that is (a) greater when it is floating in oil than when floating in water. (b) greater when it is floating in water than when floating in oil. (c) the same when it is floating in water or in oil.

Problem 8P (I) Estimate the pressure needed to raise a column of water to the same height as a 46-m-tall pine tree.

Problem 8Q A barge filled high with sand approaches a low bridge over the river and cannot quite pass under it. Should sand be added to, or removed from, the barge? [Hint: Consider Archimedes’ principle.]

Problem 9MCQ As water flows from a low elevation to a higher elevation through a pipe that changes in diameter, (a) the water pressure will increase. (b) the water pressure will decrease. (c) the water pressure will stay the same. (d) Need more information to determine how the water pressure changes.

Problem 9P Estimate the pressure exerted on a floor by (a) one pointed heel of area \(=0.45\mathrm{\ cm}^2\), and (b) one wide heel of area \(16 \mathrm{\ cm}^{2}\), Fig. 10–48. The person wearing the shoes has a mass of 56 kg. ________________ Equation Transcription: Text Transcription: =0.45 cm^2 16 cm^2

Problem 9Q Explain why helium weather balloons, which are used to measure atmospheric conditions at high altitudes, are normally released while filled to only 10–20% of their maximum volume.

Problem 10EA Return to Chapter-Opening Question 1, page 260, and answer it again now. Try to explain why you may have answered differently the first time. 1. Which container has the largest pressure at the bottom? Assume each container holds the same volume of water.

Problem 10EB A dam holds back a lake that is 85 m deep at the dam. If the lake is 20 km long, how much thicker should the dam be than if the lake were smaller, only 1.0 km long?

Problem 10EC Which of the following objects, submerged in water, experiences the largest magnitude of the buoyant force? (a) A 1-kg helium balloon; (b) 1 kg of wood; (c) 1 kg of ice; (d) 1 kg of iron; (e) all the same.

Problem 10ED Which of the following objects, submerged in water, experiences the largest magnitude of the buoyant force? (a) A 1-m3 helium balloon; (b) 1-m3 of wood; (c) 1-m3 of ice; (d) 1-m3 of iron; (e) all the same.

Problem 10EE If you throw a flat 60-kg aluminum plate into water, the plate sinks. But if that aluminum is shaped into a rowboat, it floats. Explain.

Problem 10EG Return to Chapter-Opening Question 2, page 260, and answer it again now. Try to explain why you may have answered differently the first time. Try it and see. 2. Two balloons are tied and hang with their nearest edges about 3 cm apart. If you blow between the balloons (not at the balloons, but at the opening between them), what will happen? (a) Nothing. (b) The balloons will move closer together. (c) The balloons will move farther apart.

As water in a level pipe passes from a narrow cross section of pipe to a wider cross section, how does the pressure against the walls change?

Problem 10MCQ Water flows in a horizontal pipe that is narrow but then widens and the speed of the water becomes less. The pressure in the water moving in the pipe is (a) greater in the wide part. (b) greater in the narrow part. (c) the same in both parts. (d) greater where the speed is higher. (e) greater where the speed is lower.

(I) What is the difference in blood pressure (mm-Hg) between the top of the head and bottom of the feet of a 1.75-m-tall person standing vertically?

Will an empty balloon have precisely the same apparent weight on a scale as a balloon filled with air? Explain.

Problem 11MCQ When a baseball curves to the right (a curveball), air is flowing (a) faster over the left side than over the right side. (b) faster over the right side than over the left side. (c) faster over the top than underneath. (d) at the same speed all around the baseball, but the ball curves as a result of the way the wind is blowing on the field.

(I) (a) Calculate the total force of the atmosphere acting on the top of a table that measures \(1.7 \times 2.6\ m\). (b) What is the total force acting upward on the underside of the table?

Why do you float higher in salt water than in fresh water?

Problem 12MCQ How is the smoke drawn up a chimney affected when a wind is blowing outside? (a) Smoke rises more rapidly in the chimney. (b) Smoke rises more slowly in the chimney. (c) Smoke is forced back down the chimney. (d) Smoke is unaffected.

Problem 12P (II) How high would the level be in an alcohol barometer at normal atmospheric pressure?

Why does the stream of water from a faucet become narrower as it falls (Fig. 10–43)? FIGURE 10–43 Question 12. Water coming from a faucet.

Problem 13P (II) In a movie, Tarzan evades his captors by hiding under water for many minutes while breathing through a long, thin reed. Assuming the maximum pressure difference his lungs can manage and still breathe is – 85 mm Hg, calculate the deepest he could have been.

Problem 13Q Children are told to avoid standing too close to a rapidly moving train because they might get sucked under it. Is this possible? Explain.

Problem 14Q A tall Styrofoam cup is filled with water. Two holes are punched in the cup near the bottom, and water begins rushing out. If the cup is dropped so it falls freely, will the water continue to flow from the holes? Explain.

Problem 14P (II) The maximum gauge pressure in a hydraulic lift is 17.0 atm. What is the largest-size vehicle (kg) it can lift if the diameter of the output line is 25.5 cm?

Problem 15P (II) The gauge pressure in each of the four tires of an automobile is 240 kPa. If each tire has a “footprint” of 190 cm2 (area touching the ground), estimate the mass of the car.

Problem 15Q Why do airplanes normally take off into the wind?

Problem 16P (II) (a) Determine the total force and the absolute pressure on the bottom of a swimming pool 28.0 m by 8.5 m whose uniform depth is 1.8 m. (b) What will be the pressure against the side of the pool near the bottom?

Two ships moving in parallel paths close to one another risk colliding. Why?

(II) A house at the bottom of a hill is fed by a full tank of water 6.0 m deep and connected to the house by a pipe that is 75 m long at an angle of 61° from the horizontal (Fig. 10–49). () Determine the water gauge pressure at the house. () How high could the water shoot if it came vertically out of a broken pipe in front of the house?

If you dangle two pieces of paper vertically, a few inches apart (Fig. 10–44), and blow between them, how do you think the papers will move? Try it and see. Explain. FIGURE 10–44 Question 17.

(II) Water and then oil (which don’t mix) are poured into a U-shaped tube, open at both ends. They come to equilibrium as shown in Fig. 10–50. What is the density of the oil? [Hint: Pressures at points a and b are equal. Why?]

(II) How high would the atmosphere extend if it were of uniform density throughout, equal to half the present density at sea level?

Problem 18Q Why does the canvas top of a convertible bulge out when the car is traveling at high speed? [Hint: The windshield deflects air upward, pushing streamlines closer together.]

Problem 19Q Roofs of houses are sometimes “blown” off (or are they pushed off?) during a tornado or hurricane. Explain using Bernoulli’s principle.

Problem 20P (II) Determine the minimum gauge pressure needed in the water pipe leading into a building if water is to come out of a faucet on the fourteenth floor, 44 m above that pipe.

Explain how the tube in Fig. 10–45, known as a siphon, can transfer liquid from one container to a lower one even though the liquid must flow uphill for part of its journey. (Note that the tube must be filled with liquid to start with.)

(II) A hydraulic press for compacting powdered samples has a large cylinder which is 10.0 cm in diameter, and a small cylinder with a diameter of 2.0 cm (Fig. 10–51). A lever is attached to the small cylinder as shown. The sample, which is placed on the large cylinder, has an area of \(4.0 \mathrm{~cm}^{2}\). What is the pressure on the sample if 320 N is applied to the lever? Equation transcription: Text transcription: 4.0{~cm}^{2}

When blood pressure is measured, why must the arm cuff be held at the level of the heart?

(II) An open-tube mercury manometer is used to measure the pressure in an oxygen tank. When the atmospheric pressure is 1040 mbar, what is the absolute pressure (in Pa) in the tank if the height of the mercury in the open tube is () 18.5 cm higher, () 5.6 cm lower, than the mercury in the tube connected to the tank? See Fig. 10–7a.

Problem 24P (II) A geologist finds that a Moon rock whose mass is 9.28 kg has an apparent mass of 6.18 kg when submerged in water. What is the density of the rock?

Problem 25P (II) A crane lifts the 18,000-kg steel hull of a sunken ship out of the water. Determine (a) the tension in the crane’s cable when the hull is fully submerged in the water, and (b) the tension when the hull is completely out of the water.

Problem 26P (II) A spherical balloon has a radius of 7.15 m and is filled with helium. How large a cargo can it lift, assuming that the skin and structure of the balloon have a mass of 930 kg? Neglect the buoyant force on the cargo volume itself.

(II) What is the likely identity of a metal (see Table 10–1) if a sample has a mass of 63.5 g when measured in air and an apparent mass of 55.4 g when submerged in water?

Problem 28P (II) Calculate the true mass (in vacuum) of a piece of aluminum whose apparent mass is 4.0000 kg when weighed in air.

Problem 29P (II) Because gasoline is less dense than water, drums containing gasoline will float in water. Suppose a 210-L steel drum is completely full of gasoline. What total volume of steel can be used in making the drum if the gasoline-filled drum is to float in fresh water?

Problem 30P (II) A scuba diver and her gear displace a volume of 69.6 L and have a total mass of 72.8 kg. (a) What is the buoyant force on the diver in seawater? (b) Will the diver sink or float?

Problem 31P (II) The specific gravity of ice is 0.917, whereas that of seawater is 1.025. What percent of an iceberg is above the surface of the water?

(II) Archimedes’ principle can be used to determine the specific gravity of a solid using a known liquid (Example 10–8). The reverse can be done as well. (a) As an example, a 3.80-kg aluminum ball has an apparent mass of 2.10 kg when submerged in a particular liquid: calculate the density of the liquid. (b) Determine a formula for finding the density of a liquid using this procedure.

Problem 33P (II) A 32-kg child decides to make a raft out of empty 1.0-L soda bottles and duct tape. Neglecting the mass of the duct tape and plastic in the bottles, what minimum number of soda bottles will the child need to be able stay dry on the raft?

Problem 34P (II) An undersea research chamber is spherical with an external diameter of 5.20 m. The mass of the chamber, when occupied, is 74,400 kg. It is anchored to the sea bottom by a cable. What is (a) the buoyant force on the chamber, and (b) the tension in the cable?

(II) A 0.48-kg piece of wood floats in water but is found to sink in alcohol (SG = 0.79), in which it has an apparent mass of 0.047 kg. What is the SG of the wood?

(II) A two-component model used to determine percent body fat in a human body assumes that a fraction of the body's total mass is composed of fat with a density of , and that the remaining mass of the body is composed of fat-free tissue with a density of . If the specific gravity of the entire body's density is , show that the percent body fat is given by \(\% B o d y f a t=\frac{495}{x}-450\) Equation transcription: Text transcription: % B o d y f a t=frac{495}{x}-450

(II) On dry land, an athlete weighs 70.2 kg. The same athlete, when submerged in a swimming pool and hanging from a scale, has an “apparent weight” of 3.4 kg. Using Example 10–8 as a guide, (a) find the total volume V of the submerged athlete. (b) Assume that when submerged, the athlete’s body contains a residual volume \(V_R = 1.3 \times 10^{-3}\ m^3\) of air (mainly in the lungs). Taking \(V - V_R\) to be the actual volume of the athlete’s body, find the body’s specific gravity, SG. (c) What is the athlete’s percent body fat assuming it is given by the formula (495/SG) - 450?

How many helium-filled balloons would it take to lift a person? Assume the person has a mass of 72 kg and that each helium-filled balloon is spherical with a diameter of 33 cm.

Problem 39P (III) A scuba tank, when fully submerged, displaces 15.7 L of seawater. The tank itself has a mass of 14.0 kg and, when “full,” contains 3.00 kg of air. Assuming only its weight and the buoyant force act on the tank, determine the net force (magnitude and direction) on the fully submerged tank at the beginning of a dive (when it is full of air) and at the end of a dive (when it no longer contains any air).

Problem 40P (III) A 3.65-kg block of wood (SG =0.50) floats on water. What minimum mass of lead, hung from the wood by a string, will cause the block to sink?

Problem 41P (I) A 12-cm-radius air duct is used to replenish the air of a Room 8.2 m X 5.0 m X 3.5 m every 12 min. How fast does the air flow in the duct?

Problem 43P (I) How fast does water flow from a hole at the bottom of a very wide, 4.7-m-deep storage tank filled with water? Ignore viscosity.

Problem 44P (I) Show that Bernoulli’s equation reduces to the hydrostatic variation of pressure with depth (Eq. 10–3b) when there is no flow (v1 =v2 = 0).

Problem 45P (II) What is the volume rate of flow of water from a 1.85-cm-diameter faucet if the pressure head is 12.0 m?

Problem 46P (II) A fish tank has dimensions 36 cm wide by 1.0 m long by 0.60 m high. If the filter should process all the water in the tank once every 3.0 h, what should the flow speed be in the 3.0-cm-diameter input tube for the filter?

(II) What gauge pressure in the water pipes is necessary if a fire hose is to spray water to a height of 16 m?

(II) A \(\frac{5}{8}\) -in. (inside) diameter garden hose is used to fill a round swimming pool in diameter. How long will it take to fill the pool to a depth of if water flows from the hose at a speed of \(0.40 m / s\) ? Equation transcription: Text transcription: frac{5}{8} 0.40 m / s

(II) A 180-km/h wind blowing over the flat roof of a house causes the roof to lift off the house. If the house is \(6.2\ m \times 12.4\ m\) in size, estimate the weight of the roof. Assume the roof is not nailed down.

Problem 50P (II) A 6.0-cm-diameter horizontal pipe gradually narrows to 4.5 cm. When water flows through this pipe at a certain rate, the gauge pressure in these two sections is 33.5 kPa and 22.6 kPa, respectively. What is the volume rate of flow?

(II) Estimate the air pressure inside a category 5 hurricane, where the wind speed is \(300 \mathrm{~km} / \mathrm{h}\) (Fig. 10–52). Equation transcription: Text transcription: 300{~km} / {h}

Problem 52P (II) What is the lift (in newtons) due to Bernoulli’s principle on a wing of area 88 m2 if the air passes over the top and bottom surfaces at speeds of 280 m/s and 150 m/s respectively?

(II) Water at a gauge pressure of 3.8 atm at street level flows into an office building at a speed of 0.78 m/s through a pipe 5.0 cm in diameter. The pipe tapers down to 2.8 cm in diameter by the top floor, 16 m above (Fig. 10–53), where the faucet has been left open. Calculate the flow velocity and the gauge pressure in the pipe on the top floor. Assume no branch pipes and ignore viscosity.

Problem 54P (II) Show that the power needed to drive a fluid through a pipe with uniform cross-section is equal to the volume rate of flow, Q, times the pressure difference, P1 –P2. Ignore viscosity.

(III) In Fig. , take into account the speed of the top surface of the tank and show that the speed of fluid leaving an opening near the bottom is \(v_{1}=-\sqrt{\frac{2 g h}{\left(1-A_{1}^{2} / A_{2}^{2}\right)}}\) where \(h=y_{2}-y_{1}\), and and are the areas of the opening and of the top surface, respectively. Assume \(A_{1}<<A_{2}\) so that the flow \(\mid \vec{v}_{2}\) remains nearly steady and laminar. FIGURE 10–54 Problem 55. Equation transcription: Text transcription: v{1}=-sqrt{frac{2 g h}{(1-A{1}^{2} / A{2}^{2})}} h=y{2}-y{1} A{1}<<A{2} mid vec{v}{2}

(III) (a) Show that the flow speed measured by a venturi meter (see Fig. 10–29) is given by the relation \(v_1=A_2\sqrt{\frac{2(P_1 - P_2)}{\rho(A^2 _1 - A^2 _2)}}\), (b) A venturi meter is measuring the flow of water; it has a main diameter of 3.5 cm tapering down to a throat diameter of 1.0 cm. If the pressure difference is measured to be 18 mm-Hg, what is the speed of the water entering the venturi throat?

Problem 57P (III) A fire hose exerts a force on the person holding it. This is because the water accelerates as it goes from the hose through the nozzle. How much force is required to hold a 7.0-cm-diameter hose delivering 420 L/min through a 0.75-cm-diameter nozzle?

(II) A viscometer consists of two concentric cylinders, 10.20 cm and 10.60 cm in diameter. A liquid fills the space between them to a depth of 12.0 cm. The outer cylinder is fixed, and a torque of \(0.024 \ \mathrm m \cdot \mathrm N\) keeps the inner cylinder turning at a steady rotational speed of 57 rev/min. What is the viscosity of the liquid?

(I) Engine oil (assume SAE 10, Table 10–3) passes through a fine 1.80-mm-diameter tube that is 10.2 cm long. What pressure difference is needed to maintain a flow rate of 6.2 mL/min?

(I) A gardener feels it is taking too long to water a garden with a \(\frac{3}{8}\) -in.-diameter hose. By what factor will the time be cut using a \(\frac{5}{8}\) -in.-diameter hose instead? Assume nothing else is changed. Equation transcription: Text transcription: frac{3}{8} frac{5}{8}

Problem 61P (II) What diameter must a 15.5-m-long air duct have if the ventilation and heating system is to replenish the air in a room 8.0 m X 14.0 m X 4.0 m every 15.0 min? Assume the pump can exert a gauge pressure of 0.710 X 10-3 atm.

(II) What must be the pressure difference between the two ends of a section of pipe, in diameter, if it is to transport oil \(\left(p=950 \mathrm{~kg} / \mathrm{m}^{3}, \eta=0.20 P a . s\right)\) at a rate of \(650 \mathrm{~cm}^{3} / \mathrm{s}\) ? Equation transcription: Text transcription: (p=950{~kg} /{m}^{3}, eta=0.20 P a . s) 650{~cm}^{3} /{s}

(II) Poiseuille's equation does not hold if the flow velocity is high enough that turbulence sets in. The onset of turbulence occurs when the Reynolds number, , exceeds approximately Re is defined as \(R e=\frac{2 \overline{v r p}}{\eta}\) where is the average speed of the fluid, is its density, is its viscosity, and is the radius of the tube in which the fluid is flowing. ( ) Determine if blood flow through the aorta is laminar or turbulent when the average speed of blood in the aorta during the resting part of the heart's cycle is about . (b) During exercise, the blood-flow speed approximately doubles. Calculate the Reynolds number in this case, and determine if the flow is laminar or turbulent. Equation transcription: Text transcription: R e=frac{2 overline{v r p}}{\eta}

(II) Assuming a constant pressure gradient, if blood flow is reduced by 65%, by what factor is the radius of a blood vessel decreased?

(II) Calculate the pressure drop per cm along the aorta using the data of Example 10–12 and Table 10–3.

(III) A patient is to be given a blood transfusion. The blood is to flow through a tube from a raised bottle to a needle inserted in the vein (Fig. 10–55). The inside diameter of the 25-mm-long needle is 0.80 mm, and the required flow rate is \(2.0 \mathrm{~cm}^{3}\) of blood per minute. How high should the bottle be placed above the needle? Obtain and \(\eta\) from the Tables. Assume the blood pressure is 78 torr above atmospheric pressure. Equation transcription: Text transcription: eta 2.0{~cm}^{3}

Problem 67P (I) If the force F needed to move the wire in Fig. 10–34 is 3.4 X 10-3 N,calculate the surface tension of the enclosed fluid. Assume l =0.070

(I) Calculate the force needed to move the wire in Fig. 10–34 if it holds a soapy solution (Table 10–4) and the wire is \(21.5 \mathrm{~cm}\) long. Equation transcription: Text transcription: 21.5{~cm}

Problem 69P (II) The surface tension of a liquid can be determined by measuring the force F needed to just lift a circular platinum ring of radius r from the surface of the liquid. (a) Find a formula for ? in terms of F and r. (b) At 30°C, if F = 6.20 x 10-3 N and r = 2.9 cm, calculate ? for the tested liquid.

Problem 70P (II) If the base of an insect’s leg has a radius of about 3.0 X 10-5 m and the insect’s mass is 0.016 g, would you expect the six-legged insect to remain on top of the water? Why or why not?

Estimate the diameter of a steel needle that can just barely remain on top of water due to surface tension.

Problem 73GP A 3.2-N force is applied to the plunger of a hypodermic needle. If the diameter of the plunger is 1.3 cm and that of the needle is 0.20 mm, (a) with what force does the fluid leave the needle? (b) What force on the plunger would be needed to push fluid into a vein where the gauge pressure is 75 mm-Hg? Answer for the instant just before the fluid starts to move.

(II) A physician judges the health of a heart by measuring the pressure with which it pumps blood. If the physician mistakenly attaches the pressurized cuff around a standing patient’s calf (about 1 m below the heart) instead of the arm (Fig. 10–42), what error (in Pa) would be introduced in the heart’s blood pressure measurement?

Intravenous transfusions are often made under gravity, as shown in Fig. 10–55. Assuming the fluid has a density of 1.00\(g / c m^{3}\), at what height should the bottle be placed so the liquid pressure is () \(52 m m-H g\), and () \(680 \mathrm{~mm}-\mathrm{H}_{2} \mathrm{O}\)? () If the blood pressure is 75 mm-Hg above atmospheric pressure, how high should the bottle be placed so that the fluid just barely enters the vein? Equation transcription: Text transcription: g / c m^{3} 52 m m-H g 680{~mm}-{H}{2}{O}

Problem 75GP A beaker of water rests on an electronic balance that reads 975.0 g. A 2.6-cm-diameter solid copper ball attached to a string is submerged in the water, but does not touch the bottom. What are the tension in the string and the new balance reading?

Problem 76GP Estimate the difference in air pressure between the top and the bottom of the Empire State Building in New York City. It is 380 m tall and is located at sea level. Express as a fraction of atmospheric pressure at sea level.

Problem 77GP A hydraulic lift is used to jack a 960-kg car 42 cm off the floor. The diameter of the output piston is 18 cm, and the input force is 380 N. (a) What is the area of the input piston? (b) What is the work done in lifting the car 42 cm? (c) If the input piston moves 13 cm in each stroke, how high does the car move up for each stroke? (d) How many strokes are required to jack the car up 42 cm? (e) Show that energy is conserved.

Problem 78GP When you ascend or descend a great deal when driving in a car, your ears “pop,” which means that the pressure behind the eardrum is being equalized to that outside. If this did not happen, what would be the approximate force on an eardrum of area 0.20 cm2 if a change in altitude of 1250 m takes place?

Problem 79GP Giraffes are a wonder of cardiovascular engineering. Calculate the difference in pressure (in atmospheres) that the blood vessels in a giraffe’s head must accommodate as the head is lowered from a full upright position to ground level for a drink. The height of an average giraffe is about 6 m.

Problem 80GP How high should the pressure head be if water is to come from a faucet at a speed of 9.2 m/s? Ignore viscosity.

Suppose a person can reduce the pressure in his lungs to -75 mm-Hg gauge pressure. How high can water then be “sucked” up a straw?

Problem 82GP A bicycle pump is used to inflate a tire. The initial tire (gauge) pressure is 210 kPa (30 psi). At the end of the pumping process, the final pressure is 310 kPa (45 psi). If the diameter of the plunger in the cylinder of the pump is 2.5 cm, what is the range of the force that needs to be applied to the pump handle from beginning to end?

Estimate the pressure on the mountains underneath the Antarctic ice sheet, which is typically 2 km thick.

A simple model (Fig. ) considers a continent as a block \(\left(\text { density } \approx 2800 k g / m^{3}\right)\) floating in the mantle rock around it \(\left(\text { density } \approx 3300 \mathrm{~kg} / \mathrm{m}^{3}\right)\). Assuming the continent is thick (the average thickness of the Earth's continental crust), estimate the height of the continent above the surrounding mantle rock. Equation transcription: Text transcription: { density } \approx 3300{~kg} /{m}^{3}) { density } approx 2800 k g / m^{3})

Problem 85GP A ship, carrying fresh water to a desert island in the Caribbean, has a horizontal cross-sectional area of 2240 m2 at the waterline. When unloaded, the ship rises 8.25 m higher in the sea. How much water was (m3) delivered?

Problem 86GP A raft is made of 12 logs lashed together. Each is 45 cm in diameter and has a length of 6.5 m. How many people can the raft hold before they start getting their feet wet, assuming the average person has a mass of 68 kg? Do not neglect the weight of the logs. Assume the specific gravity of wood is 0.60.

Problem 87GP Estimate the total mass of the Earth’s atmosphere, using the known value of atmospheric pressure at sea level.

During each heartbeat, approximately \(70 \ \mathrm {cm}^3\) of blood is pushed from the heart at an average pressure of 105 mm-Hg. Calculate the power output of the heart, in watts, assuming 70 beats per minute.

Four lawn sprinkler heads are fed by a 1.9-cm-diameter pipe. The water comes out of the heads at an angle of \(35^{\circ}\) above the horizontal and covers a radius of 6.0 m. (a) What is the velocity of the water coming out of each sprinkler head? (Assume zero air resistance.) (b) If the output diameter of each head is 3.0 mm, how many liters of water do the four heads deliver per second? (c) How fast is the water flowing inside the 1.9-cm-diameter pipe?

One arm of a U-shaped tube (open at both ends) contains water, and the other alcohol. If the two fluids meet at exactly the bottom of the U, and the alcohol is at a height of 16.0 cm, at what height will the water be?

Problem 91GP The contraction of the left ventricle (chamber) of the heart pumps blood to the body. Assuming that the inner surface of the left ventricle has an area of 82 cm2 and the maximum pressure in the blood is 120 mm-Hg, estimate the force exerted by that ventricle at maximum pressure.

An airplane has a mass of \(1.7 \times 10^6 \ \mathrm {kg}\) and the air flows past the lower surface of the wings at 95 m/s. If the wings have a surface area of \(1200 \ \mathrm m^2\), how fast must the air flow over the upper surface of the wing if the plane is to stay in the air?

Problem 94GP A hurricane-force wind of 180 km/h blows across the face of a storefront window. Estimate the force on the 2.0 m*3.0 m window due to the difference in air pressure inside and outside the window. Assume the store is airtight so the inside pressure remains at 1.0 atm. (This is why you should not tightly seal a building in preparation for a hurricane.)

Problem 95GP Blood is placed in a bottle 1.40 m above a 3.8-cm-long needle, of inside diameter 0.40 mm, from which it flows at a rate of 4.1 cm3/min. What is the viscosity of this blood?

A copper (Cu) weight is placed on top of a 0.40-kg block of wood \(\left(\text { density }=0.60 \times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}\right)\) floating in water, as shown in Fig. 10–58. What is the mass of the copper if the top of the wood block is exactly at the water’s surface? Equation transcription: Text transcription: { density }=0.60 times 10^{3}{~kg} /{m}^{3})

Problem 99GP If cholesterol buildup reduces the diameter of an artery by 25%, by what % will the blood flow rate be reduced, assuming the same pressure difference?

The approximate volume of the granite monolith known as El Capitan in Yosemite National Park (Fig.1047) is about 10 What is its approximate mass

What is the approximate mass of air in a living room 5.6 m * 3.6 m * 2.4 m?

If you tried to smuggle gold bricks by filling your backpack, whose dimensions are what would its mass be?

State your mass and then estimate your volume. [Hint: Because you can swim on or just under the surface of the water in a swimming pool, you have a pretty good idea of your density.]

A bottle has a mass of 35.00 g when empty and 98.44 g when filled with water. When filled with another fluid, the mass is 89.22 g. What is the specific gravity of this other fluid?

If 4.0 L of antifreeze solution (specific gravity = 0.80) is added to 5.0 L of water to make a 9.0-L mixture, what is the specific gravity of the mixture?

The Earth is not a uniform sphere, but has regions of varying density. Consider a simple model of the Earth divided into three regionsinner core, outer core, and mantle. Each region is taken to have a unique constant density (the average density of that region in the real Earth): (a) Use this model to predict the average density of the entire Earth. (b) If the radius of the Earth is 6380 km and its mass is determine the actual average density of the Earth and compare it (as a percent difference)with the one you determined in (a).

(I) Estimate the pressure needed to raise a column of water to the same height as a 46-m-tall pine tree.

What is the difference in blood pressure (mm-Hg) between the top of the head and bottom of the feet of a 1.75-m-tall person standing vertically?

(a) Calculate the total force of the atmosphere acting on the top of a table that measures (b) What is the total force acting upward on the underside of the table?

How high would the level be in an alcohol barometer at normal atmospheric pressure?

How high would the level be in an alcohol barometer at normal atmospheric pressure?

In a movie, Tarzan evades his captors by hiding under water for many minutes while breathing through a long, thin reed. Assuming the maximum pressure difference his lungs can manage and still breathe is calculate the deepest he could have been

The maximum gauge pressure in a hydraulic lift is 17.0 atm. What is the largest-size vehicle (kg) it can lift if the diameter of the output line is 25.5 cm?

(II) The gauge pressure in each of the four tires of an automobile is 240 kPa. If each tire has a “footprint” of \(190\ cm^2\) (area touching the ground), estimate the mass of the car.

(a) Determine the total force and the absolute pressure on the bottom of a swimming pool 28.0 m by 8.5 m whose uniform depth is 1.8 m. (b) What will be the pressure against the side of the pool near the bottom?

A house at the bottom of a hill is fed by a full tank of water 6.0 m deep and connected to the house by a pipe that is 75 m long at an angle of 61 from the horizontal (Fig. 1049). (a) Determine the water gauge pressure at the house. (b) How high could the water shoot if it came vertically out of a broken pipe in front of the house?

Water and then oil (which dont mix) are poured into a tube, open at both ends. They come to equilibrium as shown in Fig. 1050. What is the density of the oil? [Hint: Pressures at points a and b are equal. Why?]

How high would the atmosphere extend if it were of uniform density throughout, equal to half the present density at sea level?

(II) Determine the minimum gauge pressure needed in the water pipe leading into a building if water is to come out of a faucet on the fourteenth floor, 44 m above that pipe.

Determine the minimum gauge pressure needed in the water pipe leading into a building if water is to come out of a faucet on the fourteenth floor, 44 m above that pipe.

An open-tube mercury manometer is used to measure the pressure in an oxygen tank. When the atmospheric pressure is 1040 mbar, what is the absolute pressure (in Pa) in the tank if the height of the mercury in the open tube is (a) 18.5 cm higher, (b) 5.6 cm lower, than the mercury in the tube connected to the tank? See Fig. 107a.

What fraction of a piece of iron will be submerged when it floats in mercury?

A geologist finds that a Moon rock whose mass is 9.28 kg has an apparent mass of 6.18 kg when submerged in water. What is the density of the rock?

A crane lifts the 18,000-kg steel hull of a sunken ship out of the water. Determine (a) the tension in the cranes cable when the hull is fully submerged in the water, and (b) the tension when the hull is completely out of the water

A spherical balloon has a radius of 7.15 m and is filled with helium. How large a cargo can it lift, assuming that the skin and structure of the balloon have a mass of 930 kg? Neglect the buoyant force on the cargo volume itself.

What is the likely identity of a metal (see Table 101) if a sample has a mass of 63.5 g when measured in air and an apparent mass of 55.4 g when submerged in water?

Calculate the true mass (in vacuum) of a piece of aluminum whose apparent mass is 4.0000 kg when weighed in air

Because gasoline is less dense than water, drums containing gasoline will float in water. Suppose a 210-L steel drum is completely full of gasoline. What total volume of steel can be used in making the drum if the gasoline-filled drum is to float in fresh water?

A scuba diver and her gear displace a volume of 69.6 L and have a total mass of 72.8 kg. (a) What is the buoyant force on the diver in seawater? (b) Will the diver sink or float?

The specific gravity of ice is 0.917, whereas that of seawater is 1.025. What percent of an iceberg is above the surface of the water?

Archimedes principle can be used to determine the specific gravity of a solid using a known liquid (Example 108). The reverse can be done as well. (a) As an example, a 3.80-kg aluminum ball has an apparent mass of 2.10 kg when submerged in a particular liquid: calculate the density of the liquid. (b) Determine a formula for finding the density of a liquid using this procedure.

A 32-kg child decides to make a raft out of empty 1.0-L soda bottles and duct tape. Neglecting the mass of the duct tape and plastic in the bottles, what minimum number of soda bottles will the child need to be able stay dry on the raft?

An undersea research chamber is spherical with an external diameter of 5.20 m. The mass of the chamber, when occupied, is 74,400 kg. It is anchored to the sea bottom by a cable. What is (a) the buoyant force on the chamber, and (b) the tension in the cable?

A 0.48-kg piece of wood floats in water but is found to sink in alcohol in which it has an apparent mass of 0.047 kg. What is the SG of the wood?

(II) A two-component model used to determine percent body fat in a human body assumes that a fraction \(f(<1)\) of the body's total mass m is composed of fat with a density of \(0.90 \mathrm{~g} / \mathrm{cm}^3\), and that the remaining mass of the body is composed of fat-free tissue with a density of \(1.10 \mathrm{~g} / \mathrm{cm}^3\). If the specific gravity of the entire body's density is X, show that the percent body fat \((=f \times 100)\) is given by \(\% \text { Body fat }=\frac{495}{X}-450\)

On dry land, an athlete weighs 70.2 kg. The same athlete, when submerged in a swimming pool and hanging from a scale, has an apparent weight of 3.4 kg. Using Example 108 as a guide, (a) find the total volume V of the submerged athlete. (b) Assume that when submerged, the athletes body contains a residual volume of air (mainly in the lungs). Taking to be the actual volume of the athletes body, find the bodys specific gravity, SG. (c) What is the athletes percent body fat assuming it is given by the formula ?

How many helium-filled balloons would it take to lift a person? Assume the person has a mass of 72 kg and that each helium-filled balloon is spherical with a diameter of 33 cm.

A scuba tank, when fully submerged, displaces 15.7 L of seawater. The tank itself has a mass of 14.0 kg and, when full, contains 3.00 kg of air. Assuming only its weight and the buoyant force act on the tank, determine the net force (magnitude and direction) on the fully submerged tank at the beginning of a dive (when it is full of air) and at the end of a dive (when it no longer contains any air).

(III) A 3.65-kg block of wood (SG = 0.50) floats on water. What minimum mass of lead, hung from the wood by a string, will cause the block to sink?

A 12-cm-radius air duct is used to replenish the air of a room every 12 min. How fast does the air flow in the duct?

Calculate the average speed of blood flow in the major arteries of the body, which have a total cross-sectional area of about Use the data of Example 1012.

How fast does water flow from a hole at the bottom of a very wide, 4.7-m-deep storage tank filled with water? Ignore viscosity.

Show that Bernoullis equation reduces to the hydrostatic variation of pressure with depth (Eq. 103b) when there is no flow (v1 = v2 = 0).

(II) What is the volume rate of flow of water from a 1.85-cm-diameter faucet if the pressure head is 12.0 m?

A fish tank has dimensions 36 cm wide by 1.0 m long by 0.60 m high. If the filter should process all the water in the tank once every 3.0 h, what should the flow speed be in the 3.0-cm-diameter input tube for the filter?

What gauge pressure in the water pipes is necessary if a fire hose is to spray water to a height of 16 m?

A (inside) diameter garden hose is used to fill a round swimming pool 6.1 m in diameter. How long will it take to fill the pool to a depth of 1.4 m if water flows from the hose at a speed of 0.40 ms?

A wind blowing over the flat roof of a house causes the roof to lift off the house. If the house is in size, estimate the weight of the roof. Assume the roof is not nailed down.

(II) A 6.0-cm-diameter horizontal pipe gradually narrows to 4.5 cm. When water flows through this pipe at a certain rate, the gauge pressure in these two sections is 33.5 kPa and 22.6 kPa, respectively.What is the volume rate of flow?

Estimate the air pressure inside a category 5 hurricane, where the wind speed is 300 km/h (Fig. 10–52).

What is the lift (in newtons) due to Bernoullis principle on a wing of area if the air passes over the top and bottom surfaces at speeds of and 150 m/s, respectively?

Water at a gauge pressure of 3.8 atm at street level flows into an office building at a speed of through a pipe 5.0 cm in diameter. The pipe tapers down to 2.8 cm in diameter by the top floor, 16 m above (Fig. 1053), where the faucet has been left open. Calculate the flow velocity and the gauge pressure in the pipe on the top floor. Assume no branch pipes and ignore viscosity

(II) Show that the power needed to drive a fluid through a pipe with uniform cross-section is equal to the volume rate of flow, Q, times the pressure difference, \(P_1-P_2\). Ignore viscosity.

In Fig. 1054, take into account the speed of the top surface of the tank and show that the speed of fluid leaving an opening near the bottom is where and and are the areas of the opening and of the top surface, respectively. Assume so that the flow remains nearly steady and laminar.

(a) Show that the flow speed measured by a venturi meter (see Fig. 1029) is given by the relation (b) A venturi meter is measuring the flow of water; it has a main diameter of 3.5 cm tapering down to a throat diameter of 1.0 cm. If the pressure difference is measured to be 18 mm-Hg, what is the speed of the water entering the venturi throat?

A fire hose exerts a force on the person holding it. This is because the water accelerates as it goes from the hose through the nozzle. How much force is required to hold a 7.0-cm-diameter hose delivering through a 0.75-cm-diameter nozzle?

A viscometer consists of two concentric cylinders, 10.20 cm and 10.60 cm in diameter. A liquid fills the space between them to a depth of 12.0 cm. The outer cylinder is fixed, and a torque of keeps the inner cylinder turning at a steady rotational speed of What is the viscosity of the liquid?

Engine oil (assume SAE 10, Table 103) passes through a fine 1.80-mm-diameter tube that is 10.2 cm long. What pressure difference is needed to maintain a flow rate of 6.2 mL/min?

(I) A gardener feels it is taking too long to water a garden with a \(\frac{3}{8}-in\), -diameter hose. By what factor will the time be cut using a \(\frac{5}{8}-in.\)-diameter hose instead? Assume nothing else is changed.

(II) What diameter must a 15.5-m-long air duct have if the ventilation and heating system is to replenish the air in a room \(8.0\ m \times 14.0\ m \times 4.0\ m\) every 15.0 min? Assume the pump can exert a gauge pressure of \(0.710 \times 10^{-3}\ atm\).

What must be the pressure difference between the two ends of a 1.6-km section of pipe, 29 cm in diameter, if it is to transport oil

Poiseuilles equation does not hold if the flow velocity is high enough that turbulence sets in. The onset of turbulence occurs when the Reynolds number, Re, exceeds approximately 2000. Re is defined as where is the average speed of the fluid, is its density, is its viscosity, and r is the radius of the tube in which the fluid is flowing. (a) Determine if blood flow through the aorta is laminar or turbulent when the average speed of blood in the aorta during the resting part of the hearts cycle is about (b) During exercise, the blood-flow speed approximately doubles. Calculate the Reynolds number in this case, and determine if the flow is laminar or turbulent.

Assuming a constant pressure gradient, if blood flow is reduced by 65%, by what factor is the radius of a blood vessel decreased?

Calculate the pressure drop per cm along the aorta using the data of Example 1012 and Table 103.

Calculate the pressure drop per cm along the aorta using the data of Example 1012 and Table 103.

If the force F needed to move the wire in Fig. 1034 is calculate the surface tension of the enclosed fluid. Assume

Calculate the force needed to move the wire in Fig. 1034 if it holds a soapy solution (Table 104) and the wire is 21.5 cm long.

The surface tension of a liquid can be determined by measuring the force F needed to just lift a circular platinum ring of radius r from the surface of the liquid. (a) Find a formula for in terms of F and r. (b) At 30C, if and calculate for the tested liquid

(II) If the base of an insect’s leg has a radius of about \(3.0 \times 10^{-5}\ m\) and the insect’s mass is 0.016 g, would you expect the six-legged insect to remain on top of the water? Why or why not?

If the base of an insects leg has a radius of about and the insects mass is 0.016 g, would you expect the six-legged insect to remain on top of the water? Why or why not?

A physician judges the health of a heart by measuring the pressure with which it pumps blood. If the physician mistakenly attaches the pressurized cuff around a standing patients calf (about 1 m below the heart) instead of the arm (Fig. 1042), what error (in Pa) would be introduced in the hearts blood pressure measurement?

A 3.2-N force is applied to the plunger of a hypodermic needle. If the diameter of the plunger is 1.3 cm and that of the needle is 0.20 mm, (a) with what force does the fluid leave the needle? (b) What force on the plunger would be needed to push fluid into a vein where the gauge pressure is 75 mm-Hg? Answer for the instant just before the fluid starts to move

Intravenous transfusions are often made under gravity, as shown in Fig. 10–55. Assuming the fluid has a density of \(1.00 \ \mathrm {g/cm}^3\) at what height h should the bottle be placed so the liquid pressure is (a) 52 mm-Hg, and (b) \(680 \ \mathrm {mm-H}_2\mathrm O\)? (c) If the blood pressure is 75 mm-Hg above atmospheric pressure, how high should the bottle be placed so that the fluid just barely enters the vein?

A beaker of water rests on an electronic balance that reads 975.0 g. A 2.6-cm-diameter solid copper ball attached to a string is submerged in the water, but does not touch the bottom. What are the tension in the string and the new balance reading?

Estimate the difference in air pressure between the top and the bottom of the Empire State Building in New York City. It is 380 m tall and is located at sea level. Express as a fraction of atmospheric pressure at sea level.

A hydraulic lift is used to jack a 960-kg car 42 cm off the floor. The diameter of the output piston is 18 cm, and the input force is 380 N. (a) What is the area of the input piston? (b) What is the work done in lifting the car 42 cm? (c) If the input piston moves 13 cm in each stroke, how high does the car move up for each stroke? (d) How many strokes are required to jack the car up 42 cm? (e) Show that energy is conserved

When you ascend or descend a great deal when driving in a car, your ears pop, which means that the pressure behind the eardrum is being equalized to that outside. If this did not happen, what would be the approximate force on an eardrum of area if a change in altitude of 1250 m takes place?

Giraffes are a wonder of cardiovascular engineering. Calculate the difference in pressure (in atmospheres) that the blood vessels in a giraffes head must accommodate as the head is lowered from a full upright position to ground level for a drink. The height of an average giraffe is about 6 m.

How high should the pressure head be if water is to come from a faucet at a speed of 9.2 m/s? Ignore viscosity.

Suppose a person can reduce the pressure in his lungs to gauge pressure. How high can water then be sucked up a straw?

A bicycle pump is used to inflate a tire. The initial tire (gauge) pressure is 210 kPa (30 psi). At the end of the pumping process, the final pressure is 310 kPa (45 psi). If the diameter of the plunger in the cylinder of the pump is 2.5 cm, what is the range of the force that needs to be applied to the pump handle from beginning to end?

Estimate the pressure on the mountains underneath the Antarctic ice sheet, which is typically 2 km thick.

A simple model (Fig. 1056) considers a continent as a block floating in the mantle rock around it Assuming the continent is 35 km thick (the average thickness of the Earths continental crust), estimate the height of the continent above the surrounding mantle rock.

A ship, carrying fresh water to a desert island in the Caribbean, has a horizontal cross-sectional area of \(2240\ m^2\) at the waterline. When unloaded, the ship rises 8.25 m higher in the sea. How much water \((m^3)\) was delivered?

A raft is made of 12 logs lashed together. Each is 45 cm in diameter and has a length of 6.5 m. How many people can the raft hold before they start getting their feet wet, assuming the average person has a mass of 68 kg? Do not neglect the weight of the logs. Assume the specific gravity of wood is 0.60.

Estimate the total mass of the Earths atmosphere, using the known value of atmospheric pressure at sea level.

During each heartbeat, approximately of blood is pushed from the heart at an average pressure of 105 mm-Hg. Calculate the power output of the heart, in watts, assuming 70 beats per minute.

Four lawn sprinkler heads are fed by a 1.9-cm-diameter pipe. The water comes out of the heads at an angle of \(35^{\circ}\) above the horizontal and covers a radius of 6.0 m. (a) What is the velocity of the water coming out of each sprinkler head? (Assume zero air resistance.) (b) If the output diameter of each head is 3.0 mm, how many liters of water do the four heads deliver per second? (c) How fast is the water flowing inside the 1.9-cm-diameter pipe?

One arm of a tube (open at both ends) contains water, and the other alcohol. If the two fluids meet at exactly the bottom of the and the alcohol is at a height of 16.0 cm, at what height will the water be?

The contraction of the left ventricle (chamber) of the heart pumps blood to the body. Assuming that the inner surface of the left ventricle has an area of and the maximum pressure in the blood is 120 mm-Hg, estimate the force exerted by that ventricle at maximum pressure.

An airplane has a mass of \(1.7 \times 10^6\ kg\), and the air flows past the lower surface of the wings at 95 m/s. f the wings have a surface area of \(1200\ m^2\), how fast must the air flow over the upper surface of the wing if the plane is to stay in the air?

A drinking fountain shoots water about 12 cm up in the air from a nozzle of diameter 0.60 cm (Fig. 10–57). The pump at the base of the unit (1.1 m below the nozzle) pushes water into a 1.2-cm-diameter supply pipe that goes up to the nozzle. What gauge pressure does the pump have to provide? Ignore the viscosity; your answer will therefore be an underestimate.

A hurricane-force wind of blows across the face of a storefront window. Estimate the force on the window due to the difference in air pressure inside and outside the window. Assume the store is airtight so the inside pressure remains at 1.0 atm. (This is why you should not tightly seal a building in preparation for a hurricane.)

Blood is placed in a bottle 1.40 m above a 3.8-cm-long needle, of inside diameter 0.40 mm, from which it flows at a rate of What is the viscosity of this blood?

You are watering your lawn with a hose when you put your finger over the hose opening to increase the distance the water reaches. If you are holding the hose horizontally, and the distance the water reaches increases by a factor of 4, what fraction of the hose opening did you block?

A copper (Cu) weight is placed on top of a 0.40-kg block of wood floating in water, as shown in Fig. 1058. What is the mass of the copper if the top of the wood block is exactly at the waters surface?

You need to siphon water from a clogged sink. The sink has an area of \(0.38 \ \mathrm m^2\) and is filled to a height of 4.0 cm. Your siphon tube rises 45 cm above the bottom of the sink and then descends 85 cm to a pail as shown in Fig. 10–59. The siphon tube has a diameter of 2.3 cm. (a) Assuming that the water level in the sink has almost zero velocity, use Bernoulli’s equation to estimate the water velocity when it enters the pail. (b) Estimate how long it will take to empty the sink. Ignore viscosity.

If cholesterol buildup reduces the diameter of an artery by 25%, by what % will the blood flow rate be reduced, assuming the same pressure difference?