(a) The mass and the radius of the sun are, respectively,

One of the concrete pillars that support a house is 2.2 m tall and has a radius of 0.50 m. The density of concrete is about 2.2 3 103 kg/m3 . Find the weight of this pillar in pounds (1 N 5 0.2248 lb).

A cylindrical storage tank has a radius of 1.22 m. When fi lled to a height of 3.71 m, it holds 14 300 kg of a liquid industrial solvent. What is the density of the solvent?

Accomplished silver workers in India can pound silver into incredibly thin sheets, as thin as 3.00 3 1027 m (about one-hundredth of the thickness of this sheet of paper). Find the area of such a sheet that can be formed from 1.00 kg of silver

Neutron stars consist only of neutrons and have unbelievably high densities. A typical mass and radius for a neutron star might be 2.7 3 1028 kg and 1.2 3 103 m. (a) Find the density of such a star. (b) If a dime (V 5 2.0 3 1027 m3 ) were made from this material, how much would it weigh (in pounds)?

One end of a wire is attached to a ceiling, and a solid brass ball is tied to the lower end. The tension in the wire is 120 N. What is the radius of the brass ball?

Planners of an experiment are evaluating the design of a sphere of radius R that is to be fi lled with helium (0 8C, 1 atm pressure). Ultrathin silver foil of thickness T will be used to make the sphere, and the designers claim that the mass of helium in the sphere will equal the mass of silver used. Assuming that T is much less than R, calculate the ratio T/R for such a sphere

A bar of gold measures 0.15 m 3 0.050 m 3 0.050 m. How many gallons of water have the same mass as this bar?

A full can of black cherry soda has a mass of 0.416 kg. It contains 3.54 3 1024 m3 of liquid. Assuming that the soda has the same density as water, fi nd the volume of aluminum used to make the can.

A hypothetical spherical planet consists entirely of iron. What is the period of a satellite that orbits this planet just above its surface? Consult Table 11.1 as necessary.

An antifreeze solution is made by mixing ethylene glycol (r 5 1116 kg/m3 ) with water. Suppose that the specifi c gravity of such a solution is 1.0730. Assuming that the total volume of the solution is the sum of its parts, determine the volume percentage of ethylene glycol in the solution.

An airtight box has a removable lid of area 1.3 3 1022 m2 and negligible weight. The box is taken up a mountain where the air pressure outside the box is 0.85 3 105 Pa. The inside of the box is completely evacuated. What is the magnitude of the force required to pull the lid off the box?

A person who weighs 625 N is riding a 98-N mountain bike. Suppose that the entire weight of the rider and bike is supported equally by the two tires. If the pressure in each tire is 7.60 3 105 Pa, what is the area of contact between each tire and the ground?

A solid concrete block weighs 169 N and is resting on the ground. Its dimensions are 0.400 m 3 0.200 m 3 0.100 m. A number of identical blocks are stacked on top of this one. What is the smallest number of whole blocks (including the one on the ground) that can be stacked so that their weight creates a pressure of at least two atmospheres on the ground beneath the fi rst block?

United States currency is printed using intaglio presses that generate a printing pressure of 8.0 3 104 lb/in.2 A $20 bill is 6.1 in. by 2.6 in. Calculate the magnitude of the force that the printing press applies to one side of the bill

A glass bottle of soda is sealed with a screw cap. The absolute pressure of the carbon dioxide inside the bottle is 1.80 3 105 Pa. Assuming that the top and bottom surfaces of the cap each have an area of 4.10 3 1024 m2 , obtain the magnitude of the force that the screw thread exerts on the cap in order to keep it on the bottle. The air pressure outside the bottle is one atmosphere.

A 58-kg skier is going down a slope oriented 358 above the horizontal. The area of each ski in contact with the snow is 0.13 m2 . Determine the pressure that each ski exerts on the snow.

A suitcase (mass m 5 16 kg) is resting on the fl oor of an elevator. The part of the suitcase in contact with the fl oor measures 0.50 m 3 0.15 m. The elevator is moving upward with an acceleration of magnitude 1.5 m/s2 . What pressure (in excess of atmospheric pressure) is applied to the fl oor beneath the suitcase?

A cylinder is fi tted with a piston, beneath which is a spring, as in the drawing. The cylinder is open to the air at the top. Friction is absent. The spring constant of the spring is 3600 N/m. The piston has a negligible mass and a radius of 0.024 m. (a) When the air beneath the piston is completely pumped out, how much does the atmospheric pressure cause the spring to compress? (b) How much work does the atmospheric pressure do in compressing the spring?

As the initially empty urinary bladder fi lls with urine and expands, its internal pressure increases by 3300 Pa, which triggers the micturition refl ex (the feeling of the need to urinate). The drawing shows a horizontal, square section of the bladder wall with an edge length of 0.010 m. Because the bladder is stretched, four tension forces of equal magnitude T act on the square section, one at each edge, and each force is directed at an angle u below the horizontal. What is the magnitude T of the tension force acting on one edge of the section when the internal bladder pressure is 3300 Pa and each of the four tension forces is directed 5.08 below the horizontal?

The Mariana trench is located in the fl oor of the Pacifi c Ocean at a depth of about 11 000 m below the surface of the water. The density of seawater is 1025 kg/m3 . (a) If an underwater vehicle were to explore such a depth, what force would the water exert on the vehicles observation window (radius 5 0.10 m)? (b) For comparison, determine the weight of a jetliner whose mass is 1.2 3 105 kg.

Review Conceptual Example 6 as an aid in understanding this problem. Consider the pump on the right side of Figure 11.10, which acts to reduce the air pressure in the pipe. The air pressure outside the pipe is one atmosphere. Find the maximum depth from which this pump can extract water from the well.

A meat baster consists of a squeeze bulb attached to a plastic tube. When the bulb is squeezed and released, with the open end of the tube under the surface of the basting sauce, the sauce rises in the tube to a distance h, as the drawing shows. Using 1.013 3 105 Pa for the atmospheric pressure and 1200 kg/m3 for the density of the sauce, fi nd the absolute pressure in the bulb when the distance h is (a) 0.15 m and (b) 0.10 m.

The main water line enters a house on the fi rst fl oor. The line has a gauge pressure of 1.90 3 105 Pa. (a) A faucet on the second fl oor, 6.50 m above the fi rst fl oor, is turned off . What is the gauge pressure at this faucet? (b) How high could a faucet be before no water would fl ow from it, even if the faucet were open?

The drawing shows an intravenous feeding. With the distance shown, nutrient solution (r 5 1030 kg/m3 ) can just barely enter the blood in the vein. What is the gauge pressure of the venous blood? Express your answer in millimeters of mercury.

The human lungs can function satisfactorily up to a limit where the pressure diff erence between the outside and inside of the lungs is one-twentieth of an atmosphere. If a diver uses a snorkel for breathing, how far below the water can she swim? Assume the diver is in salt water whose density is 1025 kg/m3

At a given instant, the blood pressure in the heart is 1.6 3 104 Pa. If an artery in the brain is 0.45 m above the heart, what is the pressure in the artery? Ignore any pressure changes due to blood fl ow.

A water tower is a familiar sight in many towns. The purpose of such a tower is to provide storage capacity and to provide suffi cient pressure in the pipes that deliver the water to customers. The drawing shows a spherical reservoir that contains 5.25 3 105 kg of water when full. The reservoir is vented to the atmosphere at the top. For a full reservoir, fi nd the gauge pressure that the water has at the faucet in (a) house A and (b) house B. Ignore the diameter of the delivery pipes.

A mercury barometer reads 747.0 mm on the roof of a building and 760.0 mm on the ground. Assuming a constant value of 1.29 kg/m3 for the density of air, determine the height of the building.

A 1.00-m-tall container is fi lled to the brim, partway with mercury and the rest of the way with water. The container is open to the atmosphere. What must be the depth of the mercury so that the absolute pressure on the bottom of the container is twice the atmospheric pressure?

Two identical containers are open at the top and are connected at the bottom via a tube of negligible volume and a valve that is closed. Both containers are fi lled initially to the same height of 1.00 m, one with water, the other with mercury, as the drawing indicates. The valve is then opened. Water and mercury are immiscible. Determine the fl uid level in the left container when equilibrium is reestablished.

The vertical surface of a reservoir dam that is in contact with the water is 120 m wide and 12 m high. The air pressure is one atmosphere. Find the magnitude of the total force acting on this surface in a completely fi lled reservoir. (Hint: The pressure varies linearly with depth, so you must use an average pressure.)

A house has a roof with the dimensions shown in the drawing. Determine the magnitude and direction of the net force that the atmosphere applies to the roof when the outside pressure drops suddenly by 75.0 mm of mercury before the air pressure in the attic can adjust. Express your answer in (a) newtons and (b) pounds.

The atmospheric pressure above a swimming pool changes from 755 to 765 mm of mercury. The bottom of the pool is a rectangle (12 m 3 24 m). By how much does the force on the bottom of the pool increase?

A barbers chair with a person in it weighs 2100 N. The output plunger of a hydraulic system begins to lift the chair when the barbers foot applies a force of 55 N to the input piston. Neglect any height diff erence between the plunger and the piston. What is the ratio of the radius of the plunger to the radius of the piston?

Multiple-Concept Example 8 presents an approach to problems of this kind. The hydraulic oil in a car lift has a density of 8.30 3 102 kg/m3 . The weight of the input piston is negligible. The radii of the input piston and output plunger are 7.70 3 1023 m and 0.125 m, respectively. What input force F is needed to support the 24 500-N combined weight of a car and the output plunger, when (a) the bottom surfaces of the piston and plunger are at the same level, and (b) the bottom surface of the output plunger is 1.30 m above that of the input piston?

In the process of changing a fl at tire, a motorist uses a hydraulic jack. She begins by applying a force of 45 N to the input piston, which has a radius r1. As a result, the output plunger, which has a radius r2, applies a force to the car. The ratio r2/r1 has a value of 8.3. Ignore the height diff erence between the input piston and output plunger and determine the force that the output plunger applies to the car.

A dump truck uses a hydraulic cylinder, as the drawing illustrates. When activated by the operator, a pump injects hydraulic oil into the cylinder at an absolute pressure of 3.54 3 106 Pa and drives the output plunger, which has a radius of 0.150 m. Assuming that the plunger remains perpendicular to the fl oor of the load bed, fi nd the torque that the plunger creates about the axis identifi ed in the drawing.

The drawing shows a hydraulic chamber with a spring (spring constant 5 1600 N/m) attached to the input piston and a rock of mass 40.0 kg resting on the output plunger. The piston and plunger are nearly at the same height, and each has a negligible mass. By how much is the spring compressed from its unstrained position?

The drawing shows a hydraulic system used with disc brakes. The force F B is applied perpendicularly to the brake pedal. The pedal rotates about the axis shown in the drawing and causes a force to be applied perpendicularly to the input piston (radius 5 9.50 3 1023 m) in the master cylinder. The resulting pressure is transmitted by the brake fl uid to the output plungers (radii 5 1.90 3 1022 m), which are covered with the brake linings. The linings are pressed against both sides of a disc attached to the rotating wheel. Suppose that the magnitude of F B is 9.00 N. Assume that the input piston and the output plungers are at the same vertical level, and fi nd the force applied to each side of the rotating disc.

The density of ice is 917 kg/m3 , and the density of seawater is 1025 kg/m3 . A swimming polar bear climbs onto a piece of fl oating ice that has a volume of 5.2 m3 . What is the weight of the heaviest bear that the ice can support without sinking completely beneath the water?

A 0.10-m 3 0.20-m 3 0.30-m block is suspended from a wire and is completely under water. What buoyant force acts on the block?

A hydrometer is a device used to measure the density of a liquid. It is a cylindrical tube weighted at one end, so that it fl oats with the heavier end downward. The tube is contained inside a large medicine dropper, into which the liquid is drawn using the squeeze bulb (see the drawing). For use with your car, marks are put on the tube so that the level at which it fl oats indicates whether the liquid is battery acid (more dense) or antifreeze (less dense). The hydrometer has a weight of W 5 5.88 3 1022 N and a crosssectional area of A 5 7.85 3 1025 m2 . How far from the bottom of the tube should the mark be put that denotes (a) battery acid (r 5 1280 kg/m3 ) and (b) antifreeze (r 5 1073 kg/m3 )?

A duck is fl oating on a lake with 25% of its volume beneath the water. What is the average density of the duck?

A paperweight, when weighed in air, has a weight of W 5 6.9 N. When completely immersed in water, however, it has a weight of Win water 5 4.3 N. Find the volume of the paperweight.

An 81-kg person puts on a life jacket, jumps into the water, and fl oats. The jacket has a volume of 3.1 3 1022 m3 and is completely submerged under the water. The volume of the persons body that is under water is 6.2 3 1022 m3 . What is the density of the life jacket?

A lost shipping container is found resting on the ocean fl oor and completely submerged. The container is 6.1 m long, 2.4 m wide, and 2.6 m high. Salvage experts attach a spherical balloon to the top of the container and infl ate it with air pumped down from the surface. When the balloons radius is 1.5 m, the shipping container just begins to rise toward the surface. What is the mass of the container? Ignore the mass of the balloon and the air within it. Do not neglect the buoyant force exerted on the shipping container by the water. The density of seawater is 1025 kg/m3 .

Refer to Multiple-Concept Example 11 to see a problem similar to this one. What is the smallest number of whole logs (r 5 725 kg/ m3 , radius 5 0.0800 m, length 5 3.00 m) that can be used to build a raft that will carry four people, each of whom has a mass of 80.0 kg?

A hot-air balloon is accelerating upward under the infl uence of two forces, its weight and the buoyant force. For simplicity, consider the weight to be only that of the hot air within the balloon, thus ignoring the balloon fabric and the basket. The hot air inside the balloon has a density of rhot air 5 0.93 kg/m3 , and the density of the cool air outside is rcool air 5 1.29 kg/m3 . What is the acceleration of the rising balloon?

A hollow cubical box is 0.30 m on an edge. This box is fl oating in a lake with one-third of its height beneath the surface. The walls of the box have a negligible thickness. Water from a hose is poured into the open top of the box. What is the depth of the water in the box just at the instant that water from the lake begins to pour into the box from the lake?

To verify her suspicion that a rock specimen is hollow, a geologist weighs the specimen in air and in water. She fi nds that the specimen weighs twice as much in air as it does in water. The density of the solid part of the specimen is 5.0 3 103 kg/m3 . What fraction of the specimens apparent volume is solid?

A solid cylinder (radius 5 0.150 m, height 5 0.120 m) has a mass of 7.00 kg. This cylinder is fl oating in water. Then oil (r 5 725 kg/m3 ) is poured on top of the water until the situation shown in the drawing results. How much of the height of the cylinder is in the oil?

A spring is attached to the bottom of an empty swimming pool, with the axis of the spring oriented vertically. An 8.00-kg block of wood (r 5 840 kg/m3 ) is fi xed to the top of the spring and compresses it. Then the pool is fi lled with water, completely covering the block. The spring is now observed to be stretched twice as much as it had been compressed. Determine the percentage of the blocks total volume that is hollow. Ignore any air in the hollow space.

One kilogram of glass (r 5 2.60 3 103 kg/m3 ) is shaped into a hollow spherical shell that just barely fl oats in water. What are the inner and outer radii of the shell? Do not assume that the shell is thin.

A fuel pump sends gasoline from a cars fuel tank to the engine at a rate of 5.88 3 1022 kg/s. The density of the gasoline is 735 kg/m3 , and the radius of the fuel line is 3.18 3 1023 m. What is the speed at which the gasoline moves through the fuel line?

A patient recovering from surgery is being given fl uid intravenously. The fl uid has a density of 1030 kg/m3 , and 9.5 3 1024 m3 of it fl ows into the patient every six hours. Find the mass fl ow rate in kg/s.

a) The volume fl ow rate in an artery supplying the brain is 3.6 3 1026 m3 /s. If the radius of the artery is 5.2 mm, determine the average blood speed. (b) Find the average blood speed at a constriction in the artery if the constriction reduces the radius by a factor of 3. Assume that the volume fl ow rate is the same as that in part (a).

A room has a volume of 120 m3 . An air-conditioning system is to replace the air in this room every twenty minutes, using ducts that have a square cross section. Assuming that air can be treated as an incompressible fl uid, fi nd the length of a side of the square if the air speed within the ducts is (a) 3.0 m/s and (b) 5.0 m/s.

Water fl ows straight down from an open faucet. The cross-sectional area of the faucet is 1.8 3 1024 m2 , and the speed of the water is 0.85 m/s as it leaves the faucet. Ignoring air resistance, fi nd the cross-sectional area of the water stream at a point 0.10 m below the faucet.

The aorta carries blood away from the heart at a speed of about 40 cm/s and has a radius of approximately 1.1 cm. The aorta branches eventually into a large number of tiny capillaries that distribute the blood to the various body organs. In a capillary, the blood speed is approximately 0.07 cm/s, and the radius is about 6 3 1024 cm. Treat the blood as an incompressible fl uid, and use these data to determine the approximate number of capillaries in the human body.

Three fi re hoses are connected to a fi re hydrant. Each hose has a radius of 0.020 m. Water enters the hydrant through an underground pipe of radius 0.080 m. In this pipe the water has a speed of 3.0 m/s. (a) How many kilograms of water are poured onto a fi re in one hour by all three hoses? (b) Find the water speed in each hose.

Prairie dogs are burrowing rodents. They do not suff ocate in their burrows, because the eff ect of air speed on pressure creates suffi cient air circulation. The animals maintain a diff erence in the shapes of two entrances to the burrow, and because of this diff erence, the air (r 5 1.29 kg/m3 ) blows past the openings at diff erent speeds, as the drawing indicates. Assuming that the openings are at the same vertical level, fi nd the diff erence in air pressure between the openings and indicate which way the air circulates.

Review Conceptual Example 14 before attempting this problem. The truck in that example is traveling at 27 m/s. The density of air is 1.29 kg/m3 . By how much does the pressure inside the cargo area beneath the tarpaulin exceed the outside pressure?

An airplane wing is designed so that the speed of the air across the top of the wing is 251 m/s when the speed of the air below the wing is 225 m/s. The density of the air is 1.29 kg/m3 . What is the lifting force on a wing of area 24.0 m2 ?

Water fl owing out of a horizontal pipe emerges through a nozzle. The radius of the pipe is 1.9 cm, and the radius of the nozzle is 0.48 cm. The speed of the water in the pipe is 0.62 m/s. Treat the water as an ideal fl uid, and determine the absolute pressure of the water in the pipe.

The blood speed in a normal segment of a horizontal artery is 0.11 m/s. An abnormal segment of the artery is narrowed down by an arteriosclerotic plaque to one-fourth the normal cross-sectional area. What is the diff erence in blood pressures between the normal and constricted segments of the artery?

A small crack occurs at the base of a 15.0-m-high dam. The eff ective crack area through which water leaves is 1.30 3 1023 m2 . (a) Ignoring viscous losses, what is the speed of water fl owing through the crack? (b) How many cubic meters of water per second leave the dam?

Water is circulating through a closed system of pipes in a two-fl oor apartment. On the fi rst fl oor, the water has a gauge pressure of 3.4 3 105 Pa and a speed of 2.1 m/s. However, on the second fl oor, which is 4.0 m higher, the speed of the water is 3.7 m/s. The speeds are diff erent because the pipe diameters are diff erent. What is the gauge pressure of the water on the second fl oor?

A ship is fl oating on a lake. Its hold is the interior space beneath its deck; the hold is empty and is open to the atmosphere. The hull has a hole in it, which is below the water line, so water leaks into the hold. The eff ective area of the hole is 8.0 3 1023 m2 and is located 2.0 m beneath the surface of the lake. What volume of water per second leaks into the ship?

A Venturi meter is a device that is used for measuring the speed of a fl uid within a pipe. The drawing shows a gas fl owing at speed v2 through a horizontal section of pipe whose cross-sectional area is A2 5 0.0700 m2 . The gas has a density of r 5 1.30 kg/m3 . The Venturi meter has a cross-sectional area of A1 5 0.0500 m2 and has been substituted for a section of the larger pipe. The pressure diff erence between the two sections is P2 2 P1 5 120 Pa. Find (a) the speed v2 of the gas in the larger, original pipe and (b) the volume fl ow rate Q of the gas

A hand-pumped water gun is held level at a height of 0.75 m above the ground and fi red. The water stream from the gun hits the ground a horizontal distance of 7.3 m from the muzzle. Find the gauge pressure of the water guns reservoir at the instant when the gun is fi red. Assume that the speed of the water in the reservoir is zero and that the water fl ow is steady. Ignore both air resistance and the height diff erence between the reservoir and the muzzle.

A liquid is fl owing through a horizontal pipe whose radius is 0.0200 m. The pipe bends straight upward through a height of 10.0 m and joins another horizontal pipe whose radius is 0.0400 m. What volume fl ow rate will keep the pressures in the two horizontal pipes the same?

An airplane has an eff ective wing surface area of 16 m2 that is generating the lift force. In level fl ight the air speed over the top of the wings is 62.0 m/s, while the air speed beneath the wings is 54.0 m/s. What is the weight of the plane?

The construction of a fl at rectangular roof (5.0 m 3 6.3 m) allows it to withstand a maximum net outward force that is 22 000 N. The density of the air is 1.29 kg/m3 . At what wind speed will this roof blow outward?

A pump and its horizontal intake pipe are located 12 m beneath the surface of a large reservoir. The speed of the water in the intake pipe causes the pressure there to decrease, in accord with Bernoullis principle. Assuming nonviscous fl ow, what is the maximum speed with which water can fl ow through the intake pipe?

A uniform rectangular plate is hanging vertically downward from a hinge that passes along its left edge. By blowing air at 11.0 m/s over the top of the plate only, it is possible to keep the plate in a horizontal position, as illustrated in part a of the drawing. To what value should the air speed be reduced so that the plate is kept at a 30.08 angle with respect to the vertical, as in part b of the drawing? (Hint: Apply Bernoullis equation in the form of Equation 11.12.)

Two circular holes, one larger than the other, are cut in the side of a large water tank whose top is open to the atmosphere. The center of one of these holes is located twice as far beneath the surface of the water as the other. The volume fl ow rate of the water coming out of the holes is the same. (a) Decide which hole is located nearest the surface of the water. (b) Calculate the ratio of the radius of the larger hole to the radius of the smaller hole.

Poiseuilles law remains valid as long as the fl uid fl ow is laminar. For suffi ciently high speed, however, the fl ow becomes turbulent, even if the fl uid is moving through a smooth pipe with no restrictions. It is found experimentally that the fl ow is laminar as long as the Reynolds number Re is less than about 2000: Re 5 2vrR/h. Here v, r, and h are, respectively, the average speed, density, and viscosity of the fl uid, and R is the radius of the pipe. Calculate the highest average speed that blood (r 5 1060 kg/m3 , h 5 4.0 3 1023 Pa ? s) could have and still remain in laminar fl ow when it fl ows through the aorta (R 5 8.0 31023 m).

A pipe is horizontal and carries oil that has a viscosity of 0.14 Pa ?s. The volume fl ow rate of the oil is 5.3 3 1025 m3 /s. The length of the pipe is 37 m, and its radius is 0.60 cm. At the output end of the pipe the pressure is atmospheric pressure. What is the absolute pressure at the input end?

In the human body, blood vessels can dilate, or increase their radii, in response to various stimuli, so that the volume fl ow rate of the blood increases. Assume that the pressure at either end of a blood vessel, the length of the vessel, and the viscosity of the blood remain the same, and determine the factor Rdilated/Rnormal by which the radius of a vessel must change in order to double the volume fl ow rate of the blood through the vessel.

A blood transfusion is being set up in an emergency room for an accident victim. Blood has a density of 1060 kg/m3 and a viscosity of 4.0 3 1023 Pa ?s. The needle being used has a length of 3.0 cm and an inner radius of 0.25 mm. The doctor wishes to use a volume fl ow rate through the needle of 4.5 3 1028 m3 /s. What is the distance h above the victims arm where the level of the blood in the transfusion bottle should be located? As an approximation, assume that the level of the blood in the transfusion bottle and the point where the needle enters the vein in the arm have the same pressure of one atmosphere. (In reality, the pressure in the vein is slightly above atmospheric pressure.)

A pressure diff erence of 1.8 3 103 Pa is needed to drive water (h 5 1.0 3 1023 Pa ?s) through a pipe whose radius is 5.1 3 1023 m. The volume fl ow rate of the water is 2.8 3 1024 m3 /s. What is the length of the pipe?

A cylindrical air duct in an air conditioning system has a length of 5.5 m and a radius of 7.2 3 1022 m. A fan forces air (h 5 1.8 3 1025 Pa ?s) through the duct, so that the air in a room (volume 5 280 m3 ) is replenished every ten minutes. Determine the diff erence in pressure between the ends of the air duct.

Two hoses are connected to the same outlet using a Y-connector, as the drawing shows. The hoses A and B have the same length, but hose B has the larger radius. Each is open to the atmosphere at the end where the water exits. Water fl ows through both hoses as a viscous fl uid, and Poiseuilles law [Q 5 pR4 (P2 2 P1)/(8hL)] applies to each. In this law, P2 is the pressure upstream, P1 is the pressure downstream, and Q is the volume fl ow rate. The ratio of the radius of hose B to the radius of hose A is RB/RA 5 1.50. Find the ratio of the speed of the water in hose B to the speed in hose A.

When an object moves through a fl uid, the fl uid exerts a viscous force F B on the object that tends to slow it down. For a small sphere of radius R, moving slowly with a speed v, the magnitude of the viscous force is given by Stokes law, F 5 6phRv, where h is the viscosity of the fl uid. (a) What is the viscous force on a sphere of radius R 5 5.0 3 1024 m that is falling through water (h51.00 3 1023 Pa ?s) when the sphere has a speed of 3.0 m/s? (b) The speed of the falling sphere increases until the viscous force balances the weight of the sphere. Thereafter, no net force acts on the sphere, and it falls with a constant speed called the terminal speed. If the sphere has a mass of 1.0 3 1025 kg, what is its terminal speed?

Measured along the surface of the water, a rectangular swimming pool has a length of 15 m. Along this length, the fl at bottom of the pool slopes downward at an angle of 118 below the horizontal, from one end to the other. By how much does the pressure at the bottom of the deep end exceed the pressure at the bottom of the shallow end?

One way to administer an inoculation is with a gun that shoots the vaccine through a narrow opening. No needle is necessary, for the vaccine emerges with suffi cient speed to pass directly into the tissue beneath the skin. The speed is high, because the vaccine (r 5 1100 kg/m3 ) is held in a reservoir where a high pressure pushes it out. The pressure on the surface of the vaccine in one gun is 4.1 3 106 Pa above the atmospheric pressure outside the narrow opening. The dosage is small enough that the vaccines surface in the reservoir is nearly stationary during an inoculation. The vertical height between the vaccines surface in the reservoir and the opening can be ignored. Find the speed at which the vaccine emerges.

Multiple-Concept Example 11 reviews the concepts that are important in this problem. What is the radius of a hydrogen-fi lled balloon that would carry a load of 5750 N (in addition to the weight of the hydrogen) when the density of air is 1.29 kg/m3 ?

If a scuba diver descends too quickly into the sea, the internal pressure on each eardrum remains at atmospheric pressure, while the external pressure increases due to the increased water depth. At suffi cient depths, the diff erence between the external and internal pressures can rupture an eardrum. Eardrums can rupture when the pressure diff erence is as little as 35 kPa. What is the depth at which this pressure diff erence could occur? The density of seawater is 1025 kg/m3 .

A water bed for sale has dimensions of 1.83 m 3 2.13 m 3 0.229 m. The fl oor of the bedroom will tolerate an additional weight of no more than 6660 N. Find the weight of the water in the bed and determine whether the bed should be purchased.

An underground pump initially forces water through a horizontal pipe at a fl ow rate of 740 gallons per minute. After several years of operation, corrosion and mineral deposits have reduced the inner radius of the pipe to 0.19 m from 0.24 m, but the pressure diff erence between the ends of the pipe is the same as it was initially. Find the fi nal fl ow rate in the pipe in gallons per minute. Treat water as a viscous fl uid.

The karat is a dimensionless unit that is used to indicate the proportion of gold in a gold-containing alloy. An alloy that is one karat gold contains a weight of pure gold that is one part in twenty-four. What is the volume of gold in a 14.0-karat gold necklace whose weight is 1.27 N?

A volume of 7.2 m3 of glycerol (h 5 0.934 Pa ?s) is pumped through a 15-m length of pipe in 55 minutes. The pressure at the input end of the pipe is 8.6 3 105 Pa, and the pressure at the output end is atmospheric pressure. What is the pipes radius?

As background for this problem, review Conceptual Example 6. A submersible pump is put under the water at the bottom of a well and is used to push water up through a pipe. What minimum output gauge pressure must the pump generate to make the water reach the nozzle at ground level, 71 m above the pump?

(a) The mass and the radius of the sun are, respectively, 1.99 3 1030 kg and 6.96 3 108 m. What is its density? (b) If a solid object is made from a material that has the same density as the sun, would it sink or fl oat in water? Why? (c) Would a solid object sink or fl oat in water if it were made from a material whose density was the same as that of the planet Saturn (mass 5 5.7 3 1026 kg, radius 5 6.0 3 107 m)? Provide a reason for your answer

A water line with an internal radius of 6.5 3 1023 m is connected to a shower head that has 12 holes. The speed of the water in the line is 1.2 m/s. (a) What is the volume fl ow rate in the line? (b) At what speed does the water leave one of the holes (eff ective hole radius 5 4.6 3 1024 m) in the head?

A log splitter uses a pump with hydraulic oil to push a piston, which is attached to a chisel. The pump can generate a pressure of 2.0 3 107 Pa in the hydraulic oil, and the piston has a radius of 0.050 m. In a stroke lasting 25 s, the piston moves 0.60 m. What is the power needed to operate the log splitters pump?

An object is solid throughout. When the object is completely submerged in ethyl alcohol, its apparent weight is 15.2 N. When completely submerged in water, its apparent weight is 13.7 N. What is the volume of the object?

Mercury is poured into a tall glass. Ethyl alcohol (which does not mix with mercury) is then poured on top of the mercury until the height of the ethyl alcohol itself is 110 cm. The air pressure at the top of the ethyl alcohol is one atmosphere. What is the absolute pressure at a point that is 7.10 cm below the ethyl alcoholmercury interface?

A tube is sealed at both ends and contains a 0.0100-m-long portion of liquid. The length of the tube is large compared to 0.0100 m. There is no air in the tube, and the vapor in the space above the liquid may be ignored. The tube is whirled around in a horizontal circle at a constant angular speed. The axis of rotation passes through one end of the tube, and during the motion, the liquid collects at the other end. The pressure experienced by the liquid is the same as it would experience at the bottom of the tube, if the tube were completely fi lled with liquid and allowed to hang vertically. Find the angular speed (in rad/s) of the tube.

A gold prospector fi nds a solid rock that is composed solely of quartz and gold. The mass and volume of the rock are, respectively, 12.0 kg and 4.00 3 1023 m3 . Find the mass of the gold in the rock.

A fountain sends a stream of water straight up into the air to a maximum height of 5.00 m. The eff ective cross-sectional area of the pipe feeding the fountain is 5.00 3 1024 m2 . Neglecting air resistance and any viscous eff ects, determine how many gallons per minute are being used by the fountain. (Note: 1 gal 5 3.79 3 1023 m3 .)

As the drawing illustrates, a pond has the shape of an inverted cone with the tip sliced off and has a depth of 5.00 m. The atmospheric pressure above the pond is 1.01 3 105 Pa. The circular top surface (radius 5 R2) and circular bottom surface (radius 5 R1) of the pond are both parallel to the ground. The magnitude of the force acting on the top surface is the same as the magnitude of the force acting on the bottom surface. Obtain (a) R2 and (b) R1.

A lighter-than-air balloon and its load of passengers and ballast are fl oating stationary above the earth. Ballast is weight (of negligible volume) that can be dropped overboard to make the balloon rise. The radius of this balloon is 6.25 m. Assuming a constant value of 1.29 kg/m3 for the density of air, determine how much weight must be dropped overboard to make the balloon rise 105 m in 15.0 s.

A siphon tube is useful for removing liquid from a tank. The siphon tube is fi rst fi lled with liquid, and then one end is inserted into the tank. Liquid then drains out the other end, as the drawing illustrates. (a) Using reasoning similar to that employed in obtaining Torricellis theorem (see Example 15), derive an expression for the speed v of the fl uid emerging from the tube. This expression should give v in terms of the vertical height y and the acceleration due to gravity g. (Note that this speed does not depend on the depth d of the tube below the surface of the liquid.) (b) At what value of the vertical distance y will the siphon stop working? (c) Derive an expression for the absolute pressure at the highest point in the siphon (point A) in terms of the atmospheric pressure P0, the fl uid density r, g, and the heights h and y. (Note that the fl uid speed at point A is the same as the speed of the fl uid emerging from the tube, because the cross-sectional area of the tube is the same everywhere.)

An aneurysm is an abnormal enlargement of a blood vessel such as the aorta. Because of the aneurysm, the normal cross-sectional area A1 of the aorta increases to a value of A2 5 1.7A1. The speed of the blood (r 5 1060 kg/m3 ) through a normal portion of the aorta is v1 5 0.40 m/s. Assuming that the aorta is horizontal (the person is lying down), determine the amount by which the pressure P2 in the enlarged region exceeds the pressure P1 in the normal region.

The figure shows a rear view of a loaded two-wheeled wheelbarrow on a horizontal surface. It has balloon tires and a weight W 5 684 N, which is uniformly distributed. The left tire has a contact area with the ground of AL 5 6.6 3 1024 m2 , whereas the right tire is underinflated and has a contact area of AR 5 9.9 3 1024 m2 . Concepts: (i) Force is a vector. Therefore both a direction and a magnitude are needed to specify it. Are both a direction and magnitude needed to specify a pressure? (ii) How is the force each tire applies to the ground related to the force the ground applies to each tire? (iii) Do the left and right tires apply the same force to the ground? Explain. (iv) Do the left and right tires apply the same pressure to the ground? Calculations: Find the force and pressure that each tire applies to the ground.

A father (weight W 5 830 N) and his daughter (weight W 5 340 N) are spending the day at the lake. They are each sitting on a beach ball that is just submerged beneath the water (see the fi gure). Concepts: (i) Each ball is in equilibrium, being stationary and having no acceleration. Thus, the net force acting on each ball is zero. What balances the downward-acting weight in each case? (ii) In which case is the buoyant force greater? (iii) In this situation, what determines the magnitude of the buoyant force? (iv) Which beach ball has the larger radius? Calculations: Ignoring the weight of the air in each ball, and the volumes of their legs that are under the water, fi nd the radius of each ball.