Solved: A fish maintains its depth in fresh water by

A fish maintains its depth in fresh water by adjusting the air content of porous bone or air sacs to make its average density the same as that of the water. Suppose that with its air sacs collapsed, a fish has a density of 1.08 g/cm3. To what fraction of its expanded body volume must the fish inflate the air sacs to reduce its density to that of water?

A partially evacuated airtight container has a tight-fitting lid of surface area 77 m2 and negligible mass. If the force required to remove the lid is 480 N and the atmospheric pressure is 1.0 X 105 Pa, what is the internal air pressure?

Find the pressure increase in the fluid in a syringe when a nurse applies a force of 42 N to the syringe's circular piston, which has a radius of 1.1 cm.

Three liquids that will not mix are poured into a cylindrical container. The volumes and densities of the liquids are 0.50 L, 2.6 g/cm3; 0.25 L, 1.0 g/cm3; and 0.40 L, 0.80 g/cm3. What is the force on the bottom of the container due to these liquids? One liter = 1 L = 1000 cm3. (Ignore the contribution due to the atmosphere.)

An office window has dimensions 3.4 m by 2.1 m. As a result of the passage of a storm, the outside air pressure drops to 0.96 atm, but inside the pressure is held at 1.0 atm. What net force pushes out on the window?

You inflate the front tires on your car to 28 psi. Later, you measure your blood pressure, obtaining a reading of 120/80, the readings being in mm Hg. In metric countries (which is to say, most of the world), these pressures are customarily reported in kilopascals (kPa). In kilopascals, what are (a) your tire pressure and (b) your blood pressure?

In 1654 Otto von Guericke, inventor of the air pump, gave a demonstration before the noblemen of the Holy Roman Empire in which two teams of eight horses could not pull apart two evacuated brass hemispheres. (a) Assuming the hemispheres have (strong) thin walls, so that R in Fig. 14-29 may be considered both the inside and outside radius, show that the force F required to pull apart the hemi- Fig. 14-29 Problem 7. spheres has magnitude F = 1TR2 D.p, where D.p is the difference between the pressures outside and inside the sphere. (b) Taking R as 30 cm, the inside pressure as 0.10 atm, and the outside pressure as 1.00 atm, find the force magnitude the teams of horses would have had to exert to pull apart the hemispheres. (c) Explain why one team of horses could have proved the point just as well if the hemispheres were attached to a sturdy wall.

The bends during/fight. Anyone who scuba dives is advised not to fly within the next 24 h because the air mixture for diving can introduce nitrogen to the bloodstream. Without allowing the nitrogen to come out of solution slowly, any sudden air-pressure reduction (such as during airplane ascent) can result in the nitrogen forming bubbles in the blood, creating the bends, which can be painful and even fatal. Military special operation forces are especially at risk. What is the change in pressure on such a special-op soldier who must scuba dive at a depth of 20 m in seawater one day and parachute at an altitude of 7.6 km the next day? Assume that the average air density within the altitude range is 0.87 kg/m3.

Blood pressure in Argentinosaurus. (a) If this longnecked, gigantic sauropod had a head height of 21 m and a heart height of 9.0 m, what (hydrostatic) gauge pressure in its blood was required at the heart such that the blood pressure at the brain was 80 torr (just enough to perfuse the brain with blood)? Assume the blood had a density of 1.06 X 103 kg/m3. (b) What was the blood pressure (in torr or mm Hg) at the feet?

The plastic tube in Fig. 14-30 has a cross-sectional area of 5.00 cm2. The tube is filled with water until the short arm (of length d = 0.800 m) is full. Then the short arm is sealed and more water is gradually poured into the long arm. If the seal will pop off when the force on it exceeds 9.80 N, what total height of water in the long arm will put the seal on the verge of popping?

Giraffe bending to drink. In a giraffe with its head 2.0 m above its heart, and its heart 2.0 m above its feet, the (hydrostatic) gauge pressure in the blood at its heart is 250 torr. Assume that the giraffe stands upright and the blood density is 1.06 X 103 kg/m3. In torr (or mm Hg), find the (gauge) blood pressure (a) at the brain (the pressure is enough to perfuse the brain with blood, to keep the giraffe from fainting) and (b) at the feet (the pressure must be countered by tight-fitting skin acting like a pressure stocking). (c) If the giraffe were to lower its head to drink from a pond without splaying its legs and moving slowly, what would be the increase in the blood pressure in the brain? (Such action would probably be lethal.)

The maximum depth dOl ax that a diver can snorkel is set by the density of the water and the fact that human lungs can function against a maximum pressure difference (between inside and outside the chest cavity) of 0.050 atm. What is the difference in dOl ax for fresh water and the water of the Dead Sea (the saltiest natural water in the world, with a density of 1.5 X 103 kg/m3)?

At a depth of 10.9 km, the Challenger Deep in the Marianas Trench of the Pacific Ocean is the deepest site in any ocean. Yet, in 1960, Donald Walsh and Jacques Piccard reached the Challenger Deep in the bathyscaph Trieste. Assuming that seawater has a uniform density of 1024 kg/m3, approximate the hydrostatic pressure (in atmospheres) that the Trieste had to withstand. (Even a slight defect in the Trieste structure would have been disastrous.)

Calculate the hydrostatic difference in blood pressure between the brain and the foot in a person of height 1.83 m. The density of blood is 1.06 X 103 kg/m3.

What gauge pressure must a machine produce in order to suck mud of density 1800 kg/m3 up a tube by a height of 1.5 m?

Snorkeling by humans and elephants. When a person snorkels, the lungs are connected directly to the atmosphere through the snorkel tube and thus are at atmospheric pressure. In atmospheres, what is the difference D.p between this internal air pressure and the water pressure against the Fig. 14-31 Problem 16. body if the length of the snorkel tube is (a) 20 cm (standard situation) and (b) 4.0 m (probably lethal situation)? In the latter, the pressure difference causes blood vessels on the walls of the lungs to rupture, releasing blood into the lungs. As depicted in Fig. 14-31, an elephant can safely snorkel through its trunk while swimming with its lungs 4.0 m below the water surface because the membrane around its lungs contains connective tissue that holds and protects the blood vessels, preventing rupturing.

Crew members attempt to escape from a damaged submarine 100 m below the surface. What force must be applied to a pop-out hatch, which is 1.2 m by 0.60 m, to push it out at that depth? Assume that the density of the ocean water is 1024 kg/m3 and the internal air pressure is at 1.00 atm.

In Fig. 14-32, an open tube of length L = 1.8 m and cross-sectional area A = 4.6 cm2 is fixed to the top of a cylindrical barrel of diameter D = 1.2 m and height H = 1.8 m. The barrel and tube are filled with water (to the top of the tube). Calculate the ratio of the hydrostatic force on the bottom of the barrel to the gravitational force on the water contained in the barrel. Why is that ratio not equal to 1.0? (You need not consider the atmospheric pressure.)

A large aquarium of height 5.00 m is filled with fresh water to a depth of 2.00 m. One wall of the aquarium consists of thick plastic 8.00 m wide. By how much does the total force on that wall increase if the aquarium is next filled to a depth of 4.00 m?

The L..-shaped tank shown in Fig. 14- 33 is filled with water and is open at the top. If d = 5.0 m, what is the force due to the water (a) on face A and (b) on face B?

SSM Two identical cylindrical vessels with their bases at the same level each contain a liquid of density 1.30 X 103 kg/m3. The area of each base is 4.00 cm2, but in one vessel the liquid height is 0.854 m and in the other it is 1.560 m. Find the work done by the gravitational force in equalizing the levels when the two vessels are connected.

g-LOC in dogfights. When a pilot takes a tight turn at high speed in a modern fighter airplane, the blood pressure at the brain level decreases, blood no longer perfuses the brain, and the blood in the brain drains. If the heart maintains the (hydrostatic) gauge pressure in the aorta at 120 torr (or mm Hg) when the pilot undergoes a horizontal centripetal acceleration of 4g, what is the blood pressure (in torr) at the brain, 30 cm radially inward from the heart? The perfusion in the brain is small enough that the vision switches to black and white and narrows to "tunnel vision" and the pilot can undergo g- LOC ("g-induced loss of consciousness"). Blood density is 1.06 X 103 kg/m3.

In analyzing certain geological features, it is often appropriate to assume that the pressure at some horizontal level of compensation, deep inside Earth, is the same over a large region and is equal to the pressure due to the gravitational force on the overlying material. Thus, the pressure on the level of compensation is given by the fluid pressure formula. This model requires, for one thing, that mountains have roots of continental rock extending into the denser ({ Fig. 14-34 Problem 23. mantle (Fig. 14-34). Consider a mountain of height H = 6.0 km on a continent of thickness T = 32 km. The continental rock has a density of 2.9 g/cm3, and beneath this rock the mantle has a density of 3.3 g/cm3. Calculate the depth D of the root. (Hint: Set the pressure at points a and b equal; the depth y of the level of compensation will cancel out.)

In Fig. 14-35, water stands at depth D = 35.0 m behind the vertical upstream face of a dam of width W = 314 m. Find (a) the net horizontal force on the dam from the gauge pressure of the water and (b) the net torque due to that force about a Fig. 14-35 Problem 24. horizontal line through 0 parallel to the (long) width of the dam. This torque tends to rotate the dam around that line, which would cause the dam to fail. (c) Find the moment arm of the torque.

In one observation, the column in a mercury barometer (as is shown in Fig. 14-5a) has a measured height h of 740.35 mm. The temperature is -5.0C, at which temperature the density of mercury p is 1.3608 X 104 kg/m3. The free-fall acceleration g at the site of the barometer is 9.7835 rn/s2 What is the atmospheric pressure at that site in pascals and in torr (which is the common unit for barometer readings)?

To suck lemonade of density 1000 kg/m3 up a straw to a maximum height of 4.0 cm, what minimum gauge pressure (in atmospheres) must you produce in your lungs?

What would be the height of the atmosphere if the air density (a) were uniform and (b) decreased linearly to zero with height? Assume that at sea level the air pressure is 1.0 atm and the air density is 1.3 kg/m3.

A piston of cross-sectional area a is used in a hydraulic press to exert a small force of magnitude f on the enclosed liquid. A connecting pipe leads to a larger piston of cross-sectional area A (Fig. 14-36). (a) What force magnitude Fwill the larger piston sustain without moving? (b) If the piston diameters are 3.80 cm and 53.0 cm, what force (/ Fig. 14-36 Problem 28. F magnitude on the small piston will balance a 20.0 kN force on the large piston?

In Fig. 14-37, a spring of spring constant 3.00 X 104 N/m is between a rigid beam and the output piston of a hydraulic lever. An empty container with negligible mass sits on the input piston. The input piston has area Ai, and the Beamu Container Spring"=l output piston has area 18.0Ai Fig. 14-37 Problem 29. Initially the spring is at its rest length. How many kilograms of sand must be (slowly) poured into the container to compress the spring by 5.00 cm?

A 5.00 kg object is released from rest while fully submerged in a liquid. The liquid displaced by the submerged object has a mass of 3.00 kg. How far and in what direction does the object move in 0.200 s, assuming that it moves freely and that the drag force on it from the liquid is negligible?

volume V submerged and in oil with 0.90V submerged. Find the density of (a) the wood and (b) the oil.

In Fig. 14-38, a cube of edge length L = 0.600 m and mass 450 kg is suspended by a rope in an open tank of liquid of density 1030 kg/m3. Find (a) the magnitude of the total downward force on the top of the cube from the liquid and the atmosphere, assuming atmospheric pressure is 1.00 atm, (b) the T L -~ magnitude of the total upward Fig. 14-38 Problem 32. force on the bottom of the cube, and (c) the tension in the rope. (d) Calculate the magnitude of the buoyant force on the cube using Archimedes' principle. What relation exists among all these quantities?

An iron anchor of density 7870 kg/m3 appears 200 N lighter in water than in air. (a) What is the volume of the anchor? (b) How much does it weigh in air?

A boat floating in fresh water displaces water weighing 35.6 kN. (a) What is the weight of the water this boat displaces when floating in salt water of density 1.10 X 103 kg/m3? (b) What is the difference between the volume of fresh water displaced and the volume of salt water displaced?

Three children, each of weight 356 N, make a log raft by lashing together logs of diameter 0.30 m and length 1.80 m. How many logs will be needed to keep them afloat in fresh water? Take the density of the logs to be 800 kg/m.

In Fig. 14-39a, a rectangular block is gradually pushed facedown into a liquid. The block has height d; on the bottom and top the face area is A = 5.67 cm2 Figure 14-39b gives the apparent weight Wapp of the block as a function of the depth h of its lower face. The scale on the vertical axis is set by W, = 0.20 N. What is the density of the liquid?

A hollow spherical iron shell floats almost completely submerged in water. The outer diameter is 60.0 cm, and the density of iron is 7.87 g/cm3. Find the inner diameter

A small solid ball is released from rest while fully submerged in a liquid and then its ki- ~ netic energy is measured when it has ~ moved 4.0 cm in the liquid. Figure 14-40 gives the results after many liquids are used: The kinetic energy K is plotted versus the liquid density o 2 Plig, and Ks = 1.60 J sets the scale on Fig. 14-40 Problem 38. the vertical axis. What are (a) the density and (b) the volume of the ball?

A hollow sphere of inner radius 8.0 cm and outer radius 9.0 cm floats half-submerged in a liquid of density 800 kg/m3. (a) What is the mass ofthe sphere? (b) Calculate the density of the material of which the sphere is made.

Lurking alligators. An alligator waits for prey by floating with only the top of its head exposed, so that the prey cannot easily see it. One way it can adjust the extent of Fig. 14-41 Problem 40. sinking is by controlling the size of its lungs. Another way may be by swallowing stones (gastrolithes) that then reside in the stomach. Figure 14-41 shows a highly simplified model (a "rhombohedron gater") of mass 130 kg that roams with its head partially exposed. The top head surface has area 0.20 m2. If the alligator were to swallow stones with a total mass of 1.0% of its body mass (a typical amount),how far would it sink?

What fraction of the volume of an iceberg (density 917 kg/m3) would be visible if the iceberg floats (a) in the ocean (salt water, density 1024 kg/m3) and (b) in a river (fresh water, density 1000 kg/m3)? (When salt water freezes to form ice, the salt is excluded. So, an iceberg could provide fresh water to a community.)

A flotation device is in the shape of a right cylinder, with a height of 0.500 m and a face area of 4.00 m2 on top and bottom, and its density is 00400 times that of fresh water. It is initially held fully submerged in fresh water, with its top face at the water surface. 111en it is allowed to ascend gradually until it begins to float. How much work does the buoyant force do on the device during the ascent?

When researchers find a reasonably complete fossil of a dinosaur, they can determine the mass and weight of the living dinosaur with a scale model sculpted from plastic and based on the dimensions of the fossil bones. The scale of the model is 1120; that is, lengths are 1/20 Fig. 14-42 Problem 43. actual length, areas are (1/20)2 actual areas, and volumes are (1120)3 actual volumes. First, the model is suspended from one arm of a balance and weights are added to the other arm until equilibrium is reached. Then the model is fully submerged in water and enough weights are removed from the second arm to reestablish equilibrium (Fig. 14-42). For a model of a particular T. rex fossil, 637.76 g had to be removed to reestablish equilibrium. What was the volume of (a) the model and (b) the actual T. rex? (c) If the density of T. rex was approximately the density of water, what was its mass?

A block of wood has a mass of 3.67 kg and a density of 600 kg/m3. It is to be loaded with lead (1.14 X 104 kg/m3) so that it will float in water with 0.900 of its volume submerged. What mass of lead is needed if the lead is attached to (a) the top of the wood and (b) the bottom of the wood?

An iron casting containing a number of cavities weighs 6000 N in air and 4000 N in water. What is the total volume of all the cavities in the casting? The density of iron (that is, a sample with no cavities) is 7.87 g/cm3

Suppose that you release a small ball from rest at a depth of 0.600 m below the smiace in a pool of water. If the density of the ball is 0.300 that of water and if the drag force on the ball from the water is negligible, how high above the water surface will the ball shoot as it emerges from the water? (Neglect any transfer of energy to the splashing and waves produced by the emerging ball.)

The volume of air space in the passenger compartment of an 1800 kg car is 5.00 m3 The volume of the motor and front wheels is 0.750 m3, and the volume of the rear wheels, gas tank, and trunk is 0.800 m3; water cannot enter these two regions. The car rolls into a lake. (a) At first, no water enters the passenger compartment. How much of the car, in cubic meters, is below the water surface with the car floating (Fig. 14-43)? (b) As water slowly enters, the car sinks. How many cubic meters of water are in the car as it disappears below the water surface? (The car, with a heavy load in the trunk, remains horizontal.)

Figure 14-44 shows an iron ball suspended by thread of negligible mass from an upright cylinder that floats partially submerged in water. The cylinder has a height of 6.00 cm, a face area of 12.0 cm2 on the top and bottom, and a density of 0.30 g/cm3, and 2.00 cm of its height is above the water sUliace. What is the radius of the iron ball?

Canal effect. Figure 14-45 shows an anchored barge that extends across a canal by distance d = 30 m and into the water by distance b = 12 m. The canal has a width D = 55 m, a water depth H = 14 m, and a uniform waterflow speed Vi = 1.5 m/s. Assume that the flow around the barge is uniform. As the water passes the bow, the water level undergoes a dramatic dip known as the canal effect. If the dip has depth h = 0.80 m, what is the water speed alongside Fig. 14-45 Problem 49. the boat through the vertical cross sections at (a) point a and (b) point b? The erosion due to the speed increase is a common concern to hydraulic engineers.

Figure 14-46 shows two sections of an old pipe system that runs through a hill, with distances dA = dB = 30 m and D = 110 m. On each side of the hill, the pipe radius is 2.00 cm. However, the radius of the pipe inside the hill is no longer known. To determine it, hydraulic engineers first establish that water flows through the left and right sections at 2.50 mls. Then they release a dye in the water at point A and find that it takes 88.8 s to reach point B. What is the average radius of the pipe within the hill? " .. /~ ~ -~- ~ Fig. 14-46 Problem 50.

A garden hose with an internal diameter of 1.9 cm is connected to a (stationary) lawn sprinkler that consists merely of a container with 24 holes, each 0.13 cm in diameter. If the water in the hose has a speed of 0.91 mis, at what speed does it leave the sprinkler holes?

Two streams merge to form a river. One stream has a width of 8.2 m, depth of 304 m, and current speed of 2.3 m/s. The other stream is 6.8 m wide and 3.2 m deep, and flows at 2.6 m/s. If the river has width 10.5 m and speed 2.9 mis, what is its depth?

Water is pumped steadily out of a flooded basement at a speed of 5.0 mls through a uniform hose of radius 1.0 cm. The hose passes out through a window 3.0 m above the waterline. What is the power of the pump?

The water flowing through a 1.9 cm (inside diameter) pipe flows out through three 1.3 cm pipes. (a) If the flow rates in the three smaller pipes are 26, 19, and 11 Llmin, what is the flow rate in the 1.9 cm pipe? (b) What is the ratio of the speed in the 1.9 cm pipe to that in the pipe carrying 26 Llmin?

How much work is done by pressure in forcing 1.4 m3 of water through a pipe having an internal diameter of 13 mm if the difference in pressure at the two ends of the pipe is 1.0 atm?

Suppose that two tanks, 1 and 2, each with a large opening at the top, contain different liquids. A small hole is made in the side of each tank at the same depth h below the liquid surface, but the hole in tank 1 has half the cross-sectional area of the hole in tank 2. (a) What is the ratio p/ P2 of the densities of the liquids if the mass flow rate is the same for the two holes? (b) What is the ratio RVIIRv2 ofthe volume flow rates from the two tanks? (c) At one instant, the liquid in tank 1 is 12.0 cm above the hole. If the tanks are to have equal volume flow rates, what height above the hole must the liquid in tank 2 be just then?

A cylindrical tank with a large diameter is filled with water to a depth D = 0.30 m. A hole of cross- sectional area A = 6.5 cm2 in the bottom of the tank allows water to drain out. (a) What is the rate at which water flows out, in cubic meters per second? (b) At what distance below the bottom of the tank is the cross-sectional area of the stream equal to one-half the area of the hole?

The intake in Fig. 14-47 has cross-sectional area of 0.74 m2 and water flow at 0.40 m/s. At the outlet, distance D = 180 m below the intake, the cross-sectional area is smaller than at the intake and the water flows out at 9.5 mls into equipment. What is the pressure dif- Fig. 14-47 Problem 58. ference between inlet and outlet?

Water is moving with a speed of 5.0 mls through a pipe with a cross-sectional area of 4.0 cm2. The water graduall descends 10 m as the pipe cross-sectional area increases to 8.0 cm2 (a) What is the speed at the lower level? (b) If the pressure at the upper level is 1.5 X 105 Pa, what is the pressure at the lower level?

Models of torpedoes are sometimes tested in a horizontal pipe of flowing water, much as a wind tunnel is used to test model airplanes. Consider a circular pipe of internal diameter 25.0 cm and a torpedo model aligned along the long axis of the pipe. The model has a 5.00 cm diameter and is to be tested with water flowing past it at 2.50 mls. (a) With what speed must the water flow in the part of the pipe that is unconstricted by the model? (b) What will the pressure difference be between the constricted and unconstricted parts of the pipe?

A water pipe having a 2.5 cm inside diameter carries water into the basement of a house at a speed of 0.90 mls and a pressure of 170 kPa. If the pipe tapers to 1.2 cm and rises to the second floor 7.6 m above the input point, what are the (a) speed and (b) water pressure at the second floor?

A pitot tube (Fig. 14-48) is used to determine the airspeed of an airplane. It consists of an outer tube with a number of small holes B (four are shown) that allow air into the tube; that tube is connected to one arm of a U-tube. The other arm of the Utube is connected to hole A at the front end of the device, which points in the direction the plane is headed. At A the air becomes stagnant so that v A = O. At B, however, the speed of the air presumably equals the airspeed v of the plane. (a) Use Bernoulli's where p is the density of the liquid in the U-tube and h is the difference in the liquid levels in that tube. (b) Suppose that the tube contains alcohol and the level difference h is 26.0 cm. What is the plane's speed relative to the air? The density of the air is 1.03 kg/m3 and that of alcohol is 810 kg/m3.

A pitot tube (see Problem 62) on a high-altitude aircraft measures a differential pressure of 180 Pa. What is the aircraft's airspeed if the density of the air is 0.031 kg/m3?

In Fig. 14-49, water flows through a horizontal pipe and then out into the atmosphere at a speed VI = 15 m/s. The diameters of the left and right sections of the pipe are Fig. 14-49 Problem 64. 5.0 cm and 3.0 cm. (a) What volume of water flows into the atmosphere during a 10 min period? In the left section of the pipe, what are (b) the speed V2 and (c) the gauge pressure?

A venturi meter is used to measure the flow speed of a fluid in a pipe. The meter is connected between two sections of the pipe (Fig. 14-50); the cross-sectional area A of the entrance and exit of the meter matches the pipe's cross-sectional area. Between the entrance and exit, the fluid flows from the pipe with speed V and then through a narrow "throat" of crossMeter entrance t~lf~A .... \"/""'~R' .... Pipe Venturi meter ~ v ::::;:--a-. -~-I> 2 .. Meter exit .. A~,c Pipe Manometer Fig. 14-50 Problems 65 and 66. sectional area a with speed v. A manometer connects the wider portion of the meter to the narrower portion. The change in the fluid's speed is accompanied by a change D.p in the fluid's pressure, which causes a height difference h of the liquid in the two arms of the manometer. (Here D.p means pressure in the throat minus pressure in the pipe.) (a) By applying Bernoulli's equation and the equation of continuity to points 1 and 2 in Fig. 14-50, show that v = I 2a2 D.p \j p(a2 - A2) , where p is the density of the fluid. (b) Suppose that the fluid is fresh water, that the cross-sectional areas are 64 cm2 in the pipe and 32 cm2 in the throat, and that the pressure is 55 kPa in the pipe and 41 kPa in the throat. What is the rate of water flow in cubic meters per second?

Consider the venturi tube of Problem 65 and Fig. 14-50 without the manometer. Let A equal 5a. Suppose the pressure PI at A is 2.0 atm. Compute the values of (a) the speed Vat A and (b) the speed v at a that make the pressure P2 at a equal to zero. (c) Compute the corresponding volume flow rate if the diameter at A is 5.0 cm. The phenomenon that occurs at a when P2 falls to nearly zero is known as cavitation. The water vaporizes into small bubbles.

In Fig. 14-51, the fresh water behind a reservoir dam has depth D = 15 m. A horizontal pipe 4.0 cm in diameter passes through the dam at depth d = 6.0 m. A plug secures the pipe opening. (a) Find the magnitude of the frictional force between plug and pipe wall. (b) The plug is removed. What water volume exits the pipe in 3.0 h?

Fresh water flows horizontally from pipe section 1 of cross-sectional area A I into pipe section 2 of cross-sectional area A 2 Figure 14-52 gives a plot of the pressure difference P2 - PI versus the inverse area squared Aj2 that would be expected for a volume flow rate of a certain value if the water flow were laminar under all t d T D ~ L~ Fig. 14-51 Problem 67. Fig. 14-52 Problem 68. circumstances. The scale on the vertical axis is set by D.ps = 300 kN/m2 For the conditions of the figure, what are the values of (a) A2 and (b) the volume flow rate?

A liquid of density 900 kg/m3 flows through a horizontal pipe that has a cross-sectional area of 1.90 X 10-2 m2 in region A and a cross-sectional area of 9.50 X 10 - 2 m2 in region B. The pressure difference between the two regions is 7.20 X 103 Pa. What are (a) the volume flow rate and (b) the mass flow rate?

In Fig. 14-53, water flows steadily from the left pipe section R Fig. 14-53 Problem 70 (radius'l = 2.00R), through the middle section (radius R), and into the right section (radius '3 = 3.00R). The speed of the water in the middle section is 0.500 m/s. What is the net work done on 0.400 m3 of the water as it moves from the left section to the right section?

Figure 14-54 shows a stream of water flowing through a hole at depth h = 10 cm in a tank holding water to height H = 40 cm. (a) At what distance x does the stream strike the floor? (b) At what depth should a second hole be made to give the same value of x? (c) At what depth should a hole be made to Fig. 14-54 Problem 71. maximize x?

A very simplified schematic of the rain drainage system for a home is shown in Fig. 14-55. Rain falling on the slanted roof runs off into gutters around the roof edge; it then drains through downspouts (only one is shown) into a main drainage pipe M below the basement, which carries the water to an even larger pipe below the street. In Fig. 14-55, a floor drain in the basement is also connected to drainage pipe M. Suppose the following apply: 1. the downspouts have height hI = 11 m, 2. the floor drain has height h2 = 1.2 m, 3. pipe M has radius 3.0 cm, 4. the house has side width w = 30 m and front length L = 60 m, 5. all the water striking the roof goes through pipe M, 6. the initial speed of the water in a downspout is negligible, 7. the wind speed is negligible (the rain falls vertically). At what rainfall rate, in centimeters per hour, will water from pipe M reach the height of the floor drain and threaten to flood the basement? T LI----1lI---+jH JvI Fig. 14-55 Problem 72.

About one-third of the body of a person floating in the Dead Sea will be above the waterline. Assuming that the human body density is 0.98 g/cm3, find the density of the water in the Dead Sea. (Why is it so much greater than 1.0 g/cm3?)

A simple open U-tube contains mercury. When 11.2 cm of water is poured into the right arm of the tube, how high above its initiallevel does the mercury rise in the left arm?

If a bubble in sparkling water accelerates upward at the rate of 0.225 m/s2 and has a radius of 0.500 mm, what is its mass? Assume that the drag force on the bubble is negligible.

Suppose that your body has a uniform density of 0.95 times that of water. (a) If you float in a swimming pool, what fraction of your body's volume is above the water surface? Quicksand is a fluid produced when water is forced up into sand, moving the sand grains away from one another so they are no longer locked together by friction. Pools of quicksand can form when water drains underground from hills into valleys where there are sand pockets. (b) If you float in a deep pool of quicksand that has a density 1.6 times that of water, what fraction of your body's volume is above the quicksand surface? (c) In particular, are you submerged enough to be unable to breathe?

A glass ball of radius 2.00 cm sits at the bottom of a container of milk that has a density of 1.03 g/cm3. The normal force on the ball from the container's lower surface has magnitude 9.48 X 10-2 N. What is the mass of the ball?

Caught in an avalanche, a skier is fully submerged in flowing snow of density 96 kg/m3. Assume that the average density of the skier, clothing, and skiing equipment is 1020 kg/m3. What percentage of the gravitational force on the skier is offset by the buoyant force from the snow?

An object hangs from a spring balance. The balance registers 30 N in air, 20 N when this object is immersed in water, and 24 N when the object is immersed in another liquid of unknown density. What is the density of that other liquid?

In an experiment, a rectangular block with height h is allowed to float in four separate liquids. In the first liquid, which is water, it floats fully submerged. In liquids A, B, and C, it floats with heights h/2, 2h/3, and h/4 above the liquid surface, respectively. What are the relative densities (the densities relative to that of water) of (a) A, (b) B, and (c) C?

Figure 14-30 shows a modified U-tube: the right arm is shorter than the left arm. The open end of the right arm is height d = 10.0 cm above the laboratory bench. The radius throughout the tube is 1.50 cm. Water is gradually poured into the open end of the left arm until the water begins to flow out the open end of the right arm. Then a liquid of density 0.80 g/cm3 is gradually added to the left arm until its height in that arm is 8.0 cm (it does not mix with the water). How much water flows out of the right arm?

What is the acceleration of a rising hot-air balloon if the ratio of the air density outside the balloon to that inside is 1.39? Neglect the mass of the balloon fabric and the basket.

Figure 14-56 shows a siphon, which is a device for removing liquid from a container. Tube ABC must initially be filled, but once this has been done, liquid will flow through the tube until the liquid surface in the container is level with the tube opening at A. The liquid has density 1000 kg/m3 and negligible viscosity. The distances shown are hi = 25 cm, d = 12 cm, and h2 = 40 cm. (a) With what speed does the liquid emerge from the tube at C? (b) If the atmospheric pressure is 1.0 X 105 Pa, what is the pressure in the liquid at the topmost point B? (c) Theoretically, what is the greatest possible height h, that a siphon can lift water?

When you cough, you expel air at high speed through the trachea and upper bronchi so that the air will remove excess mucus lining the pathway. You produce the high speed by this procedure: You breathe in a large amount of air, trap it by closing the glottis (the narrow opening in the larynx), increase the air pressure by contracting the lungs, partially collapse the trachea and upper bronchi to narrow the pathway, and then expel the air through the pathway by suddenly reopening the glottis. Assume that during the expulsion the volume flow rate is 7.0 X 10-3 m3/s. What multiple of the speed of sound Vs (= 343 m/s) is the airspeed through the trachea if the trachea diameter (a) remains its normal value of 14 mm and (b) contracts to 5.2 mm?

A tin can has a total volume of 1200 cm3 and a mass of 130 g. How many grams of lead shot of density 11.4 g/cm3 could it carry without sinking in water?