Deck 13: Fluids

Question 1

Which of the following are the SI units for specific gravity?

A) kg/m³
B) g/cm³
C) lb/ft³
D) lb · s²/ft⁴
E) specific gravity has no units

Answer 1

specific gravity has no units

Question 2

A piece of wood is floating at the surface of some water as illustrated. The wood has a circular cross section and a height h = 3.0 cm. The density of the wood is 0.41 g/cm³. The distance y from the surface of the water to the bottom of the wood is

A) impossible to determine because the area of the cross section is not given.
B) 0.81 cm
C) 3.2 cm
D) 1.2 cm
E) None of these is correct.

Answer 2

1.2 cm

Question 3

What is the gauge pressure at a depth of 6 cm in a glass filled with 4 cm of mercury and
4 cm of water? Water has a density of 1000 kg/m³, and mercury has a density 13.6 times as great.

A) 3.1 kPa
B) 5.6 kPa
C) 5.8 kP
D) 310 kPa
E) 560 kPa

Answer 3

3.1 kPa

Question 4

A block of material has a density $\rho$ . A second block of equal volume has three times the mass of the first. What is the density of the second block?

A) $\rho$
B) 3 $\rho$
C) $\rho$ /3
D) 9 $\rho$
E) $\rho$ /9

Question 5

An open U-tube has water to a height h on both sides, as shown. The cross-sectional area of the left-hand tube is A₁ = 1.50 cm², and that of the right-hand tube is A₂ = 0.50 cm². A light oil (which does not mix with water) with a density of 0.83 g/cm³ is added to the right-hand side. When equilibrium is reached, which of the following is correct?

A) The level on the right-hand side is higher than that on the left.
B) The level on the right-hand side is lower than that on the left.
C) The levels of the two sides are the same.
D) The difference in the heights depends on A₁ and A₂.
E) None of these is correct.

Question 6

A glass is filled with water. The gauge pressure at the top of the glass is zero and the gauge pressure at the bottom is P. A second glass with three times the height and twice the diameter is also filled with water. What is the pressure at the bottom of the second glass?

A) P
B) 2P
C) 3P
D) 3P/2
E) 3P/4

Question 7

A tube with a radius of 4.2 cm is holding oil that has a density of 0.92 g/cm³. The pressure in the oil at a depth of 64 cm from the top of the surface is

A) 5.8 $\times$ 10² Pa
B) 5.8 $\times$ 10³ Pa
C) 1.0 $\times$ 10² Pa
D) 1.0 $\times$ 10⁶ Pa
E) 1.7 $\times$ 10³ Pa

Question 8

Your blood pressure is reported as 50 mm of Hg. The density of mercury is 13.6 g/cm³. Your pressure is equivalent to

A) 6.7 $\times$ 10⁶ Pa
B) 6.8 Pa
C) 6.8 $\times$ 10² Pa
D) 6.7 $\times$ 10³ Pa
E) 3.2 $\times$ 10² Pa

Question 9

At what depth in sea water is the gauge pressure equal to 1 atm? The density of sea water is 1.03 $\times$ 10³ kg/m³.

A) 5 m
B) 7.5 m
C) 10 m
D) 15 m
E) 20 m

Question 10

The left-hand side of an open U-tube has a radius r₁ = 0.82 cm, and the right-hand side has a radius r₂ = 0.41 cm. Mercury and oil are poured into the U-tube. The density of mercury is 13.6 g/cm³. The heights shown in the diagram are h₁ = 3.50 cm and h₂ = 57.3 cm. The density of the oil is approximately

A) 0.83 g/cm³
B) 110 g/cm³
C) 7.9 g/cm³
D) 6.9 g/cm³
E) 1.82 g/cm³

Question 11

Which gas has the lowest density under standard temperature and pressure?

A) hydrogen
B) helium
C) oxygen
D) nitrogen
E) carbon dioxide

Question 12

A block of material has a density $\rho$ . A second block of equal mass has twice the volume of the first. What is the density of the second block?

A) $\rho$
B) 2 $\rho$
C) $\rho$ /2
D) 4 $\rho$
E) $\rho$ /4

Question 13

A flat plate with a negligible mass and an area of 1.0 cm² is placed in a horizontal position well beneath the surface in a liquid that is not moving. The pressure at the location of the plate is P Pa. The total force that arises from the pressure of the liquid on this plate is

A) P N, directed down.
B) P $\times$ 10^-4 N, directed down.
C) P N, directed up.
D) P $\times$ 10^-4 N, directed up.
E) zero.

Question 14

The atmospheric pressure deceases exponentially with height. At 5.5 km, the pressure is half that at sea level. At what height is the pressure one eighth that of sea level?

A) 7.5 km
B) 11 km
C) 16.5 km
D) 22 km
E) 27.5 km

Question 15

If the atmosphere were compressed until it had the density of water, it would cover Earth to a depth of about

A) 0.81 km
B) 4.6 m
C) 1.6 km
D) 76 cm
E) 10 m

Question 16

A penny has a mass of 3.0 g, a diameter of 1.9 cm, and a thickness of 0.15 cm. What is the density of the metal of which it is made?

A) 1.8 g/cm³
B) 3.4 g/cm³
C) 3.5 g/cm³
D) 7.1 g/cm³
E) 4.5 g/cm³

Question 17

A small sphere of wood with a density $\rho$ = 0.40 g/cm³ is held at rest well under the surface of a pool of water. The magnitude of the initial acceleration of the sphere when it is released is

A) 15 m/s²
B) 9.8 m/s²
C) 33 m/s²
D) 23 m/s²
E) 3.4 m/s²

Question 18

Which of the following is the mass density of a material?

A) the material's weight per unit volume
B) the material's mass per unit volume
C) the material's specific gravity
D) the material's volume per unit weight
E) the material's volume per unit mass

Question 19

If the gauge pressure is doubled, the absolute pressure is

A) halved.
B) doubled.
C) unchanged.
D) squared.
E) Not enough information is given to determine the answer.

Question 20

A container of height, h, is filled with water of density $\rho$ , and sealed with a flexible membrane. The container is placed in the space shuttle in orbit. If the air pressure in the shuttle is P_o, the pressure in the middle of the container is

A) P_o
B) P_o + $\rho$ gh
C) $\rho$ gh
D) $\rho$ gh
E) depends how fast the shuttle is moving

Question 21

Use the figure to the right to answer the next problems. A beaker is filled with water. A small plastic container contains a solid bar of aluminum, which has a mass of 40 g, and is placed on the water so that it floats. The water level reads 60 ml. Next, the bar of aluminum is taken out of the container and placed in the water so that it sinks to the bottom.

-The water level in the beaker _____

A) drops.
B) stays unchanged.
C) rises.
D) depends on the type of container
E) unable to tell

Question 22

Is it possible to float an object that is less dense that water when the amount of the water is less than the weight of the object?

A) No, the weight of the water must at least equal the weight of the object.
B) Yes, as long as the container that holds the water allows the water to rise so that the volume of water displaced is equal to the weight of the object.
C) It is not possible to determine the answer.
D) It depends on the density of the object.
E) It depends on the mass of the object.

Question 23

Use the figure to the right to answer the next problems. A beaker is filled with water. A small plastic container contains a solid bar of aluminum, which has a mass of 40 g, and is placed on the water so that it floats. The water level reads 60 ml. Next, the bar of aluminum is taken out of the container and placed in the water so that it sinks to the bottom.

-By how much does the water level change? (density of Al is 2.7 g/cm³)

A) 40 ml
B) 14.8 ml
C) 25.2 ml
D) 0 ml
E) 30 ml

Question 24

A block of wood of relative density 0.750 and dimensions 20.3 cm $\times$ 30.5 cm $\times$ 40.6 cm is tossed into a choppy freshwater lake. After a reasonable time, the approximate vertical dimension above the water will be

A) 2.54 cm
B) 5.08 cm
C) 7.62 cm
D) 10.2 cm
E) 12.7 cm

Question 25

A stone of volume 1.42 $\times$ 10^-2 m³ lies at the bottom of a freshwater lake. If the rock's specific gravity is 3.5, the work required to lift it 1 m through the water is approximately

A) 487 J
B) 139 J
C) 348 J
D) 223 J
E) 469 J

Question 26

The vessels in the figure contain liquids of the same density. The vessel that has the greatest pressure at its base is

A) 1
B) 2
C) 3
D) 4
E) 5

Question 27

Pressure as a function of depth for a certain liquid is plotted on the graph. What is the density of the liquid?

A) 1.76 g/cm³
B) 1.36 g/cm³
C) 0.340 g/cm³
D) 1.70 g/cm³
E) 3.27 g/cm³

Question 28

If a column of liquid 52 cm high supports a column of mercury ( $\rho$ = 13.6 g/cm³) 10 cm high, the density of the liquid is

A) 6.0 g/cm³
B) 2.6 g/cm³
C) 3.8 g/cm³
D) 4.9 g/cm³
E) 5.0 g/cm³

Question 29

Two objects with different volumes have the same apparent weight when submerged in water. If they are placed in a vacuum,

A) both weigh less than before.
B) the one with the smaller volume weighs less than the other.
C) the one with the smaller volume weighs more than the other.
D) they weigh the same.
E) both weigh more than before.

Question 30

The force exerted by a stationary liquid on an inclined rectangular surface at rest in the liquid

A) acts normally to the surface.
B) is exerted equally at all points on the surface.
C) acts parallel to the surface.
D) is independent of the density of the liquid.
E) varies inversely as the depth.

Question 31

According to Pascal's principle, the pressure at every point in a confined liquid

A) depends only on the density of the liquid.
B) is equal to the weight of the liquid.
C) is the same.
D) is changed the same amount by an externally applied pressure.
E) is equal to the externally applied pressure.

Question 32

A beaker is filled with water. A ball of mass m and density $\rho$ < $\rho$ _water is tied to a string. The other end of the string is then tied to the bottom of the beaker so that the ball is completely submerged. What is the tension in the string?

A)
B)
C) mg
D)
E)

Question 33

The U-tube in the figure is sealed at both ends. It contains a gas in A, another gas in B, and mercury in C. The heights of the mercury in the two arms are as shown. The density of mercury is 13.6 g/cm³. If the pressure in A is 1 $\times$ 10⁴ dyn/cm², the pressure in B is

A) 1 $\times$ 10⁴ dyn/cm²
B) 2 $\times$ 10⁴ dyn/cm²
C) 3 $\times$ 10⁴ dyn/cm²
D) 4 $\times$ 10⁴ dyn/cm²
E) 5 $\times$ 10⁴ dyn/cm²

Question 34

Two pistons of a hydraulic lift have radii of 2.67 cm and 20.0 cm. The downward force on the 2.67-cm piston that is required to lift a mass of 2000 kg supported by the 20-cm piston is

A) 350 N
B) 270 N
C) 36 N
D) 1.5 $\times$ 10³ N
E) 2.6 $\times$ 10³ N

Question 35

A ball bearing that has a density of 5.16 g/cm³ is held at rest under the surface of a liquid that has a density of 2.50 g/cm³. The magnitude of the acceleration of the ball bearing just after it is released is

A) 5.0 m/s²
B) 14 m/s²
C) 10 m/s²
D) 6.5 m/s²
E) 1.6 m/s²

Question 36

If the same fluid fills the containers shown, the pressures at the bases are related according to which of the following expressions?

A) P_C < P_A < P_E < P_D < P_B
B) P_E < P_D < P_C < P_B < P_A
C) P_A < P_B < P_C < P_D < P_E
D) P_E < P_D = P_C < P_B < P_A
E) None of these is correct.

Question 37

Two identical beakers are filled with the same amount of water. A ball of mass m is placed in the first beaker so that it floats on the surface while a second identical ball is placed in the second beaker but tied with a string of negligible mass so that the ball is completely submerged. Each beaker is then placed on a scale. Which scale has a higher reading?

A) (a)
B) (b)
C) the same
D) depends on how far the ball is submerged in (b)
E) unable to tell

Question 38

A block of ice 30.5 cm thick floating in fresh water just supports a man weighing 801 N. If the specific gravity of ice is 0.917, the smallest area the block can have is

A) 3.25 m²
B) 3.57 m²
C) 2.88 m²
D) 1.45 m²
E) 0.269 m²

Question 39

A solid wooden sphere of volume 0.0100 m³ floats freely exactly one-half submerged in a liquid of density 800 kg/m³. A lightweight cord is now tied to the sphere and is used to pull the sphere under the surface and hold it completely submerged. What is the tension in the cord?

A) zero
B) 2.00 N
C) 39.2 N
D) 4.00 N
E) 78.4 N

Question 40

Which curve best represents the variation in pressure with depth in a fluid, assuming constant density?

A) 1
B) 2
C) 3
D) 4
E) 5

Question 41

You are floating in a boat in a swimming pool. There are some large stones, with a density of 2.5 g/cm³, in the boat. You throw the stones out of the boat and they sink to the bottom of the pool. The water level h, measured vertically at the end of the pool __________ as the stones are thrown out.

A) decreases
B) increases
C) There is not enough information to solve the problem.
D) stays the same
E) None of these is correct.

Question 42

A metal block suspended from a spring balance is submerged in water. You observe that the block displaces 55 cm³ of water and that the balance reads 4.3 N. What is the density of the block?

A) 7.0 g/cm³
B) 8.0 g/cm³
C) 9.0 g/cm³
D) 1.1 g/cm³
E) 1.2 g/cm³

Question 43

You are floating in a boat in a swimming pool. The boat contains some blocks of wood. The specific gravity of the wood is 0.66. You throw the wood blocks into the pool. When the waves settle, the depth of the water in the pool

A) has increased.
B) is the same as before.
C) has decreased.
D) is impossible to determine from the information given
E) is none of these

Question 44

A cylindrical piece of wood has a mass M = 0.235 kg. A small piece of lead with a mass m = 0.021 kg is fixed in the wood at the bottom of the cylinder so that the cylinder floats in water in a stable position, as shown. The radius of the cylinder is 1.65 cm. The depth x of the cylinder below the surface of the water is

A) 0.38 m
B) 0.57 m
C) 0.22 m
D) 0.42 m
E) None of these is correct.

Question 45

A tank is filled with water to a height H. A small hole is punched in one of the walls at a depth h below the water's surface. The water leaves the hole in a horizontal direction. The stream of water strikes the floor at a distance x, as shown. Neglecting viscosity, you can calculate the value of x from

A) x = H - h
B) x = [2h(H - h)]^1/2
C) x = h
D) x = 2[h(H - h)]^1/2
E) None of these is correct.

Question 46

Bernoulli's equation for nonviscous flow can be stated as
P₁ + $\rho$ gy₁ + $\rho$ v₁2 = P₂ + $\rho$ gy₂ + $\rho$ v₂2
A fluid is flowing through a horizontal tube that changes in cross-sectional area from
A₁= 0.75 cm² to A₂ = 0.030 cm². When v₁ = 3.5 cm/s, $\rho$ = 1.4 g/cm³, and viscosity is neglected, the difference between pressure P₂ at A₂ and P₁ at A₁ is

A) 54 $\times$ 10³ dyn/cm², with P₁ higher.
B) 59 dyn/cm², with P₂ higher.
C) 59 dyn/cm², with P₁ higher.
D) 8.3 $\times$ 10² dyn/cm², with P₂ higher.
E) None of these is correct.

Question 47

A horizontal pipe narrows from a diameter of 10 to 5 cm. For a nonviscous fluid flowing from the larger diameter to the smaller,

A) the velocity and pressure both increase.
B) the velocity increases and the pressure decreases.
C) the velocity decreases and the pressure increases.
D) the velocity and pressure both decrease.
E) either the velocity or the pressure changes but not both.

Question 48

Which conservation law governs the Bernoulli's equation?

A) Conservation of energy
B) Conservation of linear momentum
C) Conservation of angular momentum
D) Newton's universal law of gravitation
E) Bernoulli's equation does not follow from any conservation law.

Question 49

A block of wood of mass 300 g and density 0.75 g/cm³ is floating on the surface of a liquid of density 1.1 g/cm³. What mass of lead (density = 11.3 g/cm³) must be added to the block in order for the combination just to be submerged?

A) 440 g
B) 820 g
C) 140 g
D) 155 g
E) none of the above

Question 50

A raft of density 700 kg/m³ has a surface area of 7.0 m² and a volume of 0.7 m³. What depth does it sink into water of density 1000 kg/m³?

A) 10 cm
B) 0.7 cm
C) 0.7 m
D) 7 m
E) 7 cm

Question 51

The drag force on a plane is proportional to the density of the air. By what factor does the drag force change if a plane goes from an altitude 5.5 km to 11 km? The atmospheric pressure goes from to atm in going from 5.5 km to 11 km. Assume that the plane is at level flight and flies at the same speed.

A)
B)
C)
D) 1
E) 2

Question 52

Water from a tap is flowing at a uniform rate of 24 cm³/s into a cylindrical container. An exit tube is mounted on the side of the container at height h/2 from the base. The height h of the water remains constant. The volume flow at which the water leaves the container is

A) 12 cm³/s
B) 24 cm³/s
C) 36 cm³/s
D) 48 cm³/s
E) 72 cm³/s

Question 53

A large spherical air balloon is filled with helium. If the balloon is to lift three people, each approximately 80 kg, plus a basket and balloon outer covering material of mass
50 kg, calculate the minimum radius of the balloon. Assume values of the density of air and helium to be 1.29 kg/m³ and 0.18 kg/m³ respectively.

A) 62 m
B) 8.0 m
C) 4.0 m
D) 20 m
E) 5.0 m

Question 54

A block of wood of mass 400 g and density 0.8 g/cm³ is floating on the surface of a liquid of density 1.3 g/cm³. What is the difference in mass of stone (density = 1.9 g/cm³) that must be added to the block in order for the combination (wood and stone) to be just submerged rather than only the wood to be submerged?

A) 250 g
B) 540 g
C) 170 g
D) 790 g
E) none of the above

Question 55

A block of wood of length L = 21.0 cm, width w = 9.53 cm, and height h = 5.92 cm is just barely immersed in water by placing a mass m on the top of the block. The density of the wood is $\rho$ = 0.390 g/cm³. The value of m is

A) 0.72 kg
B) 7.1 kg
C) 1.2 kg
D) 1.6 kg
E) 0.36 kg

Question 56

A large tub is half full of water. A mass M = 25.0 kg, which has a specific gravity of 2.5, is attached to the right-hand side of the tub, out of the water. The entire apparatus balances perfectly horizontally on a fulcrum at F, as in (a). The tub is clamped in place and M is lowered to the bottom, completely submerged, as in (b). When the clamps are removed, the tub

A) remains balanced.
B) tips, with point L going down.
C) tips, with point L going up.
D) There is not enough information to solve the problem.
E) None of these is correct.

Question 57

A rock of mass M with a density twice that of water is sitting on the bottom of an aquarium tank filled with water. The normal force exerted on the rock by the bottom of the tank is

A) 2Mg
B) Mg
C) Mg/2
D) zero
E) impossible to determine from the information given.

Question 58

A uniform cylinder of wood of length 25 cm is floating vertically upright in a dual layered fluid. An oil layer (of density 0.9 g/cm³) that is 9 cm deep lies above a depth of water. If only 5 cm of wood lies above the oil surface calculate the density of the wood.

A) 0.76 g/ cm³
B) 0.80 g/ cm³
C) 0.70 g/ cm³
D) 0.66 g/ cm³
E) none of the above

Question 59

A rock of mass M, that has a density twice that of water, is suspended in water by a thin, massless cord. The tension in the cord is

A) 2Mg
B) Mg
C) Mg/2
D) zero
E) impossible to determine from the information given.

Question 60

A rock is thrown into a swimming pool that is filled with water at a uniform temperature. Which of the following statements is true?

A) The buoyant force on the rock is zero as it sinks.
B) The buoyant force on the rock increases as it sinks.
C) The buoyant force on the rock decreases as it sinks.
D) The buoyant force on the rock is constant as it sinks.
E) The buoyant force on the rock as it sinks is nonzero at first but becomes zero once the terminal velocity is reached.

Question 61

The figure represents the streamline flow of an incompressible fluid. Which of the following statements is true of the velocity and/or pressure at the indicated points?

A) v_A = v_B = v_C
B) v_A = v_B = v_C; p_A $\neq$ p_B $\neq$ p_C
C) v_A $\neq$ v_B $\neq$ v_C; p_A = p_B = p_C
D) v_A $\neq$ v_B $\neq$ v_C; p_A $\neq$ p_B $\neq$ p_C
E) v_A = v_B = v_C; p_A > p_B > p_C

Question 62

A small portion of an incompressible liquid in steady flow through a pipe of variable cross section, if friction is negligible, has at each point throughout its path a constant

A) kinetic energy.
B) velocity.
C) potential energy.
D) total energy.
E) momentum.

Question 63

When Bernoulli's equation is written in the form
P/ $\rho$ + v² + U = C,
The constant C represents the

A) energy per unit mass.
B) energy per unit volume.
C) net work done by outside forces.
D) power supplied by outside sources.
E) mass flow per unit time.

Question 64

A smooth stone is falling with its constant terminal velocity in a viscous liquid. The density of the stone is 2.89 $\times$ 10³ kg/m³, and the density of the liquid is 1.34 $\times$ 10³ kg/m³. The volume of the stone is 2.15 $\times$ 10^-6 m³. The drag force F of the liquid on the stone is given by F = 3.52v in SI units, where v is the terminal velocity. The value of v is

A) 8.5 $\times$ 10^-3 m/s
B) 1.1 $\times$ 10^-2 m/s
C) 3.2 $\times$ 10^-2 m/s
D) 1.7 $\times$ 10^-2 m/s
E) 1.7 $\times$ 10^-3 m/s

Question 65

Water is discharged from the tank in the manner shown. At which point is the pressure the least?

A) 1
B) 2
C) 3
D) 4
E) The pressure is the same at all points.

Question 66

A pipe of 2.54 cm inside diameter has a constriction in which the inside diameter is 1.27 cm. If water is flowing through this pipe with a velocity of 1.22 m/s in the main section, the velocity in the constricted section is

A) 0.305 m/s
B) 0.610 m/s
C) 2.44 m/s
D) 1.22 m/s
E) 4.88 m/s

Question 67

Cities across the U.S. supply fresh water to the residents at constant pressure by the use of water towers. If the diameter, d₂, of the pipe coming out of the tower is 25 cm, and the diameter, d₁, of the pipe at your home is 2.0 cm, what is the ratio of the velocity of the water at d₁ compared to d₂? Assume that all the taps are off except yours.

A) 12.5
B) 156
C) 0.0064
D) 0.08
E) 25

Question 68

A fish model that is 5.08 cm in diameter is placed in a pipe 25.4 cm in diameter and aligned along the axis of the pipe. If the water must flow past the fish at 2.44 m/s, the water in the unconstricted part of the pipe must flow at

A) 9.75 cm/s
B) 2.84 m/s
C) 2.35 m/s
D) 2.44 m/s
E) 6.10 m/s

Question 69

A liquid, such as water, with a low but not negligible viscosity is flowing from A to C with no turbulence through the horizontal tube, as shown in the figure. The cross-sectional area at A is equal to that at C. Which of the following is observed?

A) The pressure at A is the same as the pressure at C, and this pressure is smaller than the pressure at B.
B) The pressure at A is somewhat larger than that at C, and the pressures at both A and C are larger than the pressure at B.
C) The pressures at A and C are the same, and this pressure is larger than the pressure at B.
D) The pressure at A is larger than the pressure at B, which is larger than the pressure at C.
E) None of these is observed.

Question 70

Water flows through the pipe shown in the figure. The pressure

A) is greater at A than at B.
B) at A equals that at B.
C) is less at A than at B.
D) at A is unrelated to that at B.
E) at A can be greater or less than that at B depending on the rate of flow.

Question 71

Sea water of density 1.03 $\times$ 10³ kg/m³ is in streamline flow through a Venturi meter. The pressure difference between the main pipe and the constriction is 20.7 kPa, and the flow velocity in the constriction is 7.32 m/s. The flow velocity in the main pipe is

A) 2.44 m/s
B) 3.66 m/s
C) 7.32 m/s
D) 14.6 m/s
E) 29.3 m/s

Question 72

An incompressible fluid is in streamline flow through a Venturi meter, as shown. In the graph, one of the curves is a calibration curve for the meter, showing the fluid velocity plotted against the gauge reading. Which curve best represents the calibration data?

A) 1
B) 2
C) 3
D) 4
E) 5

Question 73

Water flows at speed v in a pipe of radius r. Neglecting viscosity, at what speed does the water flow through a constriction in which the radius of the pipe is r/3?

A) v/9
B) v/3
C) v
D) 3v
E) 9v

Question 74

The height of a water column as a function of time is given in the graph. From this graph, the time constant of the process is

A) 0.85 min
B) 1.4 min
C) 2.0 min
D) 2.9 min
E) infinite

Question 75

A pipe that appears to be of uniform size has constrictions on the inside. When a liquid flows through the pipe, the pressures at various points are indicated by the heights of the columns in the manometer tubes. If fluid friction is negligible, at which point is the diameter greatest?

A) 1
B) 2
C) 3
D) 4
E) 5

Question 76

Sea water of density 1.03 $\times$ 10³ kg/m³ is in streamline flow through a Venturi meter. The cross-sectional areas of the main pipe and the constriction are 0.139 m² and 0.0464 m², respectively, and the pressure difference between the two portions is 55.2 kPa. The velocity of flow in the main pipe is

A) 0.305 m/s
B) 1.73 m/s
C) 3.66 m/s
D) 11.0 m/s
E) 20.7 m/s

Question 77

A wind with speed 45 m/s blows across a roof 20 m long and 12 m wide. The pressure inside the room is 1 atm. What is the net force on this roof due to the pressure difference inside and outside the roof? (The density of air is equal to 1.3 kg/m³.)

A) 3.2 $\times$ 10⁵ N
B) 2.4 $\times$ 10⁷ N
C) 6.3 $\times$ 10⁵ N
D) 7.0 $\times$ 10³ N
E) 3.2 $\times$ 10⁸ N

Question 78

One statement of Bernoulli's law is
At any two points along a pipe in which there is a liquid in steady flow, the sum of the pressure, the kinetic energy per unit volume, and the potential energy per unit volume has the same value.
For this statement to be true, it is not necessary to have

A) streamline flow.
B) frictionless flow.
C) an incompressible fluid.
D) fluid of constant density.
E) constant acceleration of the fluid between the two points.

Question 79

For the streamlined flow of a viscous liquid, such as water, in a capillary tube, which of the following is correct?

A) The coefficient of viscosity depends on the radius of the inside of the tube raised to the fourth power.
B) The velocity of the liquid is essentially zero at the tube walls and increases toward the center of the tube.
C) There is no pressure difference along the tube provided the tube is less than 10 cm in length.
D) The volume flow rate through the tube can never be constant.
E) None of these is correct.

Question 80

Using a motion sensor, Susana finds that the acceleration of a 4-kg rock that has been dropped from the roof of a building is 6 m/s². She concludes that the magnitude of force of air resistance acting on the rock is approximately

A) 39.2 N
B) 24.0 N
C) 15.2 N
D) 9.81 N
E) None of these is correct.