Deck 18: Fluid Mechanics

Question 1

All of the following are units of pressure except

A) Pascal.
B) atm.
C) N/m³.
D) psi.
E) Hold on! All of the above are acceptable units for pressure.

Answer 1

N/m³.

Question 2

The SI base units associated with density are

A) cm³/g.
B) m³/kg.
C) g/cm³.
D) kg/m³.

Answer 2

kg/m³.

Question 3

The mass of the water in a cylindrical container that is 0.50 m in height and 0.25 m in diameter is

A) 2.5 kg.
B) 15 kg.
C) 7.6 kg.
D) 24 kg.

Answer 3

24 kg.

Question 4

The Earth has a radius of 6.38 *10⁶ m and a mass of 5.97 * 10²⁴ kg. The ratio of the average density of the Earth and that of water is

A) 1:1.
B) 5:2.
C) 11:2.
D) 10:1.

Question 5

The diameter of a 10.0-kg ball of water is

A) 0.0032 m.
B) 0.134 m.
C) 0.147 m.
D) 1.60 m.

Question 6

A tank capable of holding 2000 $l$ (1 $l$ = 10^-3 m³) of water is being filled through a pipe that has a diameter of 5.0 cm. The flow rate that is required to fill the tank in two hours is

A) 140 m/s.
B) 14 m/s.
C) 1.4 m/s.
D) 0.14 m/s.

Question 7

If small-diameter tubing is used to empty a bucket of water that contains 9.0 $l$ (1 $l$ = 10^-3 m³) of water in 5.0 minutes, the mass flow rate through the tube is

A) 1.8 g/s.
B) 30. g/s.
C) 1.8 kg/s.
D) 3.0 kg/s.

Question 8

The flow velocity in a 2.5-cm-diameter tube is 0.015 m/s. If a tube restriction narrows the tube down to 1.5 cm in diameter, the flow in this region is

A) 0.009 m/s.
B) 0.025 m/s.
C) 0.042 m/s
D) 0.051 m/s.

Question 9

A fluid with a density of 790 kg/m³ flows at a rate of 0.05 kg/s through a pipe of radius 2.5 cm. The flow velocity is

A) 2.5 cm/s.
B) 3.2 cm/s.
C) 25 cm/s.
D) 32 cm/s.

Question 10

Atmospheric pressure is approximately

A) 1 Pa.
B) 1 kPa.
C) 10 kPa.
D) 100 kPa.

Question 11

The following statements are true about steady flow streamlines except

A) streamlines trace out paths followed by a small volume of fluid.
B) the fluid velocity is the smallest where the streamlines are the densest.
C) streamlines never cross.
D) the fluid velocity is tangent to the streamlines at any given point.

Question 12

A fountain produces a stream of water 3.0 cm in diameter at the nozzle that rises to a height of 40.0 m above the nozzle. The velocity of the water at the mouth of the nozzle is

A) 10 m/s.
B) 14 m/s.
C) 28 m/s.
D) 42 m/s.

Question 13

The volume of water that would be displaced by a 2.5-kg cylinder of copper (the density of copper is 8900 kg/m³) is

A) 2800 cm³.
B) 280 cm³.
C) 28 cm³.
D) 2.8 cm³.

Question 14

A pipe whose diameter is 2.00 cm contains a fluid that is moving at a speed of 5.00 cm/s. If the pipe's diameter expands to 4.00 cm, the speed of the fluid in this section is

A) 1.00 cm/s.
B) 1.25 cm/s.
C) 1.50 cm/s.
D) 2.00 cm/s.

Question 15

Given that the density of air is 1.2 kg/m³, the change in air pressure between the floor and the ceiling in a typical room is

A) 3.5 Pa.
B) 35 Pa.
C) 350 Pa.
D) 3500 Pa.

Question 16

Given that the density of seawater is 1.025 *10³ kg/m³, the pressure 3.0 m above the sea floor (in the middle of the ocean) is

A) 30 kPa.
B) 131 kPa.
C) 200 kPa.
D) Hold on! The solution is not determinable from the information given.

Question 17

An elephant, whose mass is 5000 kg, stands on his two back feet. If the diameter of the elephant's foot is 16 cm, the pressure exerted by the elephant on the ground is

A) 1.2 MPa.
B) 1.8 MPa.
C) 2.4 MPa.
D) 3.0 MPa.

Question 18

A 250-g cup filled with 0.1 $l$ (1 $l$ = 10^-3 m³) of liquid (density =1000 kg/m³) is placed on a table. The radius of the bottom of the cup is 3.0 cm. The pressure exerted by the cup on the table is

A) 12 N/m².
B) 3.4 N/m².
C) 3400 N/m².
D) 1200 N/m².

Question 19

The diameters of a set of connected pistons are 6.0 mm and 24 mm. If a 2.0-kg mass is placed on the smaller piston, the force generated at the second piston is

A) 1.2 N.
B) 4.9 N.
C) 78 N.
D) 310 N.

Question 20

The diameters of a set of connected pistons are 6.0 mm and 24 mm. If a 2.0-kg mass is placed on the smaller piston and the piston is displaced 5.0 mm, the distance the second piston moves is

A) 0.31 mm.
B) 5.0 mm.
C) 1.3 mm.
D) Hold on; not enough information is given.

Question 21

The diameters of a set of connected pistons are 6.0 mm and 24 mm. If a 2.0-kg mass is placed on the smaller piston and the piston moves 5.0 mm, the work done by the larger piston is

A) greater than the work done by the smaller piston.
B) less than the work done by the smaller piston.
C) equal to the work done by the smaller piston.
D) Hold on; not enough information is given to answer the question.

Question 22

The pressure at a depth of 1.0 km below the surface of the ocean (the density of seawater is 1025 kg/m³) is

A) 1.0 x 10⁶ Pa.
B) 1.0 x 10⁷ Pa.
C) 1.0 x 10⁸ Pa.
D) Hold on; not enough information is given to answer the question.

Question 23

A mercury barometer utilizes mercury (density = 13,600 kg/m³) in the column and requires a height of 0.8 m. A barometer that uses water in the column would require an approximate height of

A) 0.1 m.
B) 1 m.
C) 10 m.
D) 20 m.

Question 24

A car, whose mass is 2000 kg, is raised on a hydraulic lift that has a piston of radius 0.15 m. The pressure required to lift the car is

A) 280 kPa.
B) 130 kPa.
C) 41 kPa.
D) 28 kPa.

Question 25

The gauge pressure reading of an automobile tire is 210 kPa. The absolute pressure of the tire is

A) 110 kPa.
B) 210 kPa.
C) 310 kPa.
D) 410 kPa.

Question 26

An open tube manometer consists of a U-shaped tube containing mercury (density = 13,600 kg/m³) with one end of the tube open to the atmosphere and the other end connected to the container whose pressure is to be measured. The difference in heights between the two arms of the tube is 12.5 cm, indicating that the pressure in the container is

A) 11,000 N/m².
B) 17,000 N/m².
C) 110,000 N/m².
D) 170,000 N/m².

Question 27

A U-shaped tube with an inner diameter of 1.5 cm is open to the atmosphere at both ends. Water (density = 1000 kg/m³) is added to the tube until each arm of the U is half full (well above the bend in the tube). A 6.0-cm³ volume of oil is added to one arm of the U. After the fluid is added, the difference in levels of the two arms is 0.30 cm. The density of the oil is

A) 1080 kg/m³.
B) 1040 kg/m³.
C) 962 kg/m³.
D) 912 kg/m³.

Question 28

A barrel that is 0.250 m in radius and 1.00 m in height is filled with Texas crude oil (density of 875 kg/m³) and dropped into a lake (density of 1000 kg/m³). Neglecting the mass of the container, the percentage of the barrel that will be submerged is

A) 13.5%.
B) 50.0%.
C) 87.5%.
D) 100%.

Question 29

A barrel that is 0.25 m in radius and 1.0 m in height is filled with oil (density of 920 kg/m³) and dropped into a lake (density of 1000 kg/m³). The axis of the barrel is perpendicular to the surface of the water. If the barrel is displaced from equilibrium by a small amount and released, the resulting period of oscillation is

A) 0.50 s.
B) 1.9 s.
C) 1.5 s.
D) 0.67 s.

Question 30

A barrel that is 0.250 m in radius and 1.00 m in height is completely submerged in water. The buoyant force acting on the barrel is

A) 1920 N.
B) 3850 N.
C) 7700 N.
D) Hold on! The contents of the barrel are required to answer this question.

Question 31

A block of wood is floating in the water with 80% of the block submerged. The density of the wood is

A) 800 kg/m³.
B) 900 kg/m³.
C) 1000 kg/m³.
D) 1100 kg/m³.

Question 32

Why a hot air balloon floats in air is described by

A) Bernoulli's Principle.
B) Archimedes' Principle.
C) the continuity equation.
D) Pascal's Principle.

Question 33

A brass object has a density of 8600 kg/m³ and a mass of 0.500 kg. The object is attached to a spring balance with a string and then submerged in oil of density 920 kg/m³. The reading of the spring balance when the object is completely submerged is

A) 5.0 N.
B) 4.9 N.
C) 4.7 N.
D) 4.4 N.

Question 34

A spring balance supporting a suspended solid brick indicates a mass of 1.5 kg. When the brick is submerged in water, the balance indicates a mass of 0.62 kg. The density of the brick is

A) 875 kg/m³.
B) 1000 kg/m³.
C) 1700 kg/m³.
D) 2100 kg/m³.

Question 35

A 1.5-kg aluminum cylinder with a density of 2700 kg/m³ is at the bottom of a pool. The force acting on the cylinder from the floor of the pool is

A) 5.4 N.
B) 9.3 N.
C) 15 N.
D) 20 N.

Question 36

A block consists of an undetermined amount of gold (density of 19.3 kg/m³) and lead (density of 11.3 kg/m³). A spring balance indicates that the block has a mass of 16.9 g in air and 15.9 g when submerged in water. The percentage of the volume of the block that is gold is

A) 75%.
B) 70%.
C) 65%.
D) 60%.

Question 37

A 10.0-cm³ object floats in water with 90.0% of the object below the surface. The object's mass is

A) 1.0 g.
B) 9.0 g.
C) 11 g.
D) Hold on! The solution of this problem requires the object's density.

Question 38

Two objects have the same volumes but different densities. The density of object A is greater than the density of object B. The buoyant force acting on object A is

A) less than the buoyant force acting on object B.
B) greater than the buoyant force acting on object B.
C) equal to the buoyant force acting on object B.
D) Hold on! The two forces cannot be compared.

Question 39

Water flows at a rate of 2.0 $\times$ 10^-3 m³/s through a horizontal pipe of 2.5-cm² cross-sectional area at a pressure of 150 kPa. The flow is constricted at a valve having an effective cross-sectional area of 1.5 cm². The pressure at the valve is

A) 57 kPa.
B) 93 kPa.
C) 160 kPa.
D) 210 kPa.

Question 40

Oil (density = 900 kg/m³) flows through a horizontal pipe at 2.0 m/s at a pressure of 55 kPa. If the pipe is reduced to half its original area, the pressure in the reduced region is

A) 65 kPa.
B) 60 kPa.
C) 55 kPa.
D) 50 kPa.

Question 41

The pressure, above atmosphere, required to send water a vertical height of 25 m is

A) 1.8 atmospheres.
B) 2.4 atmospheres.
C) 2.8 atmospheres.
D) 3.4 atmospheres.

Question 42

A large water tower has a small hole that is 1.5 m below the surface. The initial speed of the water leaving the hole is

A) 3.8 m/s.
B) 5.4 m/s.
C) 7.0 m/s.
D) 7.4 m/s.

Question 43

The radius of a pipe is doubled. The velocity of the fluid inside the pipe will

A) increase by a factor of 2.
B) decrease by a factor of 2.
C) decrease by a factor of 4.
D) decrease by a factor of 8.

Question 44

An incompressible fluid flows through a pipe. The radius of the pipe at point A is twice as large as the radius at point B. The pressure of the fluid at point B is

A) greater than the pressure at point A.
B) less than the pressure at point A.
C) equal to the pressure at point A.
D) not determinable from the information given.

Question 45

An incompressible fluid flows through a pipe. The radius of the pipe at point A is twice as large as the radius at point B. The velocity of the fluid at point B is

A) greater than the velocity at point A.
B) less than the velocity at point A.
C) equal to the velocity at point A.
D) not determinable from the information given.

Question 46

An incompressible fluid (density of 920 kg/m³) flows at 10.0 m/s through a level pipe with a cross-sectional area of 1.5 cm². The pressure of the fluid in this section of the pipe is 150 kPa. The pipe is connected to a second pipe whose cross-sectional area is 2.5 cm². The speed of the flow in the second pipe is

A) 8.0 m/s.
B) 6.0 m/s.
C) 10. m/s.
D) 12 m/s.

Question 47

An incompressible fluid, whose density is 1000 kg/m³, flows at 4.5 m/s through a horizontal pipe with a radius of 1.0 cm. The pressure in the fluid is 115 kPa. The pipe is connected to a second pipe with a radius of 1.5 cm. The speed of the flow in the second pipe is

A) 6.0 m/s.
B) 4.5 m/s.
C) 3.0 m/s.
D) 2.0 m/s.

Question 48

An incompressible fluid is moving at 12 m/s through a pipe that has a radius of 1.25 cm. The pipe descends a distance of 4.0 m. To maintain the same pressure at each section of the pipe, the velocity of the fluid in the lower region is

A) 9.0 m/s.
B) 11 m/s.
C) 14 m/s.
D) 15 m/s.

Question 49

An incompressible fluid moves at 12 m/s through a pipe that has a radius of 1.25 cm. The pipe descends a distance of 4.0 m. To maintain the same pressure at each end of the pipe, the radius of the pipe in the lower region is

A) 0.90 cm.
B) 1.1 cm.
C) 1.3 cm.
D) 1.4 cm.

Question 50

The face of a dam can be considered a vertical rectangle of height 20 m and width of 50 m. Find the total fluid force exerted on the dam by the water when the water surface level is near the top of the dam:

A) 5 * 10⁶ N
B) 1 * 10⁷ N
C) 5 *10⁷ N
D) 1*10⁸ N