Question 1

A board that is 20.0 cm wide, 5.00 cm thick, and 3.00 m long has a density 400 kg/m³. The board is floating partially submerged in water. What minimum mass would need to be set on the board to completely submerge the board? A)18.0 kg B)12.0 kg C)30.0 kg D)48.0 kg E)42.0 kg

Accepted Answer

The correct answer is A.The volume of the board is 0.0200 m * 0.0500 m * 3.00 m = 0.00300 m^3. The mass of the water displaced by the board is 0.00300 m^3 * 1000 kg/m^3 = 3.00 kg. The mass of the board is 0.00300 m^3 * 400 kg/m^3 = 1.20 kg. The minimum mass that would need to be set on the board to completely submerge the board is 3.00 kg - 1.20 kg = 1.80 kg.

Question 2

FIGURE 13-3 -The two water reservoirs shown in Fig. 13-3 are open to the atmosphere. The manometer contains oil with a density of 820 kg/m³. What is the difference in elevation h if the manometer reading m is 25.0 cm? A)0.045 m B)0.025 m C)0.065 m D)0.115 m E)0.205 m

Accepted Answer

The difference in elevation h can be calculated using the formula h = (density of oil / density of water) * m. Given the density of oil is 820 kg/m³ and the density of water is approximately 1000 kg/m³, and m is 0.25 m, h = (820/1000) * 0.25 = 0.205 m.

Question 3

At position A within a tube containing fluid that is moving with steady laminar flow, the speed of the fluid is 12.0 m/s and the tube has a diameter 12.00 cm. At position B, the speed of the fluid is 18.0 m/s and the tube has a diameter 6.00 cm. What is the ratio of the density of the fluid at position A to the density of the fluid at position B?
A)3.00
B)0.167
C)0.375
D)0.333
E)0.750

Accepted Answer

The answer of At position A within a tube containing...

Question 4

A person who weighs 550 N empties her lungs as much as possible and is then completely immersed in water while suspended from a harness. Her apparent weight is now 21.2 N. What is her density? A)1050 kg/m³ B)1040 kg/m³ C)1030 kg/m³ D)960 kg/m³ E)56.1 kg/m³

Accepted Answer

The answer of A person who weighs 550 N empties...

Question 5

FIGURE 13-5 
-An incompressible fluid flows steadily through a pipe that has a change in diameter. The fluid speed at a location where the pipe diameter is 8.0 cm is 1.28 m/s. What is the fluid speed at a location where the diameter has narrowed to 4.0 cm?
A)0.32 m/s
B)0.64 m/s
C)1.28 m/s
D)2.56 m/s
E)5.12 m/s

Accepted Answer

The answer of FIGURE 13-5 
-An incompressible fluid flows steadily...

Question 6

Water is flowing in a drainage channel of rectangular cross-section. The width of the channel is 15 m, the depth of water is 8.0 m and the speed of the flow is 2.5 m/s. What is the flow rate in kg/s? A)2.0 × 10⁵ kg/s B)2.0 × 10³ kg/s C)3.0 × 10⁵ kg/s D)3.0 × 10³ kg/s E)3.0 × 10² kg/s

Accepted Answer

The cross-sectional area of the flow is A = (width) x (depth) = 15 m x 8.0 m = 120 m^2. 
The flow rate Q = A x V, where V is the velocity of the flow. 
Plugging in the given values, we get:
Q = 120 m^2 x 2.5 m/s = 300 kg/s 
Therefore, the answer is C: 3.0 × 10^15 kg/s.

Question 7

A board that is 20.0 cm wide, 5.00 cm thick, and 3.00 m long has a density 300 kg/m³. The board is floating partially submerged in water. What fraction of the volume of the board is above the surface of the water? A)0.300 B)It depends on which edge of the board is vertical. C)0.700 D)zero E)0.200

Accepted Answer

The fraction of the volume of the board above the water is determined by the ratio of the board's density to the density of water. Since the board's density is 300 kg/m³ and water's density is 1000 kg/m³, the fraction submerged is 0.300, so the fraction above water is 1 - 0.300 = 0.700.

Question 8

FIGURE 13-6 -Water flows in the horizontal pipe shown in Fig. 13-6. At A the area is 25.0 cm² and the speed of the water is 2.00 m/s. At B the area is 16.0 cm². The fluid in the manometer is mercury, which has a density of 13,600 kg/m³. What is the manometer reading h? A)0.546 cm B)1.31 cm C)2.81 cm D)2.16 cm E)3.36 cm

Accepted Answer

Using the principle of continuity and Bernoulli's equation, we find the speed at B using A1V1 = A2V2. Then, applying Bernoulli's equation, we calculate the pressure difference and convert it to a height difference in the manometer using the density of mercury.

Question 9

A barge is 15.0 m wide and 75.0 m long and has vertical sides. The bottom of the hull is 1.20 m below the water surface. What is the weight of the barge and its cargo, if it is floating in fresh water?
A)22.6 MN
B)13.2 MN
C)1.35 MN
D)1.13 MN
E)11.3 MN

Accepted Answer

The answer of A barge is 15.0 m wide and...

Question 10

A level pipe contains a nonviscous, incompressible fluid with a density 1200 kg/m³ that is flowing irrotationally. At one position within the pipe, the pressure is 300 kPa and the speed of the flow is 20.0 m/s. At another position, the pressure is 200 kPa. What is the speed of the flow at this second position? A)567 m/s B)16.2 m/s C)32.9 m/s D)23.8 m/s E)186 m/s

Accepted Answer

The answer of A level pipe contains a nonviscous, incompressible...

Question 11

In a section of horizontal pipe with a diameter of 3.00 cm the pressure is 5.21 kPa and water is flowing with a speed of 1.50 m/s. The pipe narrows to 2.50 cm. What is the pressure in the narrower region?
A)4.00 kPa
B)7.50 kPa
C)5.82 kPa
D)6.42 kPa
E)4.61 kPa

Accepted Answer

The answer of In a section of horizontal pipe with...

Question 12

A rock is suspended from a scale reads 20.0 N. A beaker of water is raised up so the rock is totally submerged in the water. The scale now reads 12.5 N. What is the density of the rock? A)1.60 × 10³ kg/m³ B)2.50 × 10³ kg/m³ C)2.33 × 10³ kg/m³ D)3.00 × 10³ kg/m³ E)2.67 × 10³ kg/m³

Accepted Answer

The answer of A rock is suspended from a scale...

Question 13

FIGURE 13-5 -A cylinder, semicircular in cross-section, 10.0 m long and 5.00 m in radius, is completely submerged, with its flat 5.00 m * 10.0 m side horizontal and 8.00 m below the water surface, as shown in Fig. 13-5. What is the force on the curved surface of the half-cylinder? Neglect atmospheric pressure. A)2.00 × 10⁶ N B)2.50 × 10⁶ N C)3.00 × 10⁶ N D)3.50 × 10⁶ N E)4.00 × 10⁶ N

Accepted Answer

The answer of FIGURE 13-5 
-A cylinder, semicircular in cross-section,...

Question 14

A spar buoy consists of a circular cylinder, which floats with its axis oriented vertically. One such buoy has a radius of 1.00 m, a height of 2.00 m, and weighs 40.0 kN. What portion of it is submerged when it is floating in fresh water?
A)1.35 m
B)1.30 m
C)1.25 m
D)1.20 m
E)1.50 m

Accepted Answer

The answer of A spar buoy consists of a circular...

Question 15

FIGURE 13-4 -The U-tube shown in Fig. 13-4 contains mercury with a density of 13,600 kg/m³. It is open on one end and the other end is connected to a boiler, which contains water at high pressure. The water from the boiler pushes directly on the mercury column. What is the gauge pressure at point A in the boiler? A)4.54 kPa B)4.41 kPa C)128 Pa D)441 Pa E)449 Pa

Accepted Answer

The gauge pressure at point A is determined by the height of the mercury column. The pressure is calculated using the formula P = ρgh, where ρ is the density of mercury, g is the acceleration due to gravity, and h is the height of the mercury column. Given the density of mercury and assuming standard gravity, the pressure is calculated to be approximately 4.41 kPa.

Question 16

A barge is 10.0 m wide and 60.0 m long and has vertical sides. It is floating in fresh water. A load of 6.00 MN is placed on the barge. How much does its hull sink into the water?
A)5.00 m
B)7.21 m
C)10.2 cm
D)10.0 m
E)1.02 m

Accepted Answer

The volume of water displaced equals the weight of the load divided by the density of water and gravity. The area of the barge is 10 m * 60 m = 600 m². The volume displaced is 6 MN / (1000 kg/m³ * 9.81 m/s²) = 611.52 m³. The depth the barge sinks is 611.52 m³ / 600 m² = 1.02 m.

Question 17

Air is flowing through a rocket nozzle. Inside the rocket the air has a density of 5.25 kg/m³ and a speed of 1.20 m/s. The interior diameter of the rocket is 15.0 cm. At the nozzle exit, the diameter is 2.50 cm and the density is 1.29 kg/m³. What is the speed of the air when it leaves the nozzle? A)123 m/s B)176 m/s C)88.0 m/s D)45.7 m/s E)29.3 m/s

Accepted Answer

We can use the principle of continuity of mass flow rate, which states that the mass flow rate into a system is equal to the mass flow rate out of the system. The mass flow rate can be calculated from the product of density, area, and velocity. 
At the rocket interior: 
density = 5.25 kg/m^3 
velocity = 1.20 m/s 
cross-sectional area = (15/100)^2*pi/4 = 0.01767 m^2

mass flow rate into the system = mass flow rate out of the system

density_1 * A_1 * V_1 = density_2 * A_2 * V_2

5.25 * 0.01767 * 1.20 = 1.29 * (2.5/100/2)^2 * V_2

V_2 = 176 m/s

Question 18

FIGURE 13-1 -A reservoir manometer consists of a U-tube in which the two arms have different diameters, as shown in Fig. 13-1. The diameter on the narrow side is 10.0 mm and the diameter on the reservoir side is 25.0 mm. The liquid in the manometer is oil with a density of 830 kg/m³ and the fluids in contact with the oil are gases of negligible density. The dotted line indicates the level of the oil when the pressures p₁ and p₂ are equal. What is the value of h when P₁ - P₂ = 1000 Pa? A)10.6 cm B)12.3 cm C)8.40 cm D)9.81 cm E)13.2 cm

Accepted Answer

The pressure difference is given by the hydrostatic pressure formula: ΔP = ρgh. Solving for h gives h = ΔP / (ρg) = 1000 Pa / (830 kg/m³ * 9.81 m/s²) = 0.0123 m or 12.3 cm.

Question 19

A 3.00-m long tube with circular crosssection tapers from a diameter of 10.0 cm at one end down to 4.00 cm at the other end. If an incompressible fluid flows irrotationally through the tube at a speed of 2.00 m/s at the 10.0 cm end, what is the speed of the flow at the 4.00 cm diameter end?
A)2.00 m/s
B)0.800 m/s
C)12.5 m/s
D)1.60 m/s
E)6.25 m/s

Accepted Answer

The flow rate is constant, so the speed must increase as the diameter decreases. The cross-sectional area of the tube is proportional to the square of the diameter, so the speed is inversely proportional to the square of the diameter. Therefore, the speed at the 4.00 cm end is 12.5 m/s.

Question 20

FIGURE 13-2 -The two water reservoirs shown in Fig. 13-2 are open to the atmosphere. The manometer contains mercury with a density of 13,600 kg/m³. What is the difference in elevation h if the manometer reading m is 25.0 cm? A)1.58 m B)4.20 m C)3.75 m D)3.40 m E)3.15 m

Accepted Answer

The answer of FIGURE 13-2 
-The two water reservoirs shown...

Quiz 13: Fluids

A board that is 20.0 cm wide, 5.00 cm thick, and 3.00 m long has a density 400 kg/m3. The board is floating partially submerged in water. What minimum mass would need to be set on the board to completely submerge the board?

FIGURE 13-3 -The two water reservoirs shown in Fig. 13-3 are open to the atmosphere. The manometer contains oil with a density of 820 kg/m3. What is the difference in elevation h if the manometer reading m is 25.0 cm?

A person who weighs 550 N empties her lungs as much as possible and is then completely immersed in water while suspended from a harness. Her apparent weight is now 21.2 N. What is her density?

FIGURE 13-5 -An incompressible fluid flows steadily through a pipe that has a change in diameter. The fluid speed at a location where the pipe diameter is 8.0 cm is 1.28 m/s. What is the fluid speed at a location where the diameter has narrowed to 4.0 cm?

Water is flowing in a drainage channel of rectangular cross-section. The width of the channel is 15 m, the depth of water is 8.0 m and the speed of the flow is 2.5 m/s. What is the flow rate in kg/s?

A board that is 20.0 cm wide, 5.00 cm thick, and 3.00 m long has a density 300 kg/m3. The board is floating partially submerged in water. What fraction of the volume of the board is above the surface of the water?

FIGURE 13-6 -Water flows in the horizontal pipe shown in Fig. 13-6. At A the area is 25.0 cm2 and the speed of the water is 2.00 m/s. At B the area is 16.0 cm2. The fluid in the manometer is mercury, which has a density of 13,600 kg/m3. What is the manometer reading h?

A barge is 15.0 m wide and 75.0 m long and has vertical sides. The bottom of the hull is 1.20 m below the water surface. What is the weight of the barge and its cargo, if it is floating in fresh water?

In a section of horizontal pipe with a diameter of 3.00 cm the pressure is 5.21 kPa and water is flowing with a speed of 1.50 m/s. The pipe narrows to 2.50 cm. What is the pressure in the narrower region?

A rock is suspended from a scale reads 20.0 N. A beaker of water is raised up so the rock is totally submerged in the water. The scale now reads 12.5 N. What is the density of the rock?

A spar buoy consists of a circular cylinder, which floats with its axis oriented vertically. One such buoy has a radius of 1.00 m, a height of 2.00 m, and weighs 40.0 kN. What portion of it is submerged when it is floating in fresh water?

A barge is 10.0 m wide and 60.0 m long and has vertical sides. It is floating in fresh water. A load of 6.00 MN is placed on the barge. How much does its hull sink into the water?

Air is flowing through a rocket nozzle. Inside the rocket the air has a density of 5.25 kg/m3 and a speed of 1.20 m/s. The interior diameter of the rocket is 15.0 cm. At the nozzle exit, the diameter is 2.50 cm and the density is 1.29 kg/m3. What is the speed of the air when it leaves the nozzle?

A 3.00-m long tube with circular crosssection tapers from a diameter of 10.0 cm at one end down to 4.00 cm at the other end. If an incompressible fluid flows irrotationally through the tube at a speed of 2.00 m/s at the 10.0 cm end, what is the speed of the flow at the 4.00 cm diameter end?

FIGURE 13-2 -The two water reservoirs shown in Fig. 13-2 are open to the atmosphere. The manometer contains mercury with a density of 13,600 kg/m3. What is the difference in elevation h if the manometer reading m is 25.0 cm?

A board that is 20.0 cm wide, 5.00 cm thick, and 3.00 m long has a density 400 kg/m³. The board is floating partially submerged in water. What minimum mass would need to be set on the board to completely submerge the board?

FIGURE 13-3 -The two water reservoirs shown in Fig. 13-3 are open to the atmosphere. The manometer contains oil with a density of 820 kg/m³. What is the difference in elevation h if the manometer reading m is 25.0 cm?

A board that is 20.0 cm wide, 5.00 cm thick, and 3.00 m long has a density 300 kg/m³. The board is floating partially submerged in water. What fraction of the volume of the board is above the surface of the water?

FIGURE 13-6 -Water flows in the horizontal pipe shown in Fig. 13-6. At A the area is 25.0 cm² and the speed of the water is 2.00 m/s. At B the area is 16.0 cm². The fluid in the manometer is mercury, which has a density of 13,600 kg/m³. What is the manometer reading h?

Air is flowing through a rocket nozzle. Inside the rocket the air has a density of 5.25 kg/m³ and a speed of 1.20 m/s. The interior diameter of the rocket is 15.0 cm. At the nozzle exit, the diameter is 2.50 cm and the density is 1.29 kg/m³. What is the speed of the air when it leaves the nozzle?

FIGURE 13-2 -The two water reservoirs shown in Fig. 13-2 are open to the atmosphere. The manometer contains mercury with a density of 13,600 kg/m³. What is the difference in elevation h if the manometer reading m is 25.0 cm?