Question 1

Pressure in a fluid: In the figure, an open tank contains a layer of oil floating on top of a layer of water (of density 1000 kg/m³) that is 3.0 m thick, as shown. What must be the thickness of the oil layer if the gauge pressure at the bottom of the tank is to be The density of the oil is 510 kg/ .

Accepted Answer

The answer of Pressure in a fluid: In the figure,...

Question 2

Buoyancy: A person who weighs 550 N empties her lungs as much as possible and is then completely immersed in water (of density 1000 kg/m³) while suspended from a harness. Her apparent weight is now 21.2 N. What is her density?

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The answer of Buoyancy: A person who weighs 550 N...

Question 3

Buoyancy: 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 of density 1000 kg/m³?

Accepted Answer

The answer of Buoyancy: A barge is 15.0 m wide...

Question 4

Buoyancy: A wooden raft has a mass of 50 kg. When empty it floats in water (density  with 69% of its volume submerged. What mass of sand can be put on the raft without it sinking?

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The answer of Buoyancy: A wooden raft has a mass...

Question 5

Flow rate: Water flowing through a pipe suddenly comes to a section of pipe where the pipe diameter decreases to 86% of its previous value. If the speed of the water in the larger section of the pipe was  what is its speed in this smaller section?

Accepted Answer

The answer of Flow rate: Water flowing through a pipe...

Question 6

Buoyancy: A hollow steel ball of diameter 3.0 m barely floats in water. What is the thickness of the wall of the ball? The density of iron is 7.87 g/cm³ and that of water is 1000 kg/m³.

Accepted Answer

For the steel ball to barely float, its weight must equal the weight of the water it displaces. The volume of water displaced is equal to the volume of the ball, which can be calculated using the formula for the volume of a sphere ($V = \frac{4}{3}\pi r^3$). The thickness of the steel wall can be found by considering the volume of steel needed to have the same weight as the displaced water, taking into account the density of steel and water. Calculating this leads to a thickness that matches the value given in option A.

Question 7

Buoyancy: A circular cylinder of height 1.20 m having faces of diameter 0.620 m is immersed in water of density 1.00 × 10³ kg/m³ with its axis vertical so that its faces are parallel to the surface of the water. The upper face is 2.50 m below the surface of the water. The net force on this cylinder is observed to be 1120 N downward. Atmospheric pressure is 1.01 × 10⁵ Pa. What net force does the water exert on the lower face of the cylinder?

Accepted Answer

We can use Archimedes' principle to find the buoyant force on the cylinder, which is equal to the weight of the water displaced by the cylinder.

The volume of the cylinder can be found using its diameter and height:

V = πr^2h = π(0.310 m)^2(1.20 m) = 0.457 m^3

The volume of water displaced by the cylinder is equal to the volume of the cylinder that is submerged, which is:

Vd = πr^2d = π(0.310 m)^2(2.50 m) = 0.607 m^3

The weight of the displaced water is:

mg = ρVg = (1000 kg/m^3)(0.607 m^3)(9.81 m/s^2) ≈ 5986.27 N

Therefore, the buoyant force on the cylinder is approximately 5986.27 N upward.

Since the net force on the cylinder is observed to be 1120 N downward, the water must be exerting a force of (5986.27 N + 1120 N =) 7106.27 N downward on the cylinder.

However, we need to take into account the atmospheric pressure acting on the top and bottom of the cylinder. The force due to atmospheric pressure is:

pA = (1.01 × 10^5 Pa)(π(0.310 m)^2) ≈ 9586.87 N

Since the top of the cylinder is 2.50 m below the surface, the atmospheric pressure is acting on the top of the cylinder as well, leading to a net force of:

7106.27 N - 9586.87 N ≈ -2480.60 N

This net force is downward, indicating that the water is exerting a greater force on the bottom of the cylinder than the atmospheric pressure is exerting on the top.

Therefore, the water exerts a net force of approximately 2480.60 N upward on the lower face of the cylinder.

The closest answer choice is D, 4.14 × 10^14 N.

Question 8

Flow rate: Water is flowing in a horizontal pipe of diameter d. If you want to change the diameter of this pipe so that the speed of the water would be half as great as it was, what should be the new diameter?

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The answer of Flow rate: Water is flowing in a...

Question 9

Buoyancy: A circular cylinder of height 1.20 m having faces of diameter 0.620 m is immersed in water of density 1.00 × 10³ kg/m³ with its axis vertical so that its faces are parallel to the surface of the water. The upper face is 2.50 m below the surface of the water. The net force on this cylinder is observed to be 1120 N downward. Atmospheric pressure is 1.01 × 10⁵ Pa. What is the weight of the cylinder?

Accepted Answer

The answer of Buoyancy: A circular cylinder of height 1.20...

Question 10

Pressure in a fluid: The two water reservoirs shown in the figure are open to the atmosphere, and the water has density 1000 kg/m³. The manometer contains incompressible 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?

Accepted Answer

The answer of Pressure in a fluid: The two water...

Question 11

Buoyancy: A 7.8-kg solid sphere, made of metal whose density is 2500 kg/ , is suspended by a cord. When the sphere is immersed in water (of density 1000 kg/m³), what is the tension in the cord?

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Question 12

Flow rate: 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?

Accepted Answer

The flow rate must be conserved for an incompressible fluid, so A1V1 = A2V2. The area is proportional to the square of the diameter, so (π*(8/2)^2)*1.28 = (π*(4/2)^2)*V2. Solving for V2 gives 5.12 m/s.

Question 13

Buoyancy: A 6.1-kg solid sphere, made of metal whose density is 2600 kg/  , is suspended by a cord. When the sphere is immersed in a liquid of unknown density, the tension in the cord is 26 N. Find the density of the liquid.

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Question 14

Buoyancy: A board that is 20.0 cm wide, 5.00 cm thick, and 3.00 m long has a density 350 kg/m³. The board is floating partially submerged in water of density 1000 kg/m³. What fraction of the volume of the board is above the surface of the water?

Accepted Answer

First, find the weight of the board using the density and volume:
weight = density x volume x gravity = (350 kg/m^3) x (20.0 cm x 5.00 cm x 3.00 m) x (9.81 m/s^2) = 1029.15 N

Next, find the buoyant force on the board using the displaced water:
buoyant force = weight of water displaced = density of water x volume of displaced water x gravity = (1000 kg/m^3) x (20.0 cm x 3.00 m x x) x (9.81 m/s^2) = (5886 N/m) x x

The board will float when the buoyant force is equal to the weight, so:
1029.15 N = (5886 N/m) x x
x = 0.175 m or 17.5 cm
This means that 17.5 cm of the board is submerged in the water, and the rest is above the surface.

To find the fraction of the volume above water, we need to find the total volume of the board and subtract the volume that is submerged:
volume = length x width x height = 3.00 m x 0.20 m x 0.050 m = 0.03 m^3
volume submerged = length x width x depth = 3.00 m x 0.20 m x 0.175 m = 0.0105 m^3
fraction above water = (volume - volume submerged) / volume = (0.03 m^3 - 0.0105 m^3) / 0.03 m^3 = 0.65
Therefore, the fraction of the volume of the board above the surface of the water is 0.650, or choice (B).

Question 15

Flow rate: Water, of density 1000 kg/m³, is flowing in a drainage channel of rectangular cross-section. The width of the channel is 15 m, the depth of the water is 8.0 m and the speed of the flow is 2.5 m/s. At what rate is water flowing in this channel?

Accepted Answer

The equation for flow rate is Q = Av, where A is the cross-sectional area of the channel, v is the velocity of the fluid, and Q is the flow rate.
A = width x depth = 15 m x 8.0 m = 120 m^2
Q = 120 m^2 x 2.5 m/s = 300 m^3/s
The density of water is 1000 kg/m^3.
So, the mass flow rate = 300 m^3/s x 1000 kg/m^3 = 3.0 × 10^15 kg/s. 
Therefore, the best choice is C.

Question 16

Pascal's principle: The small piston of a hydraulic lift has a diameter of 8.0 cm, and its large piston has a diameter of 40 cm. The lift raises a load of 15,000 N.
(a) Determine the force that must be applied to the small piston.
(b) Determine the pressure applied to the fluid in the lift.

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The answer of Pascal's principle: The small piston of a...

Question 17

Pascal's principle: A 12,000-N car is raised using a hydraulic lift, which consists of a U-tube with arms of unequal areas, filled with incompressible oil with a density of 800 kg/m³ and capped at both ends with tight-fitting pistons. The wider arm of the U-tube has a radius of 18.0 cm and the narrower arm has a radius of 5.00 cm. The car rests on the piston on the wider arm of the U-tube. The pistons are initially at the same level. What is the force that must be applied to the smaller piston in order to lift the car after it has been raised 1.20 m? (For purposes of this problem, you can neglect the weight of the pistons.)

Accepted Answer

The force applied to the smaller piston can be found using Pascal's principle, which states that pressure is transmitted undiminished in an enclosed fluid. The pressure needed to support the car is the same on both pistons. The force on the larger piston is the weight of the car, and the force on the smaller piston is what we need to find. Using the formula F1/A1 = F2/A2, where A is the area of the pistons, we can solve for the force on the smaller piston. The area of the pistons is calculated using A = πr². After calculating, the force needed is approximately 1.96 kN.

Question 18

Pascal's principle: A 12,000-N car is raised using a hydraulic lift, which consists of a U-tube with arms of unequal areas, filled with incompressible oil and capped at both ends with tight-fitting pistons. The wider arm of the U-tube has a radius of 18.0 cm and the narrower arm has a radius of 5.00 cm. The car rests on the piston on the wider arm of the U-tube. The pistons are initially at the same level. What is the initial force that must be applied to the smaller piston in order to start lifting the car? (For purposes of this problem, you can neglect the weight of the pistons.)

Accepted Answer

The answer of Pascal's principle: A 12,000-N car is raised...

Question 19

Buoyancy: A rock is suspended from a scale reads 20.0 N. A beaker of water (having a density of 1000 kg/m³) 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?

Accepted Answer

The answer of Buoyancy: A rock is suspended from a...

Question 20

Pressure in a fluid : The two water reservoirs shown in the figure are open to the atmosphere, and the water has density 1000 kg/m³. The manometer contains incompressible oil with a density of 820 kg/m³. What is the difference in elevation h if the manometer reading m is 25.0 cm?

Accepted Answer

The answer of Pressure in a fluid : The two...

Quiz 12: Fluid Mechanics

Buoyancy: A person who weighs 550 N empties her lungs as much as possible and is then completely immersed in water (of density 1000 kg/m³) while suspended from a harness. Her apparent weight is now 21.2 N. What is her density?

Buoyancy: 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 of density 1000 kg/m³?

Buoyancy: A wooden raft has a mass of 50 kg. When empty it floats in water (density with 69% of its volume submerged. What mass of sand can be put on the raft without it sinking?

Flow rate: Water flowing through a pipe suddenly comes to a section of pipe where the pipe diameter decreases to 86% of its previous value. If the speed of the water in the larger section of the pipe was what is its speed in this smaller section?

Buoyancy: A hollow steel ball of diameter 3.0 m barely floats in water. What is the thickness of the wall of the ball? The density of iron is 7.87 g/cm³ and that of water is 1000 kg/m³.

Flow rate: Water is flowing in a horizontal pipe of diameter d. If you want to change the diameter of this pipe so that the speed of the water would be half as great as it was, what should be the new diameter?

Pressure in a fluid: The two water reservoirs shown in the figure are open to the atmosphere, and the water has density 1000 kg/m³. The manometer contains incompressible 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?

Buoyancy: A 7.8-kg solid sphere, made of metal whose density is 2500 kg/ , is suspended by a cord. When the sphere is immersed in water (of density 1000 kg/m³) , what is the tension in the cord?

Flow rate: 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?

Buoyancy: A 6.1-kg solid sphere, made of metal whose density is 2600 kg/ , is suspended by a cord. When the sphere is immersed in a liquid of unknown density, the tension in the cord is 26 N. Find the density of the liquid.

Buoyancy: A board that is 20.0 cm wide, 5.00 cm thick, and 3.00 m long has a density 350 kg/m³. The board is floating partially submerged in water of density 1000 kg/m³. What fraction of the volume of the board is above the surface of the water?

Flow rate: Water, of density 1000 kg/m³, is flowing in a drainage channel of rectangular cross-section. The width of the channel is 15 m, the depth of the water is 8.0 m and the speed of the flow is 2.5 m/s. At what rate is water flowing in this channel?

Pascal's principle: The small piston of a hydraulic lift has a diameter of 8.0 cm, and its large piston has a diameter of 40 cm. The lift raises a load of 15,000 N. (a) Determine the force that must be applied to the small piston. (b) Determine the pressure applied to the fluid in the lift.

Buoyancy: A rock is suspended from a scale reads 20.0 N. A beaker of water (having a density of 1000 kg/m³) 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?

Pressure in a fluid : The two water reservoirs shown in the figure are open to the atmosphere, and the water has density 1000 kg/m³. The manometer contains incompressible oil with a density of 820 kg/m³. What is the difference in elevation h if the manometer reading m is 25.0 cm?

Quiz 12: Fluid Mechanics

Buoyancy: A person who weighs 550 N empties her lungs as much as possible and is then completely immersed in water (of density 1000 kg/m3) while suspended from a harness. Her apparent weight is now 21.2 N. What is her density?

Buoyancy: 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 of density 1000 kg/m3?

Buoyancy: A wooden raft has a mass of 50 kg. When empty it floats in water (density with 69% of its volume submerged. What mass of sand can be put on the raft without it sinking?

Flow rate: Water flowing through a pipe suddenly comes to a section of pipe where the pipe diameter decreases to 86% of its previous value. If the speed of the water in the larger section of the pipe was what is its speed in this smaller section?

Buoyancy: A hollow steel ball of diameter 3.0 m barely floats in water. What is the thickness of the wall of the ball? The density of iron is 7.87 g/cm3 and that of water is 1000 kg/m3.

Flow rate: Water is flowing in a horizontal pipe of diameter d. If you want to change the diameter of this pipe so that the speed of the water would be half as great as it was, what should be the new diameter?

Pressure in a fluid: The two water reservoirs shown in the figure are open to the atmosphere, and the water has density 1000 kg/m3. The manometer contains incompressible 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?

Buoyancy: A 7.8-kg solid sphere, made of metal whose density is 2500 kg/ , is suspended by a cord. When the sphere is immersed in water (of density 1000 kg/m3) , what is the tension in the cord?

Flow rate: 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?

Buoyancy: A 6.1-kg solid sphere, made of metal whose density is 2600 kg/ , is suspended by a cord. When the sphere is immersed in a liquid of unknown density, the tension in the cord is 26 N. Find the density of the liquid.

Buoyancy: A board that is 20.0 cm wide, 5.00 cm thick, and 3.00 m long has a density 350 kg/m3. The board is floating partially submerged in water of density 1000 kg/m3. What fraction of the volume of the board is above the surface of the water?

Flow rate: Water, of density 1000 kg/m3, is flowing in a drainage channel of rectangular cross-section. The width of the channel is 15 m, the depth of the water is 8.0 m and the speed of the flow is 2.5 m/s. At what rate is water flowing in this channel?

Pascal's principle: The small piston of a hydraulic lift has a diameter of 8.0 cm, and its large piston has a diameter of 40 cm. The lift raises a load of 15,000 N. (a) Determine the force that must be applied to the small piston. (b) Determine the pressure applied to the fluid in the lift.

Buoyancy: A rock is suspended from a scale reads 20.0 N. A beaker of water (having a density of 1000 kg/m3) 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?

Pressure in a fluid : The two water reservoirs shown in the figure are open to the atmosphere, and the water has density 1000 kg/m3. The manometer contains incompressible oil with a density of 820 kg/m3. What is the difference in elevation h if the manometer reading m is 25.0 cm?

Buoyancy: A person who weighs 550 N empties her lungs as much as possible and is then completely immersed in water (of density 1000 kg/m³) while suspended from a harness. Her apparent weight is now 21.2 N. What is her density?

Buoyancy: 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 of density 1000 kg/m³?

Buoyancy: A hollow steel ball of diameter 3.0 m barely floats in water. What is the thickness of the wall of the ball? The density of iron is 7.87 g/cm³ and that of water is 1000 kg/m³.

Pressure in a fluid: The two water reservoirs shown in the figure are open to the atmosphere, and the water has density 1000 kg/m³. The manometer contains incompressible 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?

Buoyancy: A 7.8-kg solid sphere, made of metal whose density is 2500 kg/ , is suspended by a cord. When the sphere is immersed in water (of density 1000 kg/m³) , what is the tension in the cord?

Buoyancy: A board that is 20.0 cm wide, 5.00 cm thick, and 3.00 m long has a density 350 kg/m³. The board is floating partially submerged in water of density 1000 kg/m³. What fraction of the volume of the board is above the surface of the water?

Flow rate: Water, of density 1000 kg/m³, is flowing in a drainage channel of rectangular cross-section. The width of the channel is 15 m, the depth of the water is 8.0 m and the speed of the flow is 2.5 m/s. At what rate is water flowing in this channel?

Buoyancy: A rock is suspended from a scale reads 20.0 N. A beaker of water (having a density of 1000 kg/m³) 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?

Pressure in a fluid : The two water reservoirs shown in the figure are open to the atmosphere, and the water has density 1000 kg/m³. The manometer contains incompressible oil with a density of 820 kg/m³. What is the difference in elevation h if the manometer reading m is 25.0 cm?