Fluid Mechanics Practice Questions — Armed Services Vocational Aptitude Battery (ASVAB) — Page 2

Question 21Question →

A heavy equipment mechanic is operating a closed hydraulic lifting system. The system's master cylinder has a piston diameter of $2 \text{ inches}$ , while the lifting cylinder has a piston diameter of $10 \text{ inches}$ . If the mechanic applies an input force of $40 \text{ lbs}$ and pushes the master piston down by a distance of $25 \text{ inches}$ , what is the resulting output force and how far does the lifting piston move?

Output force of

1000 \text{ lbs}

and a distance of

1 \text{ inch}

Output force of

200 \text{ lbs}

and a distance of

5 \text{ inches}

Output force of

1000 \text{ lbs}

and a distance of

5 \text{ inches}

Output force of

200 \text{ lbs}

and a distance of

125 \text{ inches}

Show answer & explanation

Answer: Output force of $1000 \text{ lbs}$ and a distance of $1 \text{ inch}$

Answer

Output force of

1000 \text{ lbs}

and a distance of

1 \text{ inch}

The correct answer accurately applies Pascal's Principle by first recognizing that mechanical advantage depends on the cross-sectional areas of the pistons. Since the output diameter is 5 times larger than the input diameter, the output area is

5^2 = 25

times larger. This means the force is multiplied by 25 (

40 \times 25 = 1000 \text{ lbs}

). Because work is conserved, the output piston only moves

1/25

th of the distance the input piston moves (

25 / 25 = 1 \text{ inch}

).

Step-by-Step Solution

1

Calculate the ratio of the piston diameters.

Diameter ratio =

10 \text{ inches} / 2 \text{ inches} = 5

.

The diameter ratio is needed to find the area ratio, which dictates the mechanical advantage.

2

Calculate the ratio of the piston areas.

Area ratio =

5^2 = 25

.

According to Pascal's Principle, the mechanical advantage of a hydraulic system is equal to the ratio of the piston areas, not just their diameters. Area is proportional to the square of the diameter.

3

Calculate the output force.

Output force =

40 \text{ lbs} \times 25 = 1000 \text{ lbs}

.

The output force is the input force multiplied by the mechanical advantage (area ratio).

4

Calculate the output distance.

Output distance =

25 \text{ inches} / 25 = 1 \text{ inch}

.

To conserve the volume of the incompressible fluid, the distance the output piston moves must be inversely proportional to the area ratio. Therefore, the input distance is divided by the mechanical advantage.

Key Concept

Pascal's Principle and Mechanical Advantage in Hydraulics

Question 22Question →

In a basic hydraulic lift system, modifying different components produces specific predictable effects according to Pascal's Principle. Match each modification to the hydraulic system on the left with its direct resulting effect on the right. Assume all other initial conditions remain constant.

Click a left item, then click its matching right item

Show answer & explanation

Answer

Doubling output area matches 'Doubles lifting force'; pushing input twice as far matches 'Doubles travel distance'; doubling input area matches 'Halves mechanical advantage'; applying twice the input force matches 'Doubles fluid pressure'.

Each parameter in a hydraulic system relates to force, pressure, area, and distance proportionally. Applying the formulas P = F1/A1, F2 = P×A2, and V = A×d reveals exactly how doubling one variable mathematically affects the others.

Step-by-Step Solution

1

Analyze the effect of modifying the output piston's area.

Matches 'Doubles the maximum lifting force without changing fluid pressure'.

Since output force is P × A2, increasing only A2 will increase the output force proportionally.

2

Analyze the effect of changing the input piston's travel distance.

Matches 'Doubles the total travel distance of the output piston'.

Distance is governed by volume displacement. Doubling the input distance doubles the volume moved, which doubles the output distance.

3

Analyze the effect of modifying the input piston's area.

Matches 'Halves the mechanical advantage and the resulting output force'.

Increasing the input area decreases the pressure created for a given force, which reduces the mechanical advantage.

4

Analyze the effect of changing the input force.

Matches 'Doubles the internal fluid pressure throughout the system'.

Pressure is directly proportional to the applied input force (P = F1 / A1).

Key Concept

Pascal's Principle and Proportionality in Hydraulics

Question 23Question →

A mechanic uses a hydraulic floor jack to raise the axle of a truck. The jack's lifting cylinder (output) has a cross-sectional area that is $12$ times larger than the pump cylinder's (input) area. If the mechanic pushes the pump cylinder down a total fluid-displacing distance of $36 \text{ inches}$ (accumulated over several strokes), how far upward will the truck's axle be lifted?

3 \text{ inches}

432 \text{ inches}

36 \text{ inches}

0.33 \text{ inches}

Show answer & explanation

Answer: $3 \text{ inches}$

Answer

The truck's axle will be lifted

3 \text{ inches}

.

In any simple machine, including a hydraulic system, work input equals work output (assuming no friction). Because a hydraulic jack multiplies force, it must sacrifice distance to conserve energy. Since the output piston's area is 12 times larger, it exerts 12 times the force but only travels 1/12 of the distance. Therefore,

36 \text{ inches}

of input distance results in

36 / 12 = 3 \text{ inches}

of output distance.

Step-by-Step Solution

1

Identify the relationship between fluid volume, piston area, and travel distance.

V = A \cdot d

In a closed hydraulic system, the volume of fluid displaced by the input piston must exactly equal the volume of fluid that moves the output piston.

2

Set up the conservation of volume equation for both cylinders.

A_{\text{in}} \cdot d_{\text{in}} = A_{\text{out}} \cdot d_{\text{out}}

Equating the input and output volumes allows us to solve for the missing variable.

3

Rearrange the formula to solve for the output distance (

d_{\text{out}}

).

d_{\text{out}} = d_{\text{in}} \cdot (A_{\text{in}} / A_{\text{out}})

Isolating the target variable makes calculation straightforward.

4

Substitute the known values into the equation.

d_{\text{out}} = 36 \cdot (1 / 12) = 3 \text{ inches}

The output area is 12 times the input area, making the ratio

1/12

. Multiplying the input distance by this ratio gives the final output distance.

Key Concept

Conservation of fluid volume and mechanical advantage trade-offs in hydraulics.

Question 24Question →

Arrange the following points in a fluid system in order of their gauge hydrostatic pressure, from the GREATEST pressure to the LEAST pressure. Assume standard gravity applies equally to all systems.

Drag items to arrange them in the correct order

Show answer & explanation

Answer

The correct order from greatest to least pressure is: the

15

-meter oil pipe, the layered vat, the

11

-meter lake, the

9

-meter brine tank, and finally the

14

-meter conical vessel.

By calculating the equivalent water depth (Depth

\times

Specific Gravity) for each scenario, we find the values are

12.0

(pipe),

11.5

(layered vat),

11.0

(lake),

10.8

(brine tank), and

9.8

(conical vessel). Ranking these from highest to lowest provides the correct sequence.

Step-by-Step Solution

1

Recall the formula for hydrostatic pressure.

P = \rho \cdot g \cdot h

, where

\rho

is density,

g

is gravity, and

h

is depth.

This establishes that pressure depends solely on fluid density and depth, not on container shape or total volume.

2

Determine a standard unit for comparison across all items.

Use 'equivalent meters of water' by multiplying the depth of each fluid by its Specific Gravity (SG).

This simplifies calculations and provides a single proportional metric to compare.

3

Calculate the equivalent pressure for the single-fluid containers.

Pipe:

15 \times 0.8 = 12.0

. Lake:

11 \times 1.0 = 11.0

. Brine:

9 \times 1.2 = 10.8

. Conical vessel:

14 \times 0.7 = 9.8

.

Applying the formula directly to the given depth and Specific Gravity.

4

Calculate the equivalent pressure for the layered fluids in the vat.

Top layer (water):

5 \times 1.0 = 5.0

. Bottom layer (glycerin):

5 \times 1.3 = 6.5

. Total equivalent depth =

5.0 + 6.5 = 11.5

.

The total pressure at the bottom of layered fluids is the sum of the hydrostatic pressures of each individual layer.

5

Rank the calculated equivalent water depths from greatest to least.

12.0 > 11.5 > 11.0 > 10.8 > 9.8

.

This corresponds to the final required ordering.

Key Concept

Hydrostatic pressure is determined solely by fluid density and depth, completely independent of the container's shape, width, or total fluid volume.

Alternative Method

Instead of calculating equivalent water depth, you can calculate exact pressure if you assign

g = 9.8 \text{ m/s}^2

and density of water as

1000 \text{ kg/m}^3

. For example, the pipe pressure is

0.8 \times 1000 \times 9.8 \times 15 = 117,600 \text{ Pa}

. However, comparing the relative

(h \times \text{SG})

values is much faster for mental arithmetic.

Estimated Time:2m 0s

Question 25Question →

A mechanic uses a hydraulic floor jack to lift a heavy vehicle transmission. The jack's pump (input) piston has an area of $3 \text{ in}^2$ , and the lifting (output) piston has an area of $15 \text{ in}^2$ . If the mechanic applies a downward force of $60 \text{ lbs}$ on the input piston, what is the resulting upward force exerted by the lifting piston?

300 \text{ lbs}

12 \text{ lbs}

60 \text{ lbs}

900 \text{ lbs}

Show answer & explanation

Answer: $300 \text{ lbs}$

Answer

The lifting piston exerts an upward force of

300 \text{ lbs}

.

According to Pascal's Principle, the fluid pressure is equal throughout the system. The output piston has an area

5

times larger than the input piston (

15 / 3 = 5

). Therefore, to maintain the same pressure, it will output a force

5

times greater than the input force (

60 \times 5 = 300

).

Step-by-Step Solution

1

Determine the area ratio between the output and input pistons.

\text{Area Ratio} = \frac{15 \text{ in}^2}{3 \text{ in}^2} = 5

This ratio represents the mechanical advantage of the hydraulic system.

2

Multiply the input force by the mechanical advantage to find the output force.

\text{Output Force} = 60 \text{ lbs} \times 5 = 300 \text{ lbs}

Because fluid pressure (

P = \frac{F}{A}

) is transmitted equally, a piston with

5

times the area will output

5

times the force.

Key Concept

Pascal's Principle states that pressure is transmitted equally throughout a confined fluid, allowing hydraulic systems to multiply force proportionally to the ratio of their piston areas.

Question 26Question →

A mechanical engineer is testing a hydraulic actuation system. The standard baseline configuration features an input piston with an area of $2 \text{ in}^2$ , an output piston with an area of $20 \text{ in}^2$ , an applied input force of $50 \text{ lbs}$ , and an input stroke distance of $12 \text{ in}$ . Match each experimental setup below to its resulting output force and output travel distance.

Click a left item, then click its matching right item

Show answer & explanation

Answer

Each setup modifies the mechanical advantage or the input parameters, requiring independent calculations for output force (

F_{out} = F_{in} \times \text{MA}

) and output distance (

d_{out} = d_{in} / \text{MA}

).

Correct pairings are achieved by systematically calculating the ratio of the new areas (MA), multiplying the corresponding input force by this ratio, and dividing the corresponding input stroke by this ratio. This ensures Pascal's Principle and the conservation of volume are strictly followed.

Step-by-Step Solution

1

Calculate the Mechanical Advantage (MA) for each experimental setup.

MA is found by dividing the output area by the input area (

A_{out} / A_{in}

). Setup 1:

20/4=5

; Setup 2:

60/2=30

; Setup 3:

20/2=10

; Setup 4:

60/6=10

.

MA dictates the multiplier for force and the divisor for distance.

2

Determine the resulting output force for each setup.

Multiply the applied input force by the MA. Setup 1:

50 \times 5 = 250 \text{ lbs}

; Setup 2:

50 \times 30 = 1500 \text{ lbs}

; Setup 3:

100 \times 10 = 1000 \text{ lbs}

; Setup 4:

50 \times 10 = 500 \text{ lbs}

.

According to Pascal's Principle, pressure is transmitted equally, so force scales proportionally with area.

3

Determine the resulting output travel distance for each setup.

Divide the input stroke distance by the MA. Setup 1:

12 / 5 = 2.4 \text{ in}

; Setup 2:

12 / 30 = 0.4 \text{ in}

; Setup 3:

6 / 10 = 0.6 \text{ in}

; Setup 4:

12 / 10 = 1.2 \text{ in}

.

Because the fluid is incompressible, work and volume are conserved; travel distance scales inversely to force.

Key Concept

In hydraulics, Mechanical Advantage (MA) equals the ratio of output to input areas. Output force is multiplied by MA, while output travel distance is divided by MA to conserve work.

Question 27Question →

A sealed pneumatic cylinder initially contains air at a pressure of $40 \text{ psi}$ . A mechanical linkage forces the cylinder's internal volume to be reduced to exactly half ( $1/2$ ) of its original volume. Simultaneously, an external heat source causes the absolute temperature of the confined air to double. If this newly pressurized air is then directed into a separate pneumatic actuator with a piston surface area of $5 \text{ in}^2$ , what is the total theoretical force exerted by this actuator?

32 \text{ lbs}

200 \text{ lbs}

400 \text{ lbs}

800 \text{ lbs}

Show answer & explanation

Answer: $800 \text{ lbs}$

Answer

The correct force is

800 \text{ lbs}

.

The correct answer accurately combines two gas law principles before applying fluid power mathematics. First, halving the volume of a gas doubles its pressure (Boyle's Law). Second, doubling the absolute temperature doubles that pressure again (Gay-Lussac's Law). This results in a final system pressure of

160 \text{ psi}

. When applied to a

5 \text{ in}^2

piston, the total force is

160 \text{ psi} \times 5 = 800 \text{ lbs}

.

Step-by-Step Solution

1

Determine the effect of the volume change on the gas pressure using Boyle's Law (

P_1 \times V_1 = P_2 \times V_2

).

Since the volume is halved (

1/2

), the pressure must double.

40 \text{ psi} \times 2 = 80 \text{ psi}

.

In a compressible gas, pressure and volume are inversely proportional when temperature is held constant.

2

Determine the effect of the temperature change on the gas pressure using Gay-Lussac's Law.

Since the absolute temperature is doubled, the pressure must double again.

80 \text{ psi} \times 2 = 160 \text{ psi}

.

In a confined gas, absolute pressure is directly proportional to absolute temperature.

3

Calculate the force exerted by the actuator using the final pressure and the piston area (

F = P \times A

).

160 \text{ psi} \times 5 \text{ in}^2 = 800 \text{ lbs}

.

Force is defined as pressure applied over a specific surface area.

Key Concept

The Combined Gas Law allows simultaneous evaluation of pressure, volume, and temperature changes in a pneumatic system, which is then used to calculate mechanical force.

Question 28Question →

A maintenance crew is selecting a hydraulic jack to lift a heavy machinery component. The load must be lifted exactly $2 \text{ inches}$ . Different jacks have different input (pump) and output (lifting) cylinder areas.

Match each hydraulic jack's specifications to the distance its input piston must be pushed down to achieve the $2 \text{-inch}$ output lift.

Click a left item, then click its matching right item

Show answer & explanation

Answer

To find the input distance, calculate the mechanical advantage (Output Area / Input Area) and multiply it by the desired output distance (

2 \text{ inches}

). Jack Alpha requires

10 \text{ inches}

, Jack Beta requires

8 \text{ inches}

, Jack Gamma requires

12 \text{ inches}

, and Jack Delta requires

4 \text{ inches}

.

Each correct match is found by calculating the mechanical advantage (Output Area divided by Input Area) and multiplying that ratio by the desired

2\text{-inch}

output lift. This ensures the volume of fluid pushed by the pump equals the volume required to lift the load.

Step-by-Step Solution

1

Determine the mathematical relationship for distance in a closed hydraulic system.

\text{Input Area} \times \text{Input Distance} = \text{Output Area} \times \text{Output Distance}

Because liquids are essentially incompressible, the volume of fluid displaced by the input piston must equal the volume of fluid pushing up the output piston.

2

Rearrange the formula to solve for the required Input Distance.

\text{Input Distance} = \text{Output Distance} \times (\frac{\text{Output Area}}{\text{Input Area}})

This isolates the unknown variable, making it easier to plug in the given values for each jack.

3

Calculate the required input distance for Jack Alpha.

2 \text{ inches} \times (\frac{10}{2}) = 2 \times 5 = 10 \text{ inches}

.

Applying the specific area measurements of Jack Alpha to the derived formula.

4

Apply the same formula to the remaining jacks to find their respective input distances.

Beta:

2 \times (\frac{12}{3}) = 8 \text{ inches}

. Gamma:

2 \times (\frac{24}{4}) = 12 \text{ inches}

. Delta:

2 \times (\frac{10}{5}) = 4 \text{ inches}

.

Completing the required calculations to find all corresponding values.

Key Concept

In a hydraulic system, the distance an input piston must travel is proportional to the ratio of the output area to the input area. A larger mechanical advantage requires a proportionally larger input distance to conserve the total volume of displaced fluid.

Question 29Question →

A dentist adjusts a patient's hydraulic examination chair. The system's input piston has a cross-sectional area of $8 \text{ in}^2$ , and the lifting piston beneath the chair has an area of $64 \text{ in}^2$ . If the dentist applies $35 \text{ lbs}$ of force to the input piston, how much upward force is generated by the lifting piston?

Show answer & explanation

Answer: 280

Answer

280

The hydraulic system provides a mechanical advantage equal to the ratio of the two piston areas (

64 / 8 = 8

). Multiplying the input force of

35 \text{ lbs}

by this mechanical advantage yields a total lifting force of

280 \text{ lbs}

.

Step-by-Step Solution

1

Identify the given variables.

Input area

A_1 = 8 \text{ in}^2

, output area

A_2 = 64 \text{ in}^2

, and input force

F_1 = 35 \text{ lbs}

.

These variables are required to apply Pascal's Principle.

2

Calculate the mechanical advantage (area ratio) of the hydraulic system.

\frac{A_2}{A_1} = \frac{64}{8} = 8

.

The ratio of the output area to the input area determines how much the input force will be multiplied.

3

Calculate the generated output force.

F_2 = F_1 \times \text{Area Ratio} = 35 \text{ lbs} \times 8 = 280 \text{ lbs}

.

Pascal's Principle states that pressure is transmitted equally throughout an enclosed fluid, meaning force increases proportionally with area.

Key Concept

According to Pascal's Principle, pressure applied to an enclosed fluid is transmitted equally in all directions. In a hydraulic system, this means the ratio of output force to input force is equal to the ratio of output area to input area (

F_1/A_1 = F_2/A_2

).

Estimated Time:45s

Question 30Question →

A solid machine part is suspended from a spring scale. In the air, the scale reads $60 \text{ N}$ . When the part is completely submerged in water, the scale reads $40 \text{ N}$ . The part is then removed, dried, and completely submerged in a vat of unknown oil, where the scale reads $45 \text{ N}$ . Based on these readings, what is the density of the oil compared to the density of water?

0.75 times the density of water

1.33 times the density of water

0.25 times the density of water

1.13 times the density of water

Show answer & explanation

Answer: 0.75 times the density of water

Answer

The oil is 0.75 times the density of water.

According to Archimedes' principle, buoyant force equals the weight of the displaced fluid (

F_b = \rho \cdot V \cdot g

). The buoyant force in water is

60 \text{ N} - 40 \text{ N} = 20 \text{ N}

. The buoyant force in the oil is

60 \text{ N} - 45 \text{ N} = 15 \text{ N}

. Because the part is fully submerged in both instances, the displaced volume (

V

) is identical. Therefore, the buoyant forces are directly proportional to the fluid densities. The ratio of the oil's density to the water's density is the ratio of their buoyant forces:

15 \text{ N} / 20 \text{ N} = 0.75

.

Step-by-Step Solution

1

Calculate the buoyant force exerted by the water.

60 \text{ N} - 40 \text{ N} = 20 \text{ N}

The buoyant force is equal to the object's true weight in air minus its apparent weight when submerged.

2

Calculate the buoyant force exerted by the oil.

60 \text{ N} - 45 \text{ N} = 15 \text{ N}

To compare the lifting effect of the two fluids, we need to know the specific buoyant force each exerts on the identical volume.

3

Calculate the ratio of the oil's density to the water's density.

15 \text{ N} / 20 \text{ N} = 0.75

Because the same object is completely submerged in both fluids, the displaced volume is constant. Therefore, the buoyant forces are directly proportional to the densities of the fluids.

Key Concept

Apparent weight and Archimedes' Principle

Question 31Question →

A mechanic uses a simple hydraulic lift to raise a motorcycle. The system's input piston has a cross-sectional area of $5 \text{ in}^2$ , and the output (lifting) piston has a cross-sectional area of $50 \text{ in}^2$ . If the mechanic applies a downward force of $40 \text{ lbs}$ on the input piston, what is the upward force exerted by the output piston?

4 \text{ lbs}

40 \text{ lbs}

200 \text{ lbs}

400 \text{ lbs}

Show answer & explanation

Answer: $400 \text{ lbs}$

Answer

The upward force exerted by the output piston is

400 \text{ lbs}

.

According to Pascal's Principle, pressure is transmitted equally throughout a confined fluid. The pressure generated at the input piston is

40 \text{ lbs} / 5 \text{ in}^2 = 8 \text{ psi}

. This exact same pressure acts on the larger

50 \text{ in}^2

output piston, resulting in an upward force of

8 \text{ psi} \times 50 \text{ in}^2 = 400 \text{ lbs}

. Alternatively, using the mechanical advantage ratio:

50 / 5 = 10

, so the output force is

10 \times 40 = 400 \text{ lbs}

.

Step-by-Step Solution

1

Calculate the pressure exerted by the input piston.

P = \frac{F_{in}}{A_{in}} = \frac{40 \text{ lbs}}{5 \text{ in}^2} = 8 \text{ psi}

Pascal's Principle states that pressure applied to an enclosed fluid is transmitted equally in all directions.

2

Calculate the output force by applying the pressure to the output piston's area.

F_{out} = P \times A_{out} = 8 \text{ psi} \times 50 \text{ in}^2 = 400 \text{ lbs}

The output force is the product of the constant fluid pressure and the area of the output piston.

Key Concept

Pascal's Principle and Hydraulic Multiplication

Estimated Time:45s

Question 32Question →

A barber chair uses a closed hydraulic lift mechanism to raise customers. The barber operates a foot pedal connected to an input cylinder with a cross-sectional area of $4 \text{ in}^2$ . The chair is mounted on a larger output cylinder with a cross-sectional area of $80 \text{ in}^2$ . If the total weight of the chair and the customer is $320 \text{ lbs}$ , how much downward force must the barber apply to the input cylinder to lift the load?

4 \text{ lbs}

16 \text{ lbs}

1280 \text{ lbs}

6400 \text{ lbs}

Show answer & explanation

Answer: $16 \text{ lbs}$

Answer

The barber must apply

16 \text{ lbs}

of force.

The correct answer applies Pascal's Principle, which indicates that the mechanical advantage of a hydraulic system is determined by the ratio of the piston areas. The output cylinder is

20

times larger than the input cylinder (

80 / 4 = 20

). Therefore, the input force only needs to be

1/20

th of the output load. Dividing the

320 \text{ lbs}

load by

20

yields an input force requirement of

16 \text{ lbs}

.

Step-by-Step Solution

1

Identify the given values for the hydraulic system.

Input area (

A_1

) =

4 \text{ in}^2

, Output area (

A_2

) =

80 \text{ in}^2

, Output force/load (

F_2

) =

320 \text{ lbs}

.

Organizing known variables is the first step in solving a Pascal's Principle problem.

2

State Pascal's Principle equation relating force and area.

\frac{F_1}{A_1} = \frac{F_2}{A_2}

Pascal's Principle dictates that pressure is transmitted equally throughout a confined incompressible fluid.

3

Rearrange the formula to solve for the unknown input force (

F_1

).

F_1 = F_2 \times \left(\frac{A_1}{A_2}\right)

Isolating

F_1

prepares the equation for direct substitution.

4

Substitute the known values and calculate.

F_1 = 320 \times \left(\frac{4}{80}\right) = 320 \times \left(\frac{1}{20}\right) = 16 \text{ lbs}

.

Performing the arithmetic reveals the exact force required at the pedal.

Key Concept

Pascal's Principle states that a change in pressure at any point in an enclosed fluid is transmitted equally throughout the fluid. In a hydraulic system, a small force applied over a small area can lift a large weight over a proportionally larger area.

Question 33Question →

Match the following hydraulic system components and concepts with their correct mechanical effects or descriptions.

Click a left item, then click its matching right item

Show answer & explanation

Answer

The small input piston matches with traveling a greater distance for less force. The large output piston matches with traveling a shorter distance for greater force. Hydraulic fluid matches with the incompressible medium transmitting pressure. Piston area ratio matches with determining mechanical advantage.

Each component in a basic hydraulic system has a distinct mechanical role. The small input piston trades distance for force, while the large output piston trades force for distance. The area ratio defines this mechanical advantage, and the incompressible fluid ensures the pressure is transmitted without loss.

Step-by-Step Solution

1

Analyze the mechanical relationship between piston size and movement distance.

Smaller pistons move farther with less force; larger pistons move less distance with more force.

This relationship is dictated by the conservation of work (Work = Force × Distance) in the hydraulic system.

2

Identify the primary role of the fluid in a hydraulic system.

The fluid serves as the incompressible medium that transmits pressure.

Pascal's Principle states that pressure applied to an enclosed fluid is transmitted equally in all directions.

3

Define what determines the force multiplication factor.

The ratio of the output piston area to the input piston area dictates the mechanical advantage.

Since pressure is force per unit area, applying equal pressure across different areas results in proportional forces.

Key Concept

Pascal's Principle and conservation of work in hydraulic systems

Question 34Question →

A hydraulic rescue spreader operates using a closed fluid system. The tool's spreading arms are driven by an output piston with a cross-sectional area of $20 \text{ in}^2$ . During an operation, the output piston must exert a constant force of $6000 \text{ lbs}$ and extend exactly $4 \text{ inches}$ . The hand-operated pump uses an input piston with a cross-sectional area of $2 \text{ in}^2$ .

To achieve this full $4 \text{ inch}$ extension of the output piston, what is the total distance, in inches, that the input piston must travel?

Show answer & explanation

Answer: 40

Answer

The input piston must travel a total distance of 40 inches.

In a closed hydraulic system, the volume of fluid displaced by the input piston must equal the volume received by the output piston (

A_1 \times d_1 = A_2 \times d_2

). Since the output piston requires

80 \text{ in}^3

of fluid (

20 \text{ in}^2 \times 4 \text{ in}

), the input piston, with an area of

2 \text{ in}^2

, must travel

40 \text{ inches}

(

80 / 2

) to displace that same volume. The force value (

6000 \text{ lbs}

) is not needed to find the distance.

Step-by-Step Solution

1

State the principle of conservation of volume for a closed hydraulic system.

V_{in} = V_{out}

or

A_1 \times d_1 = A_2 \times d_2

Because liquids are essentially incompressible, the volume of fluid pushed by the input piston equals the volume that moves the output piston.

2

Calculate the volume of fluid displaced at the output cylinder.

V_{out} = 20 \text{ in}^2 \times 4 \text{ inches} = 80 \text{ in}^3

This is the total volume of fluid required to extend the spreading arms by the specified distance.

3

Calculate the required travel distance for the input piston.

2 \text{ in}^2 \times d_1 = 80 \text{ in}^3 \rightarrow d_1 = 40 \text{ inches}

Dividing the total required volume by the input piston's area gives the total distance the input piston must be pushed.

Key Concept

Conservation of fluid volume and mechanical advantage in hydraulic systems.

Question 35Question →

A marine engineering lab is evaluating four solid wooden cubes of identical dimensions for a flotation device. The cubes are set adrift in a freshwater basin (density = $1.00 \text{ g/cm}^3$ ) and allowed to reach floating equilibrium. Based on the material densities provided, arrange the wood types in order of the percentage of their volume that remains ABOVE the water line, starting from the SMALLEST percentage exposed and ending with the LARGEST percentage exposed.

Drag items to arrange them in the correct order

Show answer & explanation

Answer

The correct order from smallest to largest percentage above water is: Oak wood, Teak wood, Pine wood, and Balsa wood.

The fraction of a floating object submerged is equal to its density divided by the fluid's density. Because fresh water has a density of

1.00 \text{ g/cm}^3

, a wood block's submerged percentage directly matches its density value as a percentage. The Oak block (

0.75 \text{ g/cm}^3

) is

75\%

submerged, leaving the smallest amount (

25\%

) exposed above water. Conversely, the Balsa block (

0.20 \text{ g/cm}^3

) is only

20\%

submerged, leaving the largest amount (

80\%

) exposed.

Step-by-Step Solution

1

Determine the relationship between material density and submerged volume for a floating object.

For a floating object, the fraction of its volume that is submerged is equal to the ratio of the object's density to the fluid's density (

V_{sub}/V_{total} = \rho_{obj}/\rho_{fluid}

).

This relationship is derived directly from Archimedes' principle, where the upward buoyant force equals the downward weight of the floating object.

2

Calculate the percentage of volume submerged for each type of wood.

Since the water density is

1.00 \text{ g/cm}^3

, the submerged fraction is simply the wood's density divided by 1. Oak is

75\%

submerged, Teak is

65\%

submerged, Pine is

40\%

submerged, and Balsa is

20\%

submerged.

This establishes exactly how much of each block is sitting below the water level.

3

Calculate the percentage of volume above water (exposed) for each type of wood.

The exposed percentage is calculated as

100\% - \text{submerged percentage}

. Oak =

25\%

, Teak =

35\%

, Pine =

60\%

, Balsa =

80\%

.

The question specifically asks for the percentage that remains ABOVE the water surface, requiring an inversion of the submerged values.

4

Arrange the wood types from smallest to largest exposed percentage.

Smallest to largest exposed percentage: Oak (

25\%

), Teak (

35\%

), Pine (

60\%

), Balsa (

80\%

).

This directly answers the prompt's final ordering requirement.

Key Concept

For an object floating in equilibrium, the fraction of its volume that is submerged equals the ratio of its density to the fluid's density. A higher density object will sit lower in the fluid, exposing less of its volume above the surface.

Question 36Question →

A hydraulic press used for stamping metal parts has an input piston with a cross-sectional area of $2 \text{ in}^2$ and an output piston with a cross-sectional area of $6 \text{ in}^2$ . If a downward force of $30 \text{ lbs}$ is applied to the input piston, how much force is exerted by the output piston?

10 \text{ lbs}

30 \text{ lbs}

90 \text{ lbs}

180 \text{ lbs}

Show answer & explanation

Answer: $90 \text{ lbs}$

Answer

90 \text{ lbs}

According to Pascal's Principle, pressure is transmitted equally throughout a confined fluid. The pressure generated at the input is

P = \frac{F_1}{A_1} = \frac{30}{2} = 15 \text{ psi}

. This same pressure acts on the output piston. The output force is

F_2 = P \times A_2 = 15 \times 6 = 90 \text{ lbs}

. Alternatively, using the mechanical advantage, since the output area is

3

times larger than the input area, the output force is

3

times the input force.

Step-by-Step Solution

1

Identify the given values from the problem description.

A_1 = 2 \text{ in}^2

,

F_1 = 30 \text{ lbs}

,

A_2 = 6 \text{ in}^2

These variables are required to apply Pascal's Principle.

2

Determine the mechanical advantage by finding the ratio of the output area to the input area.

Ratio =

\frac{A_2}{A_1} = \frac{6}{2} = 3

The output force is multiplied by the ratio of the piston areas.

3

Calculate the output force (

F_2

).

F_2 = 30 \times 3 = 90 \text{ lbs}

Multiplying the input force by the mechanical advantage gives the total output force.

Key Concept

Pascal's Principle and Hydraulic Multiplication

Estimated Time:45s

Question 37Question →

A factory uses a closed hydraulic press system to stamp metal parts. The system features an input piston with a cross-sectional area of $3 \text{ in}^2$ and an output stamping piston with a cross-sectional area of $15 \text{ in}^2$ . If the output stamping piston must travel a distance of $4 \text{ inches}$ to complete the stamping operation, how far must the input piston be depressed?

20 \text{ inches}

60 \text{ inches}

5 \text{ inches}

0.8 \text{ inches}

Show answer & explanation

Answer: $20 \text{ inches}$

Answer

20 \text{ inches}

In a closed hydraulic system, the volume of fluid displaced by the input piston must equal the volume gained at the output piston (

V = A \times d

). Because the output piston has

5

times the area of the input piston (

15 / 3 = 5

), the input piston must travel

5

times as far to move the required volume of fluid. Therefore, multiplying the area ratio (

5

) by the output distance (

4 \text{ inches}

) gives an input travel distance of

20 \text{ inches}

.

Step-by-Step Solution

1

Calculate the mechanical advantage (area ratio) between the output and input pistons.

15 \text{ in}^2 / 3 \text{ in}^2 = 5

The area ratio dictates the proportional difference in how far each piston must travel.

2

Apply the principle of conservation of fluid volume (

A_1 \times d_1 = A_2 \times d_2

) to find the input distance.

d_{in} = 5 \times 4 \text{ inches} = 20 \text{ inches}

Because the input piston is 5 times smaller in area, it must travel 5 times the distance of the output piston to displace the same volume of fluid.

Key Concept

Conservation of fluid volume in hydraulics (

A_1 \times d_1 = A_2 \times d_2

)

Estimated Time:1m 0s

Question 38Question →

Two solid metal blocks, one made of aluminum and one made of lead, have the exact same size and shape. Both blocks are completely submerged in a tank of freshwater. Which of the following statements about the upward buoyant force acting on the blocks is true?

The buoyant force is the same for both blocks because they displace the same volume of water.

The buoyant force is greater on the lead block because it has a greater mass.

The buoyant force is greater on the aluminum block because it has less mass.

The buoyant force acting on each block is exactly equal to its respective weight.

Show answer & explanation

Answer: The buoyant force is the same for both blocks because they displace the same volume of water.

Answer

The buoyant force is the same for both blocks because they displace the same volume of water.

According to Archimedes' Principle, buoyant force is determined entirely by the weight of the displaced fluid. Since both blocks have the exact same physical dimensions and are completely submerged in the same fluid, they displace the exact same volume of water. Therefore, they experience the exact same upward buoyant force, regardless of their individual weights or material compositions.

Step-by-Step Solution

1

Recall Archimedes' Principle.

The upward buoyant force exerted on a body immersed in a fluid is equal to the weight of the fluid that the body displaces.

This is the fundamental rule governing buoyancy.

2

Determine the displaced volume for each block.

Since both blocks have the exact same physical dimensions (size and shape) and are both completely submerged, they displace the exact same volume of water.

Displaced volume depends solely on the submerged volume of the object.

3

Compare the resulting buoyant forces.

Because they displace the same volume of the same fluid, the weight of the displaced fluid is identical for both blocks. Therefore, they experience the exact same buoyant force.

Buoyant force is independent of the object's mass, density, or weight, as long as the displaced volume is the same.

Key Concept

Archimedes' Principle (Volume vs. Mass)

Question 39Question →

An overflow container is filled to the brim with a specialized drilling mud that weighs $15 \text{ N}$ per liter. A solid geological core sample weighing $75 \text{ N}$ in the air is completely submerged in the mud, causing exactly $2$ liters of mud to spill into a measuring basin. Based on Archimedes' principle, what is the apparent weight of the core sample while it is fully suspended in the mud?

45 \text{ N}

30 \text{ N}

60 \text{ N}

105 \text{ N}

Show answer & explanation

Answer: $45 \text{ N}$

Answer

The apparent weight of the core sample is

45 \text{ N}

.

Archimedes' principle dictates that an object submerged in a fluid experiences an upward buoyant force equal to the weight of the fluid it displaces. Because the core sample displaces

2

liters of mud (which weighs

15 \text{ N}

per liter), the upward buoyant force is

30 \text{ N}

. The apparent weight is the actual downward weight (

75 \text{ N}

) minus this upward buoyant force (

30 \text{ N}

), resulting in a net apparent weight of

45 \text{ N}

.

Step-by-Step Solution

1

Calculate the weight of the displaced drilling mud.

2 \text{ liters} \times 15 \text{ N/liter} = 30 \text{ N}

According to Archimedes' principle, the upward buoyant force acting on a submerged object is exactly equal to the weight of the fluid it displaces.

2

Calculate the apparent weight of the submerged core sample.

75 \text{ N} - 30 \text{ N} = 45 \text{ N}

The apparent weight is determined by subtracting the upward buoyant force from the actual downward weight of the object.

Key Concept

Apparent weight and Archimedes' principle

Question 40Question →

Match each modification made to a standard closed hydraulic lift system with its resulting effect on the output piston. Assume the applied input force remains constant unless otherwise specified.

Click a left item, then click its matching right item

Show answer & explanation

Answer

Modifications changing the area ratio affect force and distance inversely; proportional area modifications maintain the status quo; and input distance modifications only affect output distance.

Each correct match applies Pascal's Principle (

F_2 = F_1 \times \frac{A_2}{A_1}

) and the principle of work conservation (

F_1 \times d_1 = F_2 \times d_2

). Changing the area ratio inversely affects force and distance. Changing only input distance affects fluid volume displaced, altering output distance without changing force.

Step-by-Step Solution

1

Analyze modifications changing a single piston area.

Doubling output area doubles force but halves distance; doubling input area halves force but doubles distance.

Pascal's principle states

F_2 = F_1 \times \frac{A_2}{A_1}

, and conservation of work states

d_2 = d_1 \times \frac{A_1}{A_2}

.

2

Analyze modifications changing both piston areas.

Doubling both areas keeps the ratio

A_2/A_1

constant, resulting in no change to force or distance.

The mechanical advantage depends strictly on the ratio of the areas, not their absolute sizes.

3

Analyze modifications changing only input distance.

Doubling input distance doubles output distance without affecting force.

Volume displaced (

V = A_1 \times d_1

) doubles, so output distance doubles. Force depends only on the area ratio, which is unchanged.

Key Concept

Pascal's Principle and Conservation of Energy in Hydraulics

Fluid Mechanics

Answer

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