Match each change made to a closed hydraulic system with its resulting effect on the outpu… — Armed Services Vocational Aptitude Battery (ASVAB)

Match each change made to a closed hydraulic system with its resulting effect on the output piston. Assume all other initial parameters remain constant.

The input piston area ( $A_{in}$ ) is doubled.Output force is halved, and output travel distance is doubled.
The applied input force ( $F_{in}$ ) is doubled.Output force is doubled, and output travel distance is unchanged.
The output piston area ( $A_{out}$ ) is doubled.Output force is doubled, and output travel distance is halved.
The input piston travel distance ( $d_{in}$ ) is doubled.Output force is unchanged, and output travel distance is doubled.

Answer

The input area affects both pressure (inversely) and volume pushed (directly). The output area affects output force (directly) and output distance (inversely). Input force only affects pressure, and input distance only affects volume.

Each relationship is governed by two fundamental principles of hydraulics. Pascal's Principle dictates that

F_{out} = F_{in} \times (A_{out}/A_{in})

. The conservation of volume dictates that

d_{out} = d_{in} \times (A_{in}/A_{out})

. Applying a factor of 2 to any single variable in these equations yields the correct changes to the output force and distance.

Step-by-Step Solution

Analyze the formula for mechanical advantage and output force.

F_{out} = F_{in} \times \frac{A_{out}}{A_{in}}

Pascal's Principle states that pressure is transmitted equally (

P = F/A

), allowing us to solve for the force tradeoff.

Analyze the formula for output travel distance.

d_{out} = d_{in} \times \frac{A_{in}}{A_{out}}

Because liquids are virtually incompressible, the volume of fluid pushed by the input piston must equal the volume moving the output piston (

V = A \times d

Evaluate the effect of doubling each parameter independently.

Doubling

A_{in}

halves

F_{out}

and doubles

d_{out}

. Doubling

A_{out}

doubles

F_{out}

and halves

d_{out}

The direct and inverse proportions in the formulas dictate the final force multiplication and travel distance outcomes.

Key Concept

Hydraulic Mechanical Advantage and Conservation of Work

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