A heavy-duty hydraulic lifting system features an input piston with a cross-sectional area… — Armed Services Vocational Aptitude Battery (ASVAB)

A heavy-duty hydraulic lifting system features an input piston with a cross-sectional area of $2\text{ in}^2$ and an output piston with an area of $40\text{ in}^2$ . The input piston is driven by a lever that provides a $4:1$ mechanical advantage. If the operator pushes the lever handle down a distance of $16\text{ inches}$ for each stroke, how far will the output piston move upward after $10$ complete strokes? (Assume an incompressible fluid and zero system losses.)

A
8 inches
B
32 inches
2 inchesAnswer
D
800 inches

Answer

The output piston will move upward by 2 inches.

In any hydraulic system, the volume of fluid displaced by the input piston must equal the volume received by the output piston. Due to the

4:1

mechanical advantage of the lever, the input piston only moves

1/4

of the handle's distance per stroke (

16 / 4 = 4\text{ inches}

). Displacing a

2\text{ in}^2

piston by

4\text{ inches}

pushes

8\text{ in}^3

of fluid per stroke. Over

10

strokes,

80\text{ in}^3

of fluid is moved. To accommodate this volume, the larger

40\text{ in}^2

output piston will move upward by

80 / 40 = 2\text{ inches}

Step-by-Step Solution

Calculate the distance the input piston moves during a single stroke.

d_1 = 16\text{ inches} / 4 = 4\text{ inches}

Because the lever provides a

4:1

mechanical advantage, the input piston moves one-fourth of the distance the handle moves.

Calculate the volume of fluid displaced in one stroke.

V_{\text{stroke}} = 2\text{ in}^2 \times 4\text{ inches} = 8\text{ in}^3

The volume of a cylinder is its cross-sectional area multiplied by the distance the piston travels.

Determine the total volume of fluid displaced after 10 strokes.

V_{\text{total}} = 8\text{ in}^3 \times 10 = 80\text{ in}^3

Each stroke moves the same volume of fluid, so we multiply the single-stroke volume by the total number of strokes.

Calculate the upward distance the output piston moves.

d_2 = 80\text{ in}^3 / 40\text{ in}^2 = 2\text{ inches}

Since liquids are incompressible, the volume entering the large cylinder equals the total volume displaced by the input piston.

Key Concept

Pascal's Principle and Conservation of Volume in Hydraulics

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