A hydraulic rescue spreader operates using a closed fluid system. The tool's spreading arm… — Armed Services Vocational Aptitude Battery (ASVAB)

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?

Answer: 40 inches

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

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

V_{in} = V_{out}

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.

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.

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.

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