Question

A pneumatic system is producing 75 lb/in2 of gauge pressure. A cylinder is needed to press an adhesive label onto a product. It has been determined that 4 lb of force is optimal to complete this task. What is the required diameter of the pneumatic cylinder? Assume standard atmospheric pressure (14.7 psi).
_____ in
(Precision - 0.00)

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Answer 1

The area of the cylinder required for a given pressure is directly

proportional to the applied force.

The correct response;

• The required diameter of the cylinder is approximately 0.26 inches

Method by which the diameter is found:

Given parameters;

The gauge pressure produced by the pneumatic system, P = 75 lb/in²

The force required to complete the given task, F = 4 lb.

Required parameter;

The diameter of the pneumatic cylinder.

Solution:

Derivation of the formula for area;

$\displaystyle Pressure, \, P = \mathbf{\frac{Force, \, F}{Area, \, A}}$

Therefore;

$\displaystyle Area, \, A= \mathbf{\frac{Force, \, F}{Pressure, \, P}}$

Plugging in the given values to determine the area of the cylinder;

$\displaystyle Area, \, A= \frac{4 \, lb}{75 \, lb/in^2} = \frac{4}{75} \, in.^2$

Determining the diameter of the cylinder;

A = π·r²

$\displaystyle r = \sqrt{ \frac{A}{\pi} }$

$\displaystyle r = \sqrt{\frac{4}{75 \cdot \pi} } \approx 0.13$

The required diameter, d = 2 × r

Therefore;

d ≈ 2 × 0.13 = 0.26

• The required diameter, d ≈ 0.26 inches

Learn more about the formula for pressure here:

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