What diameter of cylinder is necessary to lift 5500 lbs using a pressure of 1000 psi?

To determine the appropriate diameter of a cylinder needed to lift a specific weight using a given pressure, we can utilize the formula that relates force, pressure, and area. The force exerted by the hydraulic system can be calculated using the formula:

[

F = P \times A

]

where ( F ) is the force in pounds, ( P ) is the pressure in psi, and ( A ) is the area in square inches.

First, we need to calculate the area required to lift 5500 lbs at 1000 psi by rearranging the formula to find area:

[

A = \frac{F}{P}

]

Substituting the known values into the equation gives us:

[

A = \frac{5500 \text{ lbs}}{1000 \text{ psi}} = 5.5 \text{ in}^2

]

Next, we need to relate the area to the diameter of the cylinder. The area ( A ) of a circle (which is the cross-section of a cylinder) is given by the formula:

[

A = \pi \left( \frac{d}{2} \right)^2

]

where ( d