What should the relief valve be set at for a hydraulic hoist that cannot lift over 5000 lbs, with a piston diameter of 10 inches?

To determine the correct relief valve setting for a hydraulic hoist, it's essential to calculate the required pressure using the formula for hydraulic systems, which is based on the area of the piston and the maximum load it is required to lift.

First, calculate the area of the piston. The diameter of the piston is 10 inches, so the radius is 5 inches. The area (A) can be calculated using the formula for the area of a circle, (A = \pi r^2).

Converting the radius to feet (5 inches = 5/12 feet), we can calculate the area:

[

A = \pi \left(\frac{5}{12}\right)^2 \approx 0.2739 \text{ square feet}

]

Next, to find the necessary pressure to lift 5000 lbs using this area, we apply the formula for pressure, which is force divided by area, (P = \frac{F}{A}). Here, (F) is the force (the weight to be lifted), and (A) is the area in square feet.

Using the maximum weight of 5000 lbs:

[

P = \frac{5000 \text{ lbs