What pressure is required in a hydraulic system to cut ¼" stainless steel with a shear strength of 50,000 psi using a 4" diameter piston?

To determine the pressure required to cut a ¼" stainless steel with a shear strength of 50,000 psi using a 4" diameter piston, we first need to calculate the force needed to shear the material and then relate that force to the pressure exerted by the hydraulic system.

First, calculate the area of the piston using the formula for the area of a circle, which is ( A = \pi r^2 ). The diameter is 4 inches, so the radius is 2 inches.

[ A = \pi (2 \text{ in})^2 = \pi (4 \text{ in}^2) \approx 12.57 \text{ in}^2 ]

Next, the force required to shear the stainless steel can be calculated using the formula:

[ \text{Force} = \text{Shear Strength} \times \text{Thickness} \times \text{Width} ]

Here, the shear strength is 50,000 psi, the thickness is 0.25 inches, and we assume a unit width of 1 inch for simplicity:

[ \text{Force} = 50,000 \text{ psi} \times 0.25 \text