Using Pascal's principle, what pressure is exerted in a 10-inch cylinder connected to a 1-inch cylinder with 15 psi applied?

To determine the pressure exerted in a system with two connected cylinders of different diameters and using Pascal's principle, it's essential to understand how pressure is transmitted in an incompressible fluid. Pascal’s principle states that when pressure is applied to a confined fluid, the pressure change occurs at every point in the fluid and acts in all directions evenly.

In this scenario, you have a 10-inch diameter cylinder connected to a 1-inch diameter cylinder, with an external pressure of 15 psi applied to the smaller 1-inch cylinder. The area of each cylinder is a relevant factor in determining the pressure exerted in the larger cylinder.

First, let's calculate the cross-sectional area for both cylinders. The area of a circle is calculated using the formula:

Area = π * (radius)².

For the 1-inch cylinder:

• Radius = 0.5 inches, so Area = π * (0.5)² = π * 0.25 ≈ 0.785 square inches.

For the 10-inch cylinder:

• Radius = 5 inches, so Area = π * (5)² = π * 25 ≈ 78.54 square inches.

Next, considering Pascal's principle and the relationship of