The head of a round piston has a pressure of 210 psi pushing down on it. The piston is 3 inches in diameter. What is the force pushing the piston down?
To find the force pushing the piston down, we can use the formula for pressure:
Pressure = Force / Area
Here, we are given the pressure (210 psi) and the diameter of the piston (3 inches). We need to calculate the force.
First, let's calculate the radius (r) of the piston using the diameter (d):
r = d / 2
Given the diameter (d) is 3 inches, we can calculate the radius (r):
r = 3 / 2 = 1.5 inches
Now, we need to convert the radius to inches to radius in square feet (which is the unit required for the area calculation):
r_feet = r / 12
Given that there are 12 inches in a foot, we can calculate the radius in feet:
r_feet = 1.5 / 12 = 0.125 feet
Next, let's calculate the area (A) of the piston:
A = π * r^2
Given the value of π is approximately 3.14, we can calculate the area:
A = 3.14 * (0.125)^2
A = 3.14 * 0.015625
A = 0.0490875 square feet
Now, we can use the formula for pressure:
Pressure = Force / Area
Rearranging the formula to solve for Force:
Force = Pressure * Area
Substituting the given values:
Force = 210 psi * 0.0490875 square feet
Force = 10.298875 pounds (approximately)
Therefore, the force pushing the piston down is approximately 10.3 pounds.